Convection, melt segregation and chemical differentiation in crustal magma reservoirs: Insights from 2- and 3D numerical models

We report a three-dimensional, two-phase thermal-chemical-fluid dynamical model and its application to explore the evolution of magma bodies.  The model solves for velocity using a finite-element approach, and for transport using a control-volume scheme to ensure conservation of energy, mass and components.  Solid and melt phases are modelled as Stokes fluids with very different Newtonian viscosities.  Individual crystals in the solid matrix are incompressible, but the solid phase is compressible to account for changes in melt fraction.  The formulation captures compaction and convection of the solid matrix, and flow of melt via a Darcy-type formulation at low melt fraction, and a hindered-settling type approach at high melt fraction.  It also captures heat transport by conduction and advection, melt-solid phase change, and component transport and reaction.  A chemical model is used to calculate phase fraction and composition.  The numerical package sequentially solves for (1) melt and solid velocity (mass and momentum conservation); (2) enthalpy and component transport (energy and component conservation) and (3) phase fraction and composition (chemical model).  Material properties such as density and viscosity are coupled to solution fields such as melt fraction and composition to yield a highly non-linear system of coupled equations which are solved iteratively.

We apply the code to investigate convection and melt segregation processes in a cooling magma body.  Our findings suggest that convection is expected across a wide range of magma reservoir geometries, melt fraction and bulk composition.  The rate of cooling and crystallization is a primary control on whether convection is observed, with thin bodies cooling and crystallizing before convection becomes established.  In more slowly cooled bodies, convection and melt segregation interact to produce spatially complex and dynamically evolving variations in melt fraction and bulk composition, which often differ significantly from simple conceptual models that envisage accumulation of buoyant, evolved melt at the top of the reservoir and dense residual solid at the base.  The transition between convecting- and non-convecting behaviour is also heavily influenced by the relationship between solid phase shear viscosity and melt fraction.  The solid phase bulk viscosity, which is indistinguishable from shear viscosity in one-dimensional analysis, plays a key and distinct role in controlling the predicted magma reservoir dynamics.