Abstract
A new type of steady-state thermal conductivity apparatus is presented and described. Results of measurements on Berea sandstone, Solehofen limestone, Banders sandstone and Bakelite are presented. The measurements were made in a two-hour period at temperatures up to 80C and axial stress to 125 bars. Results show that the thermoelectric beat pump and thermistor-controlled electric heater can be used in a steady-state apparatus for measuring thermal conductivity of rock. Steady-state is reached within two hours. With Urethane foam insulation, not more than 3 per cent of heat is lost by radial flow. The apparatus can be used as a comparator or for absolute thermal conductivity determinations.
Introduction
Calculations of heat flow through the earth, both for scientific purposes and engineering design, require thermal-conductivity data on rock. However, the high variability of rock often makes handbook thermal-conductivity data of little value. For engineering purposes in particular, it is desirable to have measured data on samples of the rock mass under study. Laboratory methods for measuring thermal conductivity of rock use either time-dependent or steady - state temperatures. The time-dependent (transient) techniques give thermal diffusivity from which thermal conductivity can be calculated if the specific heat and density of the sample is known. Most transient techniques require lengthy and involved sample preparation. Also, the accuracy tends to be low. Steady-state techniques are more exact and are the most commonly used. The steady-state methods, however, also have their difficulties. A long time is often required to reach steady state, troubles have been encountered in establishing good thermal contact between the heating and cooling elements and the rock sample, and unaccounted-for heat losses are difficult to prevent. In this paper we present a description of a new type of steady-state thermal conductivity apparatus. With it, measurements have been made in two hours at temperatures up to 80C and axial stress to 125 bars. Sample preparation is simple and no thermal conductivity standard is needed.
APPARATUS
Our steady-state apparatus is an improvement over the conduction pile used by Zierfuss and van der Vliet and Somerton. A linear heat flux is established through a conduction pile consisting of the rock sample and a standard material of known thermal conductivity in series.
SPEJ
P. 113ˆ
Note on the New Type of the SO(2N+1) Time-Dependent Hartree-Bogoliubov Equation