Using a Divided Bar Apparatus to Measure Thermal Conductivity of Samples of Odd Sizes and Shapes
Abstract
Standard procedure for measuring thermal conductivity using a divided bar apparatus requires a sample that has the same surface dimensions as the heat sink/source surface in the divided bar. Heat flow is assumed to be constant throughout the column and thermal conductivity (K) is determined by measuring temperatures (T) across the sample and across standard layers and using the basic relationship Ksample=(Kstandard*(ΔT1+ΔT2)/2)/(ΔTsample). Sometimes samples are not large enough or of correct proportions to match the surface of the heat sink/source, however using the equations presented here the thermal conductivity of these samples can still be measured with a divided bar. Measurements were done on the UND Geothermal Laboratories stationary divided bar apparatus (SDB). This SDB has been designed to mimic many in-situ conditions, with a temperature range of -20C to 150C and a pressure range of 0 to 10,000 psi for samples with parallel surfaces and 0 to 3000 psi for samples with non-parallel surfaces. The heat sink/source surfaces are copper disks and have a surface area of 1,772 mm2 (2.74 in2). Layers of polycarbonate 6 mm thick with the same surface area as the copper disks are located in the heat sink and in the heat source as standards. For this study, all samples were prepared from a single piece of 4 inch limestone core. Thermal conductivities were measured for each sample as it was cut successively smaller. The above equation was adjusted to include the thicknesses (Th) of the samples and the standards and the surface areas (A) of the heat sink/source and of the sample Ksample=(Kstandard*Astandard*Thsample*(ΔT1+ΔT3))/(ΔTsample*Asample*2*Thstandard). Measuring the thermal conductivity of samples of multiple sizes, shapes, and thicknesses gave consistent values for samples with surfaces as small as 50% of the heat sink/source surface, regardless of the shape of the sample. Measuring samples with surfaces smaller than 50% of the heat sink/source surface resulted in thermal conductivity values which were too high. The cause of the error with the smaller samples is being examined as is the relationship between the amount of error in the thermal conductivity and the difference in surface areas. As more measurements are made an equation to mathematically correct for the error is being developed on in case a way to physically correct the problem cannot be determined.
- Publication:
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AGU Fall Meeting Abstracts
- Pub Date:
- December 2012
- Bibcode:
- 2012AGUFM.H13G1447C
- Keywords:
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- 0994 EXPLORATION GEOPHYSICS / Instruments and techniques;
- 1859 HYDROLOGY / Rocks: physical properties;
- 5134 PHYSICAL PROPERTIES OF ROCKS / Thermal properties;
- 5194 PHYSICAL PROPERTIES OF ROCKS / Instruments and techniques