Implications of pressure-dependent permeability for hydrothermal heat transfers

Hydrothermal convection in young oceanic lithosphere accounts for ~25% of the total global heat flow, and thus plays a critical role in Earth's thermal evolution. The permeability structure of the lithosphere is a key factor governing how efficiently heat tapped from magma bodies or hot upwelling mantle can be transferred to the overlying ocean. Drill hole measurements and laboratory experiments unambiguously show that permeability decreases with depth (i.e., pressure), either exponentially or through some power law relations. However, the impact of depth-decreasing permeability on the depth extent and heat output of seafloor hydrothermal systems has not been explored systematically.

Here we present 2-D numerical simulations of hydrothermal convection treated as Darcy porous flow, with fluid properties corresponding to a 3.2 wt% NaCl-H₂O mixture, and depth (i.e., pressure)-dependent permeability fields. We consider an empirical exponential dependence as well as a more recently proposed power-law-type dependence rooted in micromechanical modeling of experimental data. In reference simulations with uniform permeability, we find that, for a given basal temperature (T_H) imposed at the model bottom, the hydrothermal heat output at the seafloor increases with permeability, but is largely independent of the depth extent of the model domain. On the other hand, in simulations with depth-decreasing permeability, the depth extent of hydrothermal convection (Z_H) may be significantly lower than the height of the model domain. In such systems, heat extraction is intuitively more efficient when the heat source lies at a shallower depth. We find that the heat output in these simulations is primarily controlled by the harmonic mean of permeability in the hydrothermal system.

To further quantify this finding, we investigate the relationship between our simulations' Rayleigh number (Ra, estimated from model inputs using the harmonically-averaged permeability) and Nusselt number (Nu, measured from simulation results). We find that the linear relationship Nu=Ra/Ra_c that is typical of porous convection holds for Ra > 10³, with a critical Rayleigh number (Ra_c) on the order of 10². This relationship allows us to build an analytical model that predicts Z_H, given the heat output, basal temperature (T_H), and exponentially-decreasing permeability with depth Z: k= k₀ e^(-cZ). Fitting parameters against observed magma-fueled hydrothermal systems at mid-ocean ridges suggests that permeability at the seafloor (k₀) is on the order of 10^-12 - 10^-11 m², in agreement with independent estimates based on drill hole measurements and the poro-elastic tidal modulation of venting temperatures, and that the constant c is on the order of 1-4×10^-3 m^-1. Our findings further suggest that for convection to reach depths > 13 km, as has been proposed near oceanic detachment faults, permeability at the seafloor would need to be extremely large (k₀> 10^-10 m²). It remains unclear whether such conditions can be attained in the damage zone of a detachment fault.