| Abstract |
Estimations of subsurface temperatures in geothermal systems always contain uncertainties; this is especially true in early stages of exploration when only very limited information about rock physics properties and the thermal state of a system exist. We propose here that the uncertainty is related to the main heat transport mechanism: if heat transported by conduction only, then the temperatures are relatively easy to predict and the uncertainty is low. However, if advective heat transport is present, then the additional transport of heat in the fluid phase can significantly change the temperature field, making it more difficult to predict. If, in addition, free convection occurs in the system, it is becoming highly non-linear, and temperature predictions are highly uncertain. We propose here the application of thermal entropy production as a system-based measure to classify uncertainties in geothermal flow fields. Thermal entropy production provides a quantitative measure of the thermo-dynamic state of a hydrothermal system. When the entropy production is zero, the system must be in a conductive steady state for a closed system. If the entropy production is larger than zero, the system can be in a convective or transient conductive state. For higher values of entropy production, the convective units show higher complexities and, hence, the uncertainty of the hydrothermal field increases. Moreover, the average model entropy production gives a measure of the convective vigor that can be expected in the system. This is directly related to the efficiency of heat transfer over the system. The measure is therefore not only useful for comparison of different models, but also has a quantitative meaning for the productivity of heat that can be harvested from a particular setting. We present the application of entropy production as a measure of the system state with the well-known example of convection in a confined box and compare it to hydrothermal flow systems in hot sedimentary aquifer (HSA) settings. The results show that thermal entropy production provides a meaningful measure to quantify the thermal state. We then utilise the important feature that entropy production characterises the system with a single measure in a subsequent uncertainty analysis: we evaluate how uncertainties in the structural setting influence the state of the hydrothermal system. The results show that thermodynamic measures provide a way forward to understanding uncertainties on the scale of the system - an important step towards an estimation of how well we are able to predict temperatures in a given geothermal area. |