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 physical processes and differentiation in a cooling magma chamber to obtain the magma and liquid composition and model the distribution of minerals and H2O gas bubbles at any moment and place. The numerical experiments were mainly carried out simulating 10 kyr of differentiation of a 50 km3 cylindrical stock-like reservoir as one of the end-members of a wide spectrum of magma body geometries. A detailed space^time distribution of compositional varieties and exsolved phases in a chamber of initially superheated basaltic composition (corresponding to a lava of the HudsonVolcano, Chile) was obtained through numerical simulation using the finite-element method.The roof of the chamber is located at 2 km depth in a crust with a geothermal gradient of 308C/km. The model considers two spatial directions (z and r) and assumes the magma to be an incompressible non-Newtonian liquid, following the Navier^Stokes formulation, where the density and viscosity depend on the temperature and exsolved solid and volatile phase content, but viscosity also depends on the shear rate. The temperature transfer equation used includes conduction, convection and latent heat. The setting of the model considers that: (1) an extension of 1km into the country rocks around the chamber imposed on the heat flow across the margins is appropriate; (2) the reaction rates for phase (solid and gas) exsolution correspond to a Gaussian probability function; (3) the involved phases, calibrated from MELTS, are olivine, clinopyroxene, magnetite, plagioclase, orthopyroxene and H2O gas; (4) the velocity of the exsolved phase movements with respect to the hosting liquid is given by the Stokes’ velocity; (5) the sizes of crystals and bubbles in the melt vary in space and time up to a maximum given by the modal crystal size observed in the Hudson Volcano. Our results indicate that the convection dynamics of the reservoir are characterized by three distinct flows of decreasing velocity with time: convective cells, plumes and layer flows along the walls. The along-wall magma flow, which persists during most of the 10 kyr of magma cooling, contributes to the thermal insulation of the chamber interior, giving rise to a nearly permanent coexistence of liquids of contrasting composition. A strong compositional stratification is generated in the upper half of the chamber, with a downward-increasing thickness of layers. Such stratification is mainly the result of continuous upward flow and storage on top of the sidewall residual melts. The lower half of the chamber exhibits an independent convective pattern dominated by ascending plumes. A less pronounced stratification is generated here as a consequence of mixing between the residual liquid in the ascending plumes and the surrounding melt. Crystal accumulations of olivine, clinopyroxene and magnetite at the bottom generate a significant volume of ultrabasic magma at the end of 10 kyr. A plagioclase-rich solidification front along the walls is formed during the last stages of crystallization, when the along-wall magma flow diminishes in velocity. An application of the numerical modeling to a cylindrical sill-like chamber is presented to emphasize the role of the aspect ratio in the magma fluid dynamics, compositional gradients and exsolved phase distribution. The stock-like chamber favors the formation of steep compositional gradients and H2O gas concentration at the roof. Concentration of the exsolved phases along the margins is favored in a sill-like chamber. From the simulation results, it is possible to infer that stock-like chambers would be more eruptible and would exhibit a wider compositional spectrum of eruptive materials than sill-like chambers. Because solid and liquid dispersion follow different patterns in a convective chamber, the record of crystal^liquid equilibrium would be an exception.