Thermal Conductivity of Porous Media. I. Unconsolidated Sands

TLDR

The study addresses how to compute the effective thermal conductivity of two‑phase systems from component conductivities and volume fractions, reviewing solutions such as Maxwell, de Vries, Kunii & Smith, weighted geometric mean, and a resistor‑model approach. Five unconsolidated samples—three quartz sand packs, a glass bead pack, and a lead shot pack—were measured with a transient line‑heat‑source probe to determine their thermal conductivities. Results show that effective conductivity varies with porosity, solid and fluid conductivities, and gas pressure; kinetic theory indicates the pore characteristic length is about 1 % of the particle diameter, and the de Vries, Kunii & Smith, and a modified resistor‑model equations best fit the data.

Abstract

The problem of determining the effective thermal conductivity of a two-phase system, given the conductivities and volume fractions of the components, is examined. Equations are described which have been proposed as solutions to this problem, including those of Maxwell, de Vries, and Kunii and Smith, the weighted geometric mean equation, and an equation based on a three-element resistor model found applicable to the analogous electrical conductivity problem. Experimental results are presented for five unconsolidated samples: three quartz sand packs, a glass bead pack, and a lead shot pack. The method of conductivity measurement using the transient line heat source (thermal conductivity probe) is described. Data are reported showing the variation of effective thermal conductivity with porosity, solid particle conductivity, saturating fluid conductivity, and the pressure of the saturating gas. From considerations based on the kinetic theory of gases, it is shown that the characteristic dimension of the pore space, with respect to heat conduction in the gas occupying this space, is smaller than the mean particle diameter by a factor of roughly 100. The thermal conductivity equations which best represent the observed data are those of de Vries, and Kunii and Smith, and a slightly modified version of the resistor model equation.