Numerical analysis on thermal conductivity of poly-mineral rock

In order to explore the thermal conductivity of the natural poly-mineral rock, numerical tests of rock models with randomly-distributed components were conducted and compared with each other. Elaborately designed Monte Carlo method was adopted to ingratiate the requirement of the random characteristics of grain size and the grains' spatial distribution. This requirement was fulfilled by clustering the randomly generated unstructured tetrahedral elements in full three dimensions. Natural rocks are consisted of randomly distributed crystal particles or intergranular minerals. Our primary results verify that the thermal conductivity of the rock is strongly sensitive to the ingredients' volume fraction and their spatial distribution. Furthermore, we proved that, in order to reduce the measurement error to a reasonable range, the numerical specimen must be large enough or include sufficient number of mineral particles. Our numerical test results are in accordance with a variety of empirical formulas which are currently employed in petrology.