Numerical modelling of multiphase multicomponent reactive transport in the Earth’s interior

Abstract

We present a conceptual and numerical approach to model processes in the Earth's interior that involve multiple phases that simultaneously interact thermally, mechanically and chemically. The approach is truly multiphase in the sense that each dynamic phase is explicitly modelled with an individual set of mass, momentum, energy and chemical mass balance equations coupled via interfacial interaction terms. It is also truly multicomponent in the sense that the compositions of the system and its constituent phases are expressed by a full set of fundamental chemical components (e.g. SiO 2 , Al 2 O 3 , MgO, etc) rather than proxies. These chemical components evolve, react with, and partition into, different phases according to an internally-consistent thermodynamic model. We combine concepts from Ensemble Averaging and Classical Irreversible Thermodynamics to obtain sets of macroscopic balance equations that describe the evolution of systems governed by multi-phase multi-component reactive transport (MPMCRT). Equilibrium mineral assemblages, their compositions and physical properties, and closure relations for the balance equations are obtained via a "dynamic" Gibbs free-energy minimization procedure (i.e. minimizations are performed on-the-fly as needed by the simulation). Surface tension and surface energy contributions to the dynamics and energetics of the system are taken into This is a pre-copyedited, author-produced PDF of an article accepted for publication in

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

“…Our compaction model thus extends previous theories by including other processes than divergent flow (e.g., McKenzie, 1984;Bercovici & Ricard, 2003;Oliveira et al, 2018) and reactive volume change (e.g., Šrámek et al, 2007).…”

“…Depending on the mechanical and thermal structure of the crust, its thickness (Hildreth & Moorbath, 1988), and regional tectonic regime (Cembrano & Lara, 2009), transport towards the shallow crust is thought to be accommodated by diapirs rising through ductile crust (Bateman, 1984;Cruden, 1990) or by fractures propagating through brittle rock (Clemens & Mawer, 1992;Rubin, 1993;Havlin et al, 2013). Porous melt transport models have been extended to include visco-elastic/brittle-plastic rheologies (Connolly & Podladchikov, 2007;Rozhko et al, 2007;Keller et al, 2013;Yarushina & Podladchikov, 2015;Oliveira et al, 2018), though their application has remained limited.…”

“…This choice implies that there is no resistance to purely rotational motion, and that angular momentum is conserved, since q i v = q i v T now holds. In (25), we have made a distinction between mechanical and thermodynamic pressures, where the former is a third of the trace of (25), and the latter accounts for irreversible deformation internal to compressible phases, (Bennethum & Weinstein, 2004;Moulas et al, 2019;Oliveira et al, 2018). To reduce complexity, as well as to emphasise the multi-phase nature of compaction, we choose to set the volumetric coefficient to zero, Λ i V = 0, and hence maintain a single pressure definition, P i = P i , in (23c).…”

“…The reason is that we assume their systemscale volumetric deformation to be dominated by phase compaction, not phase compressibility (i.e., ∂φ i /∂t ρ i −1 ∂ρ i /∂t). The two-phase compaction model of McKenzie (1984), and the recent extension to n phases by Oliveira et al (2018) both use the volumetric term in the stress tensor to formulate phase compaction. Hence, they do not distinguish formally between system-scale volumetric flow resulting from irreversible bulk deformation internal to compressible phases, and local-scale solenoidal flow of phases accommodating changes in phase fractions.…”

Petrological Geodynamics of Mantle Melting II. AlphaMELTS + Multiphase Flow: Dynamic Fractional Melting

“…A petrological tool based on melting parameterization has been developed recently (Brown and Lesher, 2016), and in principle it could be used in combination with some dynamic model as well. Numerous studies investigated the dynamic evolution of melt and solid mantle using a twophase flow model (McKenzie, 1984;Stevenson, 1984, 1986;Spiegelman, 1993;Richardson, 1998;Ghods and Arkani-Hamed, 2000;Schmeling, 2000;Bercovici et al, 2001;Bercovici and Ricard, 2003;Spiegelman et al, 2007;Hewitt and Fowler, 2008;Katz, 2008;Hewitt, 2010;Rudge et al, 2011;Oliveira et al, 2018). The most recent one (Oliveira et al, 2018) incorporates a complex rheology and a realistic thermodynamic equilibrium model.…”