Title: Coupling the Thermodynamics, Kinetics and Geodynamics of Multiphase Reactive Transport in Earth’s Interior
Description: Multiscale multiphase reactive transport is a central phenomenon governing geologic processes in Earth's interior. In the upper mantle, melts, produced by partial melting of the peridotitic mantle, and volatile-rich fluids, derived from dehydration of subducting plates, buoyantly ascend through the mantle's porous network. Reaction between these melts and fluids and the surrounding solid matrix control the composition of magmas that reach Earth's crust. Melt-rock reaction is strongly coupled to the dynamics of melt transport: not only do the transport pathways modulate the extent of chemical interaction between melts and the solid matrix, but the melt-rock reactions also feedback into the transport dynamics through reactive changes to bulk physical properties including permeability, density, and viscosity. These feedbacks can result in the emergence of self-organized transport networks, such as the network of high-porosity dunite channels beneath mid-ocean ridges. Understanding the various feedbacks between reaction and melt transport requires consistent coupling of multicomponent multiphase thermodynamics and geodynamics.

However, the high-dimensionality of such coupled problems presents a major theoretical and computational challenge. Existing models of reactive multiphase flow have therefore tended to focus separately on the geochemistry of melt-rock interaction, or on the dynamics of melt transport, with simplified thermo-chemical couplings. In this dissertation, I present a new thermodynamically consistent and tractable framework for integrating multicomponent thermodynamics and multiphase geodynamics. I use a non-equilibrium thermodynamic formulation to describe reaction as a time-dependent irreversible process alongside heat and mass transport. This theory is implemented using new thermodynamic software developed through the ENKI project. The main benefits of this approach are two-fold. Firstly, it extends the reach of existing multiphase computational thermodynamics to model macroscopic disequilibrium reaction paths --- this is the first step towards being able to model a host of metastable reaction phenomena in igneous and metamorphic systems.

I model disequilibrium batch reaction for a simple system in chapter 2. Secondly, it allows self-consistent integration of multiphase thermodynamics in two-phase flow models, to better explore coupling between reaction and transport. This is demonstrated in chapter 5. Chapter 1 gives a broad introduction to multiphase reactive flow and further discusses the motivation for this work. I outline past work and discuss the scope of problems in which coupling between reaction and transport plays a critical role in geodynamic and geochemical evolution. In chapter 2 I present a general theory for integrating computational thermodynamics and geodynamics. This approach is based on the standard conservation equations for porous melt transport within a deformable solid matrix, but extends the governing equations to include multiple solid phases. The multiphase reactive coupling is described using a kinetic framework that includes explicit stoichiometric reactions between minerals, melts, and fluids.

Using the theory of non-equilibrium thermodynamics, the macroscopic reaction rates are controlled by the reaction affinities --- providing closed-form expressions for the net reactive mass transfers. This formulation of disequilibrium reaction is the principal contribution of this dissertation. Coupled with the conservation equations it can describe both equilibrium and disequilibrium reaction paths and is applicable to a range of geological conditions. I outline approaches for modeling melt-mediated, fluid-mediated, and subsolidus grain-boundary-mediated reaction. In extension to previous theories of two-phase flow, this framework permits modeling of more realistic melting and crystallization reactions, including eutectic and peritectic melting. The theoretical framework is supported by software developed as part of the ENKI project. I briefly summarize the software infrastructure in this chapter. In the remaining chapters I step through the workflow for implementing this approach for a series of model problems in the Mg$_2$SiO$_4$--SiO$_2$ binary system.

The Mg$_2$SiO$_4$--SiO$_2$ subsystem is an important bounding binary for understanding mantle melting and represents the simplest subsystem for exploring coupled reactive transport dynamics. Widely used thermodynamic models of silicate melting (i.e. MELTS) do not extend to the binary, and existing binary melting models involve complex treatments of melt speciation to account for significant non-ideality at high silica contents. Here, I am concerned mostly with reaction for mafic compositions relevant to mantle magmatism. Therefore, in chapter 3 I present a simple thermodynamic model for melting in the Mg$_2$SiO$_4$--SiO$_2$ system. I use a numerically efficient asymmetric binary mixing model to describe solution in the melt, which is calibrated using a compilation of phase equilibrium experimental data. This chapter is not a self-contained study in and of itself, but rather sets up the thermodynamic model that I will use in the remaining chapters. Chapter 4 applies the theoretical framework to a series of simple model problems for disequilibrium reaction and reactive melt transport in the Mg$_2$SiO$_4$--SiO$_2$ system.

Disequilibrium reaction paths can be non-intuitive, and I start by modeling reaction in uniform batch systems. All of the calculations are consistent with the phase diagram in the equilibrium limit. More general conservation equations for disequilibrium reaction in open-system batch reactors are derived in Appendix C. I then integrate irreversible reaction with the dynamics of diffusion and advection of heat and mass to model the formation of reactive fronts around fusible heterogeneities, and a eutectic/peritectic disequilibrium steady-state melting column. This is the first self-consistent inclusion of eutectic/peritectic melting into magma dynamics. Finally, in chapter 5 I apply this framework to explore the formation of dunite channels by incongruent open-system melting. I develop a series of 1-D and 2-D models to investigate the formation of dunite channels in a harzburgitic mantle within the Mg$_2$SiO$_4$--SiO$_2$ binary system. The models predict that influx of deep silica-poor melts promotes a reactive channeling instability that organizes melt into high-porosity dunite channels.

During decompression melting in the absence of a basal melt flux, no channelization is observed. This implies that an additional flux of melt is required, either from melting of deep fusible heterogeneities, or from large-scale melt focusing toward the ridge axis at depth. Alternatively, flux melting of additional melt components could help drive reactive channelization in natural peridotite systems.