Effect of elastic deformation and rough grain surface on heat conduction in partially saturated granular porous media

Accurate prediction of the effective thermal properties of partially saturated rock, soil, and other types of porous media is essential to a wide variety of phenomena and processes in engineering and natural sciences. The effective thermal conductivity of porous media depends strongly on the morphology of the media and the fluid distribution in the pore space, as well as on geomechanical processes such as dilation and microcracking. A precursor to such processes is the deformation of the grains\u27 surface due to the overburden pressure that is dependent on pore‐scale features, such as the surface texture of the grains. We report on the results of the extensive two‐dimensional computer simulations of heat conduction of granular porous media in which the grains have rough, self‐affine fractal surface, and water partially saturates the pore space, and the media are subjected to an external compressive pressure. The Young\u27s modulus of the grains and the fractal dimension of their surface profile dictate the contact area for the deformation. The spatial distribution of the fluids and the resulting saturation is generated by a lattice Boltzmann method, while the conduction process is simulated by a thermal lattice Boltzmann. Two essentially linear dependence of the effective thermal conductivity on the water saturation emerge, separated at a critical water saturation Sc that signals the formation of percolation clusters of water‐filled pores. One interval, below Sc, is dominated by heat conduction through the solid phase, assisted by conducting water globules that bridge the noncontacting grains. The second interval emerges above Sc in which the water‐filled pores create a percolating conductive cluster that dominates heat conduction through the medium. The effect of various factors on the conduction process is studied in detail