Multi-Phase and Multi-Component Reactive Transport in the Earth's interior

Multi-Phase Multi-Component Reactive Transport (MPMCRT) controls a number of important complex geodynamic/geochemical problems, such as melt generation and percolation, metasomatism, rheological weakening, magmatic differentiation, ore emplacement, and fractionation of chemical elements, to name a few. These interacting processes occur over very different spatial and temporal scales and under very different physico-chemical conditions. Therefore, there is a strong motivation in geodynamics for investigating the equations governing MPMCRT, their mathematical structure and properties, and the numerical techniques necessary to obtain reliable and accurate results.

In this thesis we attempt to outline the basic conceptual and numerical frameworks to solve multiscale MPMCRT problems in the Earth's interior. The numerical model is based on two main ingredients: 1) a general and scalable multi-phase approach based on Ensemble Averaging Theory, coupled with 2) a sound chemical thermodynamic framework for the reactive and chemical transport phenomena. Our approach combines rigorous solutions to the conservation equations (mass, energy and momentum) for each dynamic phase (instead of the more common mixturetype approach) within the context of classical irreversible thermodynamics. This is achieved via a novel particle-based Lagrangian-Eulerian Finite Element algorithm developed here, which allows for accurate tracking of phases (even in the presence of sharp fronts), and the reactions between them, valid over a wide spectrum of scales and problems. Interfacial processes such as phase changes, chemical diffusion+reaction and surface tension effects, as well as visco-elasto-plastic rheologies and REE disequilibrium partitioning are explicitly incorporated in the context of ensemble averaging. Phase assemblages, mineral and melt compositions, and all other physical parameters of the multiphase system are obtained through dynamic free-energy minimization procedures. The present numerical framework provides a reliable platform that can be used not only to study the dynamics and feedbacks of multi-phase systems of different nature and scales (the predictive forward problem) but also the possibility of making realistic comparisons with both geophysical and geochemical data sets.