A continuum model of multi-phase reactive transport in igneous systems

Abstract

Multi-phase reactive transport processes are ubiquitous in igneous systems. A challenging aspect of modelling igneous phenomena is that they range from solid-dominated porous to liquiddominated suspension flows and therefore entail a wide spectrum of rheological conditions, flow speeds, and length scales. Most previous models have been restricted to the two-phase limits of porous melt transport in deforming, partially molten rock and crystal settling in convecting magma bodies. The goal of this paper is to develop a framework that can capture igneous system from source to surface at all phase proportions including not only rock and melt but also an exsolved volatile phase. Here, we derive an n-phase reactive transport model building on the concepts of Mixture Theory, along with principles of Rational Thermodynamics and procedures of Non-equilibrium Thermodynamics. Our model operates at the macroscopic system scale and requires constitutive relations for fluxes within and transfers between phases, which are the processes that together give rise to reactive transport phenomena. We introduce a phase-and process-wise symmetrical formulation for fluxes and transfers of entropy, mass, momentum, and volume, and propose phenomenological coefficient closures that determine how fluxes and transfers respond to mechanical and thermodynamic forces. Finally, we demonstrate that the known limits of two-phase porous and suspension flow emerge as special cases of our general model and discuss some ramifications for modelling pertinent two-and three-phase flow problems in igneous systems.

Magma ascent in planetesimals: Control by grain size

“…To conclude, in this paper we have advanced the technical capabilities to simulate multi-phase and multi-component planetesimal evolution, gaining insights into features not accessible to single-phase fluid dynamics models. However, unraveling more detailed evolutionary regimes of planetesimals will require a time-dependent treatment that includes metal and volatile phases, which shape the structure and subsequent evolution of these bodies (Keller and Suckale, 2018). Further work is required to understand planetesimal evolution and its connection to the meteoritic record and rocky planet formation .…”

“…For example, our model does not reproduce the eutectic behavior expected for silicate compositions as the ones considered here (see discussion in Keller and Katz, 2016), nor does it include volatiles and incompatible elements producing low-degree, incompatible-enriched melts at temperatures below the anhydrous solidus. Using a more consistent petrological model that takes into account the non-ideal thermodynamics of the full range of major elements and mineral phases would likely lead to more complex relations between heating, melt production, and element partitioning (Keller and Suckale, 2018). Significant differences in aluminum partitioning, which is the focus here, are likely confined to the onset of melting, where low-degree, enriched melts may have important control on geochemical evolution.…”

101 Geodynamic modelling: How to design, interpret, and communicate numerical studies of the solid Earth

“…Other physical processes may require additional terms or additional equations. Examples are the generation of the magnetic field in the outer core (Jones, 2011), two-phase (McKenzie, 1984Bercovici et al, 2001) or multi-phase flow (Oliveira et al, 2018;Keller and Suckale, 2019), disequilibrium melting (Rudge et al, 2011), complex magma dynamics in the crust (Keller et al, 2013), reactive melt transport (Aharonov et al, 1995;Keller and Katz, 2016), (de)hydration reactions and water transport (Faccenda et al, 2012;Magni et al, 2014;Quinquis and Buiter, 2014;Wilson et al, 2014a;Nakagawa et al, 2015), the evolution of the mineral grain size (Hall and Parmentier, 2003;Solomatov and Reese, 2008;Bercovici and Ricard, 2012;Cerpa et al, 2017;Mulyukova and Bercovici, 2019), the fluid dynamics and thermodynamics of a magma ocean (Labrosse et al, 2007;Solomatov, 2000;Ulvrová et al, 2012), the interaction of tectonic processes with erosion and other surface processes (Burov and Cloetingh, 1997;Roe et al, 2006;Thieulot et al, 2014;Ueda et al, 2015;Sternai, 2020), anisotropic fabric Lev and Hager, 2008;Heister et al, 2017;Faccenda, 2014;Perry-Houts and Karlstrom, 2018;Király et al, 2020a), phase transformation kinetics (Bina et al, 2001;Tetzlaff and Schmeling, 2009;Quinteros and Sobolev, 2012;Agrusta et al, 2014) and inerti...…”

Combined numerical and experimental study of microstructure and permeability in porous granular media

“…Using experimental data, Carman (1956) determined that tortuosity τ is ≈ √ 2. Today, the Kozeny-Carman equation -or variants thereof -is widely used in volcanology (Klug and Cashman, 1996;Mueller et al, 2005;Miller et al, 2014), hydrogeology (Wang et al, 2017;Taheri et al, 2017), twophase and multi-phase flow studies (Wu et al, 2012;Keller and Katz, 2016;Keller and Suckale, 2019), and soil sciences (Chapuis and Aubertin, 2003;Ren et al, 2016). The Kozeny-Carman equation was derived assuming that the medium consists only of continuous curved channels with a constant cross section (Carman, 1937;Bear, 1988).…”