Effective thermal conductivity of oolitic rocks using the Maxwell homogenization method

• A new micromechanical approach to analytical modelling of effective thermal conductivity oolitic limestone is proposed.
• Limestone is modelled as a multiphase composite.
• Mesoporosity consists of oblate pores and concave pores in the shape of superspheres.
• The pores concavity factor is a key parameter affecting overall thermal conductivity.
• Maxwell's homogenization scheme is used to calculate effective thermal conductivity.

The present work focuses on effective thermal conductivity of oolitic limestones, 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.