Non thermal equilibrium two-phase flow of melt in a compacting matrix : insights on melt migration and dike initiation in the upper mantle
Final Report Abstract
This project aimed at investigating how thermal non-equilibrium at the transition from super- to sub-solidus regions may influence melt transport evolution. To explore the physical parameters controlling thermal non-equilibrium the coupled heat equations for fluid and solid phases are formulated for a fluid migrating through a resting porous solid by Darcy flow. By non-dimensionalizing the equations three non-dimensional numbers can be identified controlling thermal non-equilibrium: the Peclet number Pe describing the fluid velocity, the heat transfer number A describing the local interfacial heat transfer from the fluid to the solid, and the porosity φ. The equations are solved numerically for the fluid and solid temperature evolution for a simple 1D model setup with constant flow velocity. A simplified time-independent ordinary differential equation for depth-dependent melt-matrix temperature difference is derived and analytically solved. From these solutions simple scaling laws of the form (T f − T s ) = f(Pe, A, φ, H), where H is the non-dimensional model height, are derived. Applying the results to natural magmatic systems such as mid-ocean ridges can be done by estimating appropriate orders of Pe and A. Plotting such typical ranges in the Pe-A regime diagram reveals that a) interstitial melt flow is in thermal equilibrium, b) melt channelling as e.g. revealed by dunite channels may reach moderate thermal non-equilibrium, and c) the dyke regime is at full thermal non-equilibrium. The evolution of thermal disequilibrium in a system where Pe, A and φ evolve with depth is investigated. The 1D-model was designed to mimic a dunite anastomosing system, using geometrical parameters and melt transport characteristics contrained from dunites observation and numerical models from the literature. Models results show that a moderate thermal non-equilibrium buils up in such an anastomosing network. The resulting temperature difference at the top of the system should facilitate melt migration at the super- to sub-solidus region. This project quantifies the temperature difference that may build up in a mantellic magmatic system. It provides key insights for estimating thermal disequilibrium influence on melt transport and gives a first view of the importance of considering non-thermal equilibrium when investigating dike initiation at the super- to sub-solidus region transition.
