| Abstract |
Geological data at the depth of geothermal resources and reservoirs are rare and of varying quality. In order to evaluate how the structural geological model and simulations of the hydrothermal flow field are affected by the geological data quality, meaningful measures are required to characterize these systems. We present here system-based thermodynamic measures to classify uncertainties in geological models and in geothermal flow fields. Information entropy is proposed to evaluate uncertainties in geological models, and thermal entropy production is proposed to analyze uncertainties related to hydrothermal flow. As these measures have a fundamental theoretical basis and are related to the internal state of the system, they can be interpreted quantitatively and, consequently, give uncertainties a meaning. Information entropy values are directly related to the state of uncertainty of a geological model. For a point within the model, information entropy is a measure of the minimum number of geological units that could occur at its location. If the information entropy is zero, only one unit is possible and no uncertainty exists. If the information entropy value is greater than zero, at least two units are probable. If it increases above 1, three units can occur. In general the measure provides a weight of probability for different states. An advantage of the method is that it gives an entropy measure for the state of the entire model and therefore lends itself as a robust measure to quantitatively compare uncertainties in difference models. In a similar sense, the 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 an application of both measures for a complex case study to investigate the influence of geological data quality on the uncertainty of geological model and geothermal flow predictions. This analysis has only been possible due to a newly developed workflow that integrates geological modeling and geothermal flow simulations. Our application to the realistic case study confirms the key hypothesis that the geological uncertainty and the flow uncertainties can be subsumed in two interrelated measures: (a) information entropy, and (b) the spread of the thermal entropy. Since the measures provide single values that characterize uncertainties, they provide a promising path for physically based data compression in data intensive geothermal modeling. |