Mathematical Simulation of Measurements of Thermal Conductivity under Conditions of Optical Scanning of Standard Core Samples

摘要

The process of measurement of the thermal conductivity coefficient of core samples using the optical scanning method [1] reduces to determining the thermal conductivity by the results of recording of the level of excess temperature at individual points on the sample surface. The method, the mathematical model of which is based on the analytical solution for an infinite plane body, may be employed for samples of arbitrary shape with a flat surface. At the same time, most extensively employed in the practice of oil and gas petrophysics are standard-core sample (cylindrical samples 30 mm in diameter and length) measurements of various physical properties of rocks; this calls for assessment and development of the possibilities of the method of optical scanning in the investigation of such samples. With a view to adapting the method of optical scanning [1] to standard-core measurements, to studying the impact made by edge effects on the possible error of measurement of thermal conductivity coefficient in short core samples, and to assessing the validity in such cases of analytical quasi-steady-state solution [2] on which this method is based, we have numerically solved the thermal conductivity problem for standard core sample. The problem is solved using a hybrid finite-element control-volume method [3, 4] with a moving normally distributed heat source. The results are considered of determining the thermal conductivity coefficient for homogeneous standard core samples by the results of measurements performed on the end and side surfaces of the sample. The impact made by the curvature of the sample surface and by edge effects on the results of measurements by the method of optical scanning is investigated.