A composite sphere assemblage model for porous oolitic rocks: Application to thermal conductivity

The present work is devoted to the determination of linear effective thermal conductivity of porous rocks characterized by an assemblage of grains (oolites) coated by a matrix. Two distinct classes of pores, i.e. micropores or intra oolitic pores (oolite porosity) and mesopores or inter oolitic pores (inter oolite porosity), are taken into account. The overall porosity is supposed to be connected and decomposed into oolite porosity and matrix porosity. Within the framework of Hashin composite sphere assemblage (CSA) models, a two-step homogenization method is developed. At the first homogenization step, pores are assembled into two layers by using self-consistent scheme (SCS). At the second step, the two porous layers constituting the oolites and the matrix are assembled by using generalized self-consistent scheme (GSCS) and referred to as three-phase model. Numerical results are presented for data representative of a porous oolitic limestone. It is shown that the influence of porosity on the overall thermal conductivity of such materials may be significant.