Rock Thermal Conductivity Estimator Calculator

Thermal conductivity k is the constant in the Fourier heat conduction law, q = -k x dT/dz, and it fixes how steep a temperature gradient a given heat flow must produce. In rock it is a composite property, because the solid framework conducts far better than whatever fills the pores, so porosity dominates the result. Mineral values vary widely: quartz near 7.7, calcite about 3.6, feldspars 2.0 to 2.3 and clay minerals close to 1.9 W/(m K), while pore water is only 0.6, oil about 0.15 and air 0.025. The geometric mean k = kS^(1-phi) x kF^phi is an empirical interpolation that behaves well for randomly distributed pores and always lies between the arithmetic mean, which represents phases parallel to the heat flow, and the harmonic mean, which represents phases in series. Typical whole-rock values are 2 to 5 W/(m K) for sandstone, 2 to 3.4 for limestone, 1 to 2.5 for shale, 2.5 to 3.8 for granite, and 5 to 6.5 for rock salt, whose unusually high conductivity is why salt bodies create thermal anomalies in sedimentary basins. Two limitations matter in practice. Shales and other layered rocks are anisotropic, with conductivity along bedding commonly 1.2 to 2 times that across it, and a scalar mixing model carries no directional information. Conductivity of crystalline rock also falls with temperature by a few tenths of a percent per degree C, so a laboratory value measured at room temperature overstates conductivity at reservoir depth.

Quantitative treatment of heat conduction begins with Joseph Fourier, whose Theorie analytique de la chaleur of 1822 introduced the law that defines conductivity. Applying it to the Earth required measuring rocks rather than metals, and that became routine only in the twentieth century, driven by interest in terrestrial heat flow and the age of the Earth. Francis Birch and Harry Clark, working at Harvard, published systematic divided-bar measurements on rocks and minerals at elevated temperature in 1940, clamping a rock disc between reference standards of known conductivity and comparing the temperature drop across each. Marine heat flow work needed something faster and suited to soft sediment, and the transient needle probe, applied to ocean floor cores by Richard Von Herzen and Arthur Maxwell in 1959, supplied it by measuring the temperature rise of a thin heated line source. Later, optical scanning methods developed by Yuri Popov and colleagues allowed continuous non-contact profiling along whole cores. The mixing models used here came out of petrophysics rather than pure physics: the geometric mean was adopted because it matched measurements on fluid-saturated sandstones better than the strict parallel and series bounds did. The compilation by Christoph Clauser and Ernst Huenges in the 1995 American Geophysical Union handbook of rock physics remains the standard reference table from which most quoted mineral and rock conductivities are drawn.