Thermal conductivity and elastic modulus of 3D porous/fractured media considering percolation

Abstract

Pores, vugs, and cracks configurations affect physical and mechanical properties of porous and fractured (PF) media, specifically the percolations of pores/vugs/cracks trigger the dramatic change of conductive-like properties such as thermal conductivity, diffusivity, elastic modulus of PF media. It has been a key but unresolved issue how to accurately capture the percolation thresholds of these complex networks interacted by anisotropic-shaped pores and cracks, and their quantitative effects on the thermal conductivity and elastic modulus of PF media. This work proposes numerical and theoretical strategies for the accurate determination of percolation thresholds of penetrable spheroidal inclusions over a broad range of aspect ratios κ representing prolate pores (1 < κ ≤ 200), vugs (κ = 1) and oblate cracks (0.001 ≤ κ < 1), and the reliable predictions of effective thermal conductivity, diffusivity, and elastic modulus of PF media. The numerical and theoretical strategies include: (1) an extensive Monte Carlo finite-size scaling analysis (MCFSS) for obtaining the statistical values of percolation threshold of porous and fracture networks with κ from 200 to 0.001; (2) a Padé-type percolation model for predicting the percolation thresholds of penetrable spheroidal inclusions over a broad range of aspect ratios; (3) a continuum percolation-based generalized effective medium theory (CP-GEMT) for predicting effective thermal conductivity, diffusivity, and elastic modulus of PF media over the whole range of volume fractions of spheroidal inclusions, including near the percolation threshold. Comparison with extensive experimental, numerical and theoretical results confirms that the present models are capable of accurately determining the percolation thresholds of porous and fracture networks and the effective thermal conductivity, diffusivity, and elastic modulus of PF media as resemble to conductor-superconductor and insulator-conductor. The models can be regarded as a general theoretical framework to shed light on the intrinsic and complex interaction of components, structures and transport and elastic properties in porous and fracture materials, meanwhile the proposed models can be also well utilized to predict the percolation thresholds of spheroidal carbon nanotubes (CNTs) and graphenes, and the effective transport and elastic properties of CNT-/graphene-based composites.