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Contribution à l'étude du transfert en solution

Abstract : The intergranular pressure solution is a mechanism of deformation of sedimentary rocks, which results in a reduction of porosity and a compaction of the rock. With great depths of bury (approximately 3km), the minerals of the grains dissolve in the fluid of the intergranular contact, are transported by diffusion in the contact towards the pore, and redeposed on the free faces of the grains. Our study is based on a model of two grains in contact having undergone
a beginning of dissolution, and modelled by two truncated spheres. The contact between two grains is simply represented by a zone limited by two plane interfaces, although this zone actually consists of solid contacts and inter-connected free fluid, known as “island and channel” structure.
At this scale, a phenomenologic law of contact links the rate of shortening of the grain to the thermodynamic force of intergranular pressure solution, which is a function of the Helmholtz free energy, the intergranular normal stress, and a term corresponding to the diffusion. The intergranular normal stress can be thus expressed as a function of the quantities relative to the dissolution and the diffusion, and the rate of shortening of the grains. This intergranular stress constitutes the boundary condition on the solid/solid interface of the mechanical problem. The load applied at the solid/pore interface is the fluid pressure.
An analytical approach of the resolution of this problem makes it possible to understand that the singularity in stress at the intersection point of the contact zone and the pore, is due to the discontinuity of loading condition between the intergranular normal stress, the loading on the solid/solid interface, and the fluid pressure on the interface solid/pore fluid. This singularity is found by finite element calculation.
The numerical method allows to note that the approximation which consists in neglecting the Helmholtz free energy term in the thermodynamic force is valid for the various sizes of grains considered in this work (between 0.1mm and 2mm). It is also shown that the distribution of the intergranular normal stress is less parabolic when the grain is flattened. It is the same when the size of grain is smaller, therefore when the diffusion is the dominant process.
The (approximate) creep law which gives the shortening rate of the grain as a function of the thermodynamic force (without the Helmholtz free energy term) makes us note that the more the grain size decreases, the more the process of diffusion is fast : dissolution is in this case the mechanism which controls the intergranular pressure solution.
At a smaller scale, we focus on the stability of a solid/fluid interface by a stability analysis in 3D. The dominant mode of instability is a wave which is perpendicular to the direction of the maximal compressive effective stress. The results of this analysis are coherent with experimental observations with regard to the orientation and the wavelength of instability. Nonconformity concerning the gradient in wavelengths and the growth rate are discussed.
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Submitted on : Friday, November 10, 2006 - 3:56:11 PM
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  • HAL Id : tel-00113105, version 1

Citation

Miarana Rakotoniriana. Contribution à l'étude du transfert en solution. Mécanique [physics.med-ph]. Ecole Polytechnique X, 2005. Français. ⟨tel-00113105⟩

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