POROMECHANICS
(selected contributions)
Lewandowska, J., Auriault, J.-L., 2013, Extension of Biot theory to the problem of saturated microporous elastic media with isolated cracks or/and vugs. Int. J. Numer. Anal. Meth. Geomech. Vol. 37, Issue 16, pages 2611-2628, DOI : 10.1002/nag. 2150
By applying the asymptotic expansion homogenization method, we develop the macroscopic model of hydro-mechanical coupling for the case of a saturated porous medium containing isolated cracks or/and vugs. The model represents an extension of the phenomenological Biot model that was initially formulated for a macroscopically homogeneous and isotropic elastic saturated porous medium. The homogenization analyse shows the general structure of the Biot’s model is preserved but the Biot’s parameters are modified. In particular, the poro-elasticity parameters of the porous matrix itself, as well as the volumetric fraction of the cracks (vugs), are taken into account.
Two numerical examples of the computations of Biot’s parameters in both isotropic and anisotropic cases, are presented. It is also shown how the presence of near-zero-volume cracks influences the Biot’s parameters of the cracked porous medium which can, in turn, significantly affect the overall behaviour of the porous medium through the hydro-mechanical coupling mechanism. In order to illustrate the practical importance and impact of the presence of cracks/vugs, a macroscopic boundary value problem of water pumping from a porous aquifer is solved numerically for non-damaged and damaged cases.
Lewandowska, J., 2013, Modelling by homogenization of the long term rock dissolution and geomechanical effects. (Chapitre VIII dans l’ouvrage ‘Geomechanics in CO2 storage facilities’. Eds. G. Pijaudier-Cabot, J.M. Pereira. ISTE-Wiley, 21 pages, DOI: 10.1002/9781118577424.ch8
The formulation of the macroscopic model describing the behaviour of a porous saturated rock subjected to the injection of CO2, is presented. The analysis is focused on the long term effects when the chemical reactions between the CO2 dissolved in the pore water and the solid matrix result in the dissolution (and /or precipitation) of the rock minerals.
The theoretical framework of the modelling is the asymptotic developments homogenization method. At the microscopic scale, i.e. the scale of the microstructure, the following phenomena are taken into account: i) water flow through the pores, ii) linear elasticity of the solid phase, iii) mass transport of dissolved CO2 in water phase, iv) chemical dissolution of the solid matrix. After homogenization process, the full macroscopic model of coupled phenomena is obtained. One of the contributions of the paper is the formulation of the local chemical degradation mechanism. It is assumed that the dissolution process is governed by a diffusion-like equation for the concentration in solid (solid fraction), with a single parameter (in tensorial form) describing the rate of the process. Such a formulation enables us to capture the chemo-mechanical coupling manifesting itself at the macroscopic scale.
This general mathematical framework was illustrated by an example of numerical computations of the degradation with time of mechanical parameters of the rock in case of a three dimensional microstructure showing cubic symmetry at the macroscopic scale.
Wojtacki, K., Lewandowska, J., Gouze, Ph., Lipkowski, A., 2015, Numerical computation of rock dissolution and geomechanical effects for CO2 geological storage. International Journal of Numerical and Analytical Methods in Geomechanics, Volume 39, Issue 5, pp. 482-506, DOI: 10.1002/nag.2316
We present a methodology for the assessment of the impact of progressive rock dissolution on the mechanical behaviour of a porous rock. The method is based on the use of the X-ray tomography and the numerical dissolution technique of the rock sample. The influence of the evolution of the microstructure on the macroscopic properties of the rock is analysed by using the periodic homogenization method. The numerical computations show progressive degradation of all components of the stiffness tensor (orthotropic case). Moreover, the evolution of the associated mass transfer properties (conductivity tensor, tortuosity tensor and specific surface) is also calculated by using the same homogenization approach. The correlation analyse shows that the highest increase in the hydraulic conductivity is not associated with the highest decrease of the Young modulus in the same direction. Further, the highest decrease of the Young modulus is not associated with the appearance of percolation in this direction. The obtained results clearly show the importance of morphological information about the microstructure as a key to the understanding of the coupled multi-physics phenomena.
Finally, an incremental law for a problem of deep aquifer settlement due to the rock dissolution under constant stress and drained conditions, is proposed.