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 source and within the geothermal reservoir, are
also investigated and discussed.