Physical balances in subseafloor hydrothermal convection cells

Abstract

[1] We use a simplified model of convection in a porous medium to investigate the balances of mass and energy within a subseafloor hydrothermal convection cell. These balances control the steady state structure of the system and allow scalings for the height, permeability, and residence time of the ''reaction zone'' at the base of the cell to be calculated. The scalings are presented as functions of (1) the temperature T D of the heat source driving the convection and (2) the total power output F U . The model is then used to illustrate how the nonlinear thermodynamic properties of water may impose the observed upper limit of $400°C on vent temperatures. The properties of water at hydrothermal conditions are contrasted with those of a hypothetical ''Boussinesq fluid'' for which temperature variations in fluid properties are either linearized or ignored. At hydrothermal pressures, water transports a maximum amount of energy by buoyancy-driven advection at $400°C. This maximum is a consequence of the nonlinear thermodynamic properties of water and does not arise for a simple Boussinesq fluid. Inspired by the ''Malkus hypothesis'' and by recent work on dissipative systems, we speculate that convection cells in porous media attain a steady state in which the upwelling temperature T U maximizes the total power output of the cell. If true, this principle would explain our observation (in previous numerical simulations) that water in hydrothermal convection cells upwells at T U $ 400°C when driven by a heat source above $500°C. INDEX TERMS: 3015 Marine

Life, hierarchy, and the thermodynamic machinery of planet Earth

“…This was initially suggested by Edward Lorenz [70], and is closely related to the hypothesis formulated by Paltridge [71,13,72] that the atmospheric circulation maximizes entropy production. Since then, further work has shown that MEP yields reasonable predictions of hemispheric heat transport on other planetary bodies [14,73] and of empirical friction coefficients in atmospheric general circulation models [15,74], but also for vertical convection [71,75,49,37,51,76] and convection at hydrothermal vents at the seafloor [77]. More support comes from studies of turbulence and its effects on heat transport and entropy production [78][79][80][81][82].…”

Numerical Simulation of Multiphase Fluid Flow in Hydrothermal Systems

“…A number of studies have dealt with various aspects of this theme (e.g., Cathles 1993;Jupp andSchultz 2000, 2004). The basic principle is rather simple: if the fl uid fl ows too fast, it will stay relatively cold since the heat supply cannot keep pace; if the fl uid fl ows very slowly, heat transfer to the fl uid will be optimized.…”

Hydrodynamic modeling of magmatic–hydrothermal activity at submarine arc volcanoes, with implications for ore formation

“…The fully fluid-saturated model domain is initialized with seawater salinity, a geothermal gradient of ∼20 • C km −1 for old oceanic crust (which relates to a basal heat flux of Q c = 0.045 W m −2 applied to the bottom boundary), and the corresponding hydrostatic pressure. The host rock has a porosity of φ = 0.1, a homogeneous permeability of k = 10 −14 m 2 (a value typically assumed for hydrothermal convection in oceanic crust, e.g., Jupp and Schultz, 2004), a thermal conductivity of K = 2 W m −1 • C −1 , a heat capacity of the rock of c pr = 880 J kg −1 • C −1 , and a density of the solid rock matrix of ρ r = 2700 kg m −3 . The values correspond to the conditions used in comparable hydrothermal simulation projects (e.g., Hayba and Ingebritsen, 1997).…”