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.

Measurements have been made of the effective thermal conductivity of porous sandstones. The method is based on the transient heating effect resulting from use of a line heat source. Data are presented for six sandstones ranging in porosity from 3 to 59% and show the variation of thermal conductivity with porosity, the conductivity of the saturating fluid, the pressure of the gas filling the pore space, and overburden pressure. The results are compared with those previously obtained for unconsolidated sands. All samples, except one, exhibited a lower thermal conductivity when saturated with a gas at atmospheric pressure than when saturated with a liquid of the same conductivity as the gas. An explanation for this effect, in terms of the kinetic theory of gases, is advanced and substantiated by other data. Finally, the validity of certain equations for the thermal conductivity of two-phase systems is examined; the weighted geometric mean of the two constituent conductivities is found to agree well with the measured effective conductivities.

Thermal conductivity measurements were made on a natural Berea sandstone sample of porosity 22 per cent, with the pore space filled with various fluids at atmospheric pressure. The results indicate that the effective conductivity of the sample, when filled with a gaseous saturant, is lower than when filled with a liquid saturant of the same conductivity as the gas. This effect is qualitatively accounted for by the reduction in thermal conductivity of the gas which occurs when the gas occupies spaces which are small relative to its mean free path. The presence of such spaces is confirmed by pore size distribution data and by the increase in effective conductivity with increase in gas pressure. The effect on the thermal conductivity of a simulated net overburden pressure of 275 bars was also investigated.

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