Effective thermal conductivity of oolitic rocks using the Maxwell homogenization method

Abstract

International audienceThe present work focuses on effective thermal conductivity of oolitic lime-stones, characterized by an assemblage of porous grains (oolites), mesopores and solid grains. Two distinct scales of pores, micropores or intra oolitic pores and mesopores or inter oolitic pores are taken into account. At the first step, micropores are homogenized inside the oolites by using self consistent homogenization scheme. The second homogenization step describing transition from the mesoscale to the macroscale, is performed by using a recent reformulation of the Maxwell homogenization scheme (see [1]). At the mesoscale, porous oolitic inclusions are quasi spherical whereas two families of mesopores are considered according to analysis of photomicrographs: (1) randomly oriented oblate spheroidal pores and (2) concave pores. The proposed model is compared to a simplified one when all the pores are of ellipsoidal shape. The relevancy of the ellipsoidal approximation is then evaluated. In particular, the influence of the shape of the mesopores on the overall thermal conductivity is discussed. Comparisons between multi-scale model based on Maxwell homogenization method and experimental data show that effects of porosity and saturating fluids on overall conductivity are correctly predicted when concave pores are taken into account

Anisotropic thermal conductivity in epoxy-bonded magnetocaloric composites

“…This method for the simplification of particle shape is well known in literature (see, e.g., Refs. [16][17][18]. It can be seen in Figure 2 that the particle orientation is conserved by this means.…”