Numerical Modeling of Time-dependent Fluid Dynamics and Differentiation of a Shallow Basaltic Magma Chamber

Abstract

This contribution presents a numerical model of time-dependent
\nphysical processes and differentiation in a cooling magma chamber
\nto obtain the magma and liquid composition and model the distribution
\nof minerals and H2O gas bubbles at any moment and place.
\nThe numerical experiments were mainly carried out simulating 10
\nkyr of differentiation of a 50 km3 cylindrical stock-like reservoir as
\none of the end-members of a wide spectrum of magma body geometries.
\nA detailed space^time distribution of compositional varieties
\nand exsolved phases in a chamber of initially superheated basaltic
\ncomposition (corresponding to a lava of the HudsonVolcano, Chile)
\nwas obtained through numerical simulation using the finite-element
\nmethod.The roof of the chamber is located at 2 km depth in a crust
\nwith a geothermal gradient of 308C/km. The model considers two
\nspatial directions (z and r) and assumes the magma to be an incompressible
\nnon-Newtonian liquid, following the Navier^Stokes formulation,
\nwhere the density and viscosity depend on the temperature
\nand exsolved solid and volatile phase content, but viscosity also
\ndepends on the shear rate. The temperature transfer equation used
\nincludes conduction, convection and latent heat. The setting of the
\nmodel considers that: (1) an extension of 1km into the country rocks
\naround the chamber imposed on the heat flow across the margins is
\nappropriate; (2) the reaction rates for phase (solid and gas) exsolution
\ncorrespond to a Gaussian probability function; (3) the involved
\nphases, calibrated from MELTS, are olivine, clinopyroxene, magnetite,
\nplagioclase, orthopyroxene and H2O gas; (4) the velocity of the
\nexsolved phase movements with respect to the hosting liquid is given
\nby the Stokes’ velocity; (5) the sizes of crystals and bubbles in the
\nmelt vary in space and time up to a maximum given by the modal
\ncrystal size observed in the Hudson Volcano. Our results indicate
\nthat the convection dynamics of the reservoir are characterized by
\nthree distinct flows of decreasing velocity with time: convective cells,
\nplumes and layer flows along the walls. The along-wall magma
\nflow, which persists during most of the 10 kyr of magma cooling, contributes
\nto the thermal insulation of the chamber interior, giving
\nrise to a nearly permanent coexistence of liquids of contrasting composition.
\nA strong compositional stratification is generated in the
\nupper half of the chamber, with a downward-increasing thickness of
\nlayers. Such stratification is mainly the result of continuous upward
\nflow and storage on top of the sidewall residual melts. The lower
\nhalf of the chamber exhibits an independent convective pattern dominated
\nby ascending plumes. A less pronounced stratification is generated
\nhere as a consequence of mixing between the residual liquid in
\nthe ascending plumes and the surrounding melt. Crystal accumulations
\nof olivine, clinopyroxene and magnetite at the bottom generate
\na significant volume of ultrabasic magma at the end of 10 kyr.
\nA plagioclase-rich solidification front along the walls is formed
\nduring the last stages of crystallization, when the along-wall
\nmagma flow diminishes in velocity. An application of the numerical
\nmodeling to a cylindrical sill-like chamber is presented to emphasize
\nthe role of the aspect ratio in the magma fluid dynamics, compositional
\ngradients and exsolved phase distribution. The stock-like
\nchamber favors the formation of steep compositional gradients and
\nH2O gas concentration at the roof. Concentration of the exsolved
\nphases along the margins is favored in a sill-like chamber. From the
\nsimulation results, it is possible to infer that stock-like chambers
\nwould be more eruptible and would exhibit a wider compositional
\nspectrum of eruptive materials than sill-like chambers. Because
\nsolid and liquid dispersion follow different patterns in a convective
\nchamber, the record of crystal^liquid equilibrium would be an
\nexception.