Statistical Analysis of the Relationships Between Thermal Conductivity and Other Physical Properties of Rock

The exploration and application of geothermal resources is able to be guided by the prediction of the thermal conductivity of rock. This paper collects 58 kinds of rock property data, and uses statistical regression analysis methods to obtain the relationship between rock's thermal conductivity and factors such as density, hardness, etc., and uses qualitative analysis methods to obtain the effect of rock color on rock thermal conductivity. Through the linear regression analysis, the association between rock density (x(1)) and thermal conductivity (y) is found: y = 2.4835x(1) - 3.1043, (R-2 = 0.2708), and the relationship after excluding some data with large deviations is y = 0.9474x(1) + 0.0099, (R-2 = 0.375). Additionally, the link between rock Mohs hardness (x(2)) and thermal conductivity (y) is also obtained: y = 0.9836x(2) + 0.8137, (R-2 = 0.1766), and the result fitted only by the oxides and sulfides is y = 2.8799x(2) - 6.9024, (R-2 = 0.3912). Moreover, the multiple linear regression technique yields the following connection between rock density, hardness, and thermal conductivity: y = -3.7212 + 1.5653x(1) + 0.9828x(2), (R-2 = 0.3007). Finally, the relationship between rock color and thermal conductivity is qualitatively analyzed. The results show that the thermal conductivity of rock increases as the gray level rises and decreases as the wavelength of monochromatic light increases.