A sandstone with 25% water-filled porosity is compared to the same sandstone with negligible porosity. Which has higher thermal conductivity?
AThe water-saturated sandstone — water conducts heat much better than air and fills the pore space
BThe low-porosity sandstone — the mineral matrix conducts far better than pore fluids, so more matrix means higher conductivity
CThey are equal — porosity changes density but not conductivity
DThe water-saturated sandstone — fluid circulation distributes heat more evenly
Water has a thermal conductivity of only ~0.6 W/(m·K), while quartz-rich sandstone mineral matrix has k ≈ 4–6 W/(m·K). Adding 25% water-filled pore space therefore dilutes the high-conductivity mineral component with low-conductivity fluid, reducing bulk conductivity significantly — a sandstone with 25% porosity might drop from ~4.5 to ~2.5 W/(m·K). Dry pores (air at ~0.025 W/(m·K)) are even worse. The common misconception is that 'wet rocks conduct heat better,' but this is only true compared to dry porous rock — not compared to the same rock with no porosity.
Question 2 Multiple Choice
Moving from the shallow crust to greater depths at constant heat flow, what generally happens to thermal conductivity of crystalline rocks?
AIt increases, because higher pressure packs mineral grains together more tightly
BIt stays approximately constant, because mineralogy does not change with depth
CIt decreases, because higher temperatures increase phonon scattering, reducing the efficiency of heat conduction
DIt increases then decreases, peaking at mid-crustal depths where both pressure and temperature effects balance
For crystalline rocks, thermal conductivity decreases with increasing temperature, roughly following a 1/T relationship due to increased phonon scattering. This means the deep, hotter crust conducts heat less efficiently than the shallow, cooler crust. At constant heat flow, a lower-conductivity zone must develop a steeper temperature gradient to transmit the same amount of heat — so the geothermal gradient steepens at depth. At very high temperatures (>800°C), radiative heat transfer can increase effective conductivity, but this mainly applies to mantle conditions.
Question 3 True / False
Water-saturated pore space increases the thermal conductivity of a rock compared to the same rock with no porosity.
TTrue
FFalse
Answer: False
False. Pore space — whether filled with water or air — reduces thermal conductivity below the mineral matrix value because pore fluids conduct heat far less efficiently than most rock-forming minerals. Water (0.6 W/(m·K)) and air (~0.025 W/(m·K)) are both much lower than typical silicate mineral conductivities (2–8 W/(m·K)). The more pore space, the more the bulk conductivity is pulled toward the fluid value and away from the mineral matrix value.
Question 4 True / False
In a foliated metamorphic rock, heat flows more easily parallel to foliation than perpendicular to it.
TTrue
FFalse
Answer: True
True. Foliation aligns minerals — particularly platy minerals like mica — and creates preferred orientation in the microstructure. Heat flow parallel to foliation encounters a series of conductors in parallel (arithmetic mean, dominated by the highest-conductivity components), while heat flow perpendicular to foliation encounters conductors in series (harmonic mean, dominated by the lowest-conductivity components). This creates thermal anisotropy, with conductivity along foliation sometimes twice the value across it.
Question 5 Short Answer
Why does a quartz-rich sandstone have much higher thermal conductivity than a clay-rich shale, even if both are sedimentary rocks at similar depths?
Think about your answer, then reveal below.
Model answer: Thermal conductivity in rocks is primarily controlled by mineralogy. Quartz has exceptionally high conductivity (~7–8 W/(m·K)), so quartz-dominated sandstone bulk conductivity can reach 4–6 W/(m·K). Clay minerals are poor conductors (~1–1.5 W/(m·K)), so clay-rich shales typically have bulk conductivities below 2 W/(m·K). Shales also tend to have higher porosity filled with low-conductivity fluids. The contrast in mineral conductivity — roughly a factor of 5 between quartz and clay — propagates into a large contrast in bulk rock conductivity.
This tests whether students understand that mineralogy, not rock 'type' or geological age, is the primary control. A geophysicist reading a borehole lithological log can make a reasonable first-pass estimate of the conductivity profile from the mineralogy alone, before any measurements are taken.