Effective thermal conductivity of inhomogeneous medium containing gas‐filled inclusions

Abstract

Communicated by W. SprößigDetermination of effective physical parameters of gas-filled porous media is of practical interest to a wide spectrum of applications from construction industry to petrophysics. The classical equations of thermal conductivity are not applicable for sufficiently small pores, the characteristic size of which is comparable with the mean free path of gas molecules. In this case, for description of the gas behavior, it is necessary to use the methods of physical kinetics and rarefied gas dynamics. In this work, we have considered so-called slip flow regime, 0 < Kn < 1, where Kn D =R is the Knudsen number, is the mean free path, and R is the characteristic pore size. In this regime, we can use the classical equations of mechanics of continuum media with modified boundary conditions that take into account the temperature and energy flux jumps on the pore boundaries. We have solved the so-called one-particle problem of thermal polarization of gas-filled inclusion. The obtained solution was then used in some self-consistent homogenization methods to calculate the effective conductivity coefficient. Our calculations have shown that the effective conductivity depends substantially on the pore size (the Knudsen number). The obtained results demonstrate the feasibility of pore sizes determination by using measurements of effective thermal conductivity.

Effective thermal conductivity of oolitic rocks using the Maxwell homogenization method

“…One defines the total volume of intra oolitic pores Ω o = Ω a + Ω s o (24) and the porosity of the oolite phase at the mesoscopic scale…”

“…A detailed review of thermal conductivity data sets for geomaterials made of natural soil particles, crushed rock particles and sedimentary rock including analysis of influence of particle shape, grains pore-size distributions, fluid saturated (air and liquid water) is given in [23]. It may be noticed that [24] have recently studied thermal conductivity of gas saturated porous materials taking into account methods of statistical physics and rarefied gas dynamics. They have shown that in the slip flow regime corresponding to low Knudsen number, it is necessary to use the method of rarefied gas dynamics to correctly predict the effective thermal conductivity.…”