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We evaluate if the concept of thermal entropy production can be used as a measure to characterize hydrothermal convection in a confined porous medium as a valuable, thermodynamically motivated addition to the standard Rayleigh number analysis. Entropy production has been used widely in the field of mechanical and chemical engineering as a way to characterize the thermodynamic state and irreversibility of an investigated system. Pioneering studies have since adapted these concepts to natural systems, and we apply this measure here to investigate the specific case of hydrothermal convection in a box-shaped confined porous medium, as a simplified analog for, e.g., hydrothermal convection in deep geothermal aquifers. We perform various detailed numerical experiments to assess the response of the convective system to changing boundary conditions or domain aspect ratios, and then determine the resulting entropy production for each experiment. In systems close to the critical Rayleigh number, we derive results that are in accordance to the analytically derived predictions. At higher Rayleigh numbers, however, we observe multiple possible convection modes, and the analysis of the integrated entropy production reveals distinct curves of entropy production that provide an insight into the hydrothermal behavior in the system, both for cases of homogeneous materials, as well as for heterogeneous spatial material distributions. We conclude that the average thermal entropy production characterizes the internal behavior of hydrothermal systems with a meaningful thermodynamic measure, and we expect that it can be useful for the investigation of convection systems in many similar hydrogeological and geophysical settings.

Plain Language Summary Hydrothermal convection patterns occur naturally in the Earth, for example in geothermal and volcanic systems, in deep aquifers, and along Mid-ocean ridges. We investigate here with numerical simulations how well the specific geometry of these systems can be predicted, especially in confined spaces that are often a reality in the subsurface. To do so, we use a thermodynamic measure, entropy production, as it provides us with a meaningful summary value for the overall fluid and heat flow in these systems. We find intriguing patterns of switch-points between different convection cell geometries that go beyond the structures so far predicted by theory. The results are therefore relevant for hydrothermal settings where convection plays a key role as a heat transport mechanism in the Earth.