Relationships between reservoir permeability, magmatism and the development of geothermal systems in continental settings

A two-dimensional, time-dependent, numerical study of natural convection in porous media is presented. The finite element models are based on an idealised crustal section, including the main structural features characterising many hydrothermal systems. The onset of the thermal convection is investigated by exploring different thermal boundary conditions, accounting for variable permeability values of the geothermal reservoir and the presence of middle-crustal magmatic intrusions (10 km deep) as well as upper-crustal plutons (5 km deep). The basic mathematical framework for convection in porous media governed by Darcy's Law is outlined together with an ensemble of constitutive laws useful in the description of the macroscopic behaviour of the magmatic heat source and the porous rocks. The results are analysed together with the key parameter for convection, the Rayleigh number. Large-scale convective cells develop at moderate-to-high Rayleigh numbers, when the reservoir permeability overcomes a threshold value of the order 10^-15-10^-14 m². The temporal evolution of the surface heat flow above the hydrothermal system, together with the 2D thermal structure around the magmatic heat.