Thermal Entropy Production as a Key to Understanding Uncertainties in Geothermal Systems

Abstract

Simulations of subsurface temperature usually contain uncertainties and an important question is then: exactly how uncertain are they, or how well are we able to predict them? We propose here that the uncertainty is depending on the main heat transport mechanisms: if heat transported by conduction only, then the temperatures are relatively simple 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. We suggest here a method that enables us to evaluate the dominating heat transport mechanisms with a method based on the thermodynamic concept of entropy production. Simple examples show that the internal thermal entropy production is zero if a system is in a conductive steady state. If convection is present in the system, entropy production is greater than zero, with higher values for more vigorous convection. In fact, for a simple layer system, it can be shown that the entropy production is directly related to the efficiency of heat transport, measured with the Nusselt number. We conclude from these examples that thermal entropy production can be applied to estimate how well we will be able to predict temperatures in a specific geothermal resource area.