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Scientific background

Rock thermal properties are dependent on the mineralogical composition and the internal structure (anisotropy, texture) of the material, as well as on the pore structure and the pore-filling fluid but also display a significant dependence upon temperature (decreasing effect for thermal conductivity, and opposite for thermal diffusivity) and pressure (increasing effect for thermal conductivity, and opposite for thermal diffusivity). Most available information on thermal rock properties originates from laboratory measurements performed at ambient p/T conditions using in the best case a fluid-saturated sample. In-situ conditions of the Earth are almost never taken into account and if so, than for the deeper part of the Earth crust as part of lithosphere research. The relationships are not well constrained for the depth realm of boreholes, which is the upper part of the Earth crust to depth of about 7 km.

Key facts
  • No standard measurement technique available
  • No universally applicable correction approach available

The majority of studies on this issue focused separately either on pressure or temperature. Some of these studies derived empirical equations to correct values measured under ambient laboratory conditions to in-situ values in the Earth. For the temperature dependency, a variety of correction approaches is known from the literature. However, some correction methods show strongly diverging numerical correlations and thus ambiguity in their application. In recent years, these temperature correction approaches became again a matter of debate and critical evaluation. The pressure dependency is generally assumed to be linear (due to decreasing porosity and compressibility of the rock-forming minerals with increasing stress) for pressures above 50 to 100 MPa (corresponding to depth > 2-4 km). Below this threshold, pressure dependency is non-linear and most likely related to the closing of micro fractures leading to a decrease in internal thermal resistance. For depth ranges usually encountered by boreholes, the pressure impact on thermal conductivity in crystalline rocks is estimated to be about 10 %, which is smaller than the temperature impact and therefore often neglected in numerical temperature models. In sedimentary rocks, in contrast, the non-linear pressure increase can quickly amount to 20 to 30 % and thereby overwhelms the temperature dependent reduction in that depth range. Although the temperature effect clearly prevails over the pressure effect at larger depths (for all rock types), it is still not justified to which degree p/T impact compensate each other (at which depth) for different rock types.

Studies that consider both effects simultaneously are scarce, frequently based on the measurement of some few, usually crystalline rocks, and implemented often dry samples only. Despite all efforts in the past, no standard procedure exists to measure the thermal conductivity under simultaneously increasing p/T conditions until today. This gap is mainly caused by the large technical difficulties in the measurements of a small heat pulse in a high pressure and temperature regime (sensor sensitivity and noise level) and the constructional complexity of such an apparatus. Consequently, there is a significant lack of information on thermal rock properties measured at in-situ conditions, which, in turn, causes a lack of reliable, universally applicable correction equations that consider both effects simultaneously.

The frequently used workaround, applying a combination of independent corrections (separately for pressure and temperate), has significant drawbacks as the combined correction does not necessarily reflect the behaviour of rocks as they occur in the Earth. Moreover, to measure the effect of increasing p/T separately is highly controversial because reciprocal effects are not considered (e.g. thermal cracking caused by the thermal dilatation of the minerals and increasing pore space volume when applying temperature without pressure). Especially the anisotropy of this dilatation creates micro-cracks in the rock, whose development would be surely different under the additional effect of increasing pressure. For crustal depth levels, the differences between thermal conductivity measured at in-situ conditions and at ambient laboratory conditions may be up to 30-50%, which is insufficient for any planning and managing of subsurface applications with numerical models.
Earlier studies by other authors related to this research topic are listed here.

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