Petrological Geodynamics of Mantle Melting I. AlphaMELTS + Multiphase Flow: Dynamic Equilibrium Melting, Method and Results

The complex process of melting in the Earth's interior is studied by combining a multiphase numerical flow model with the program AlphaMELTS which provides a petrological description based on thermodynamic principles. The objective is to address the fundamental question of the effect of the mantle and melt dynamics on the composition and abundance of the melt and the residual solid. The conceptual idea is based on a 1-D description of the melting process that develops along an ideal vertical column where local chemical equilibrium is assumed to apply at some level in space and time. By coupling together the transport model and the chemical thermodynamic model, the evolution of the melting process can be described in terms of melt distribution, temperature, pressure and solid and melt velocities but also variation of melt and residual solid composition and mineralogical abundance at any depth over time. In this first installment of a series of three contributions, a two-phase flow model (melt and solid assemblage) is developed under the assumption of complete local equilibrium between melt and a peridotitic mantle (dynamic equilibrium melting, DEM). The solid mantle is also assumed to be completely dry. The present study addresses some but not all the potential factors affecting the melting process. The influence of permeability and viscosity of the solid matrix are considered in some detail. The essential features of the dynamic model and how it is interfaced with AlphaMELTS are clearly outlined. A detailed and explicit description of the numerical procedure should make this type of numerical models less obscure. The general observation that can be made from the outcome of several simulations carried out for this work is that the melt composition varies with depth, however the melt abundance not necessarily always increases moving upwards. When a quasi-steady state condition is achieved, that is when melt abundance does not varies significantly with time, the melt and solid composition approach the composition that is found from a dynamic batch melting model which assumes the velocities of melt and residual solid to be the same. Time dependent melt fluctuations can be observed under certain conditions. In this case the composition of the melt that reaches the top side of the model (exit point) may vary to some extent. A consistent result of the model under various conditions is that the volume of the first melt that arrives at the exit point is substantially larger than any later melt output. The analogy with large magma emplacements associated to continental break-up or formation of oceanic plateaus seems to suggest that these events are the direct consequence of a dynamic two-phase flow process. Even though chemical equilibrium between melt and the residual solid is imposed locally in space, bulk composition of the whole system (solid+melt) varies with depth and may also vary with time, mainly as the result of the changes of the melt abundance. Potential factors that can influence the melting process such as bulk composition, temperature and mantle upwelling velocity at the top boundary (passive flow) or bottom boundary (active flow) should be addressed more systematically before the DEM model in this study and the dynamic fractional melting (DFM) model that will be introduced in the second installment can be applied to interpret real petrological data. Complete data files of most of the simulations and four animations are available following the data repository link provided in the Supplementary Material