Mathematical modeling of conductive heat transfer from a freezing, convecting magma chamber to a single-pass hydrothermal system: implications for seafloor black smokers

Details Mathematical modeling of conductive heat transfer from a freezing, convecting magma chamber to a single-pass hydrothermal system: implications for seafloor black smokers Mathematical modeling of conductive heat transfer from a freezing, convecting magma chamber to a single-pass hydrothermal system: implications for seafloor black smokers

May 1991

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1991e%26psl.104...59l&link_type=abstract

Earth and Planetary Science Letters, Volume 104, Issue 1, p. 59-69.

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Hydrothermal systems subject to a heat flux boundary condition at the base behave differently from systems with an isothermal bottom boundary. Scaling analysis of convection in a uniform porous layer at large Rayleigh number, Ra, is used to illustrate that the core temperature of the system scales as Ra-1/2 and vertical velocity scales as Ra1/2. A time-dependent numerical model of heat transfer across a thickening conductive boundary layer between a crystallizing magma chamber and a single-pass hydrothermal system in the oceanic crust is then developed. The model shows that a layer of isotropic gabbro at the top of the magma chamber ~ 75-200 m thick during a period of high-temperature flow. The parameter kd, where k is the bulk permeability and d is the thickness of the chemical reaction-heat uptake region at the base of the hydrothermal system, exerts a strong control on the duration of high-temperature flow. The thickness d is thought to be a few tens of meters. The simulations yield temperature and flow rates that are similar to black smokers under rather restrictive conditions on kdkd ~ 5 × 10-12 m3) for a time period of ~ 100 years. But during this time interval, the temperature and flow rate decreases significantly; and these features do not appear to be characteristic of black smokers. Thus although kd exerts some control on whether high-temperature venting occurs, other factors must stabilize the temperature and heat output of black smoker vents. Downward migration of the hydrothermal system into the isotropic gabbro layer could help to stabilize the flow. Two-phase flow is not explicitly treated in this model; but the results suggest that supercritical two-phase flow may occur for tens to hundreds of years.
Present address: ERM-North Central, Inc., 102 Wilmot Rd. Suite 300, Deerfield, IL 60015, USA

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