The permeability of magma mush

Abstract

Models for the evolution of magma mush zones are of fundamental importance for understanding magma storage, differentiation in the crust, and melt extraction processes that prime eruptions. Mush mobilisation and melt segregation are predominant mechanisms that control mush evolution yet are to date still insufficiently understood and models for these are poorly constrained. These models are underpinned by calculations of the permeability of the evolving crystal frameworks in the mush, which controls the rate of melt movement relative to crystals. To date, no mush permeability model accounts for the shape of the crystals that form the crystal-framework in the mush. Herein, we assume that mush crystals are approximately cuboidal, and using that geometric approximation, we present new models for the permeability of mush in which crystal shape parameters are a key input. First, we present an extension of the Kozeny-Carman permeability law specifically for crystal packs at their maximum packing, for which the axis lengths of the crystals are the primary input. Second, we present a model for the evolution of magma mush permeability that is valid from maximum packing down to low melt fractions, ideal for simulating permeability as mush crystalises. In all cases we use a combination of numerical approaches to generate packs of cuboids for analysis, and experimental approaches to create digital 3D scans of anisotropic crystal shapes as an analogue for crystal mush. Using a combination of Avizo 3D image analysis, and a lattice-Boltzmann simulation technique, we constrain the permeability of both the numerical and experimental samples; these data then validate our models across a wide range of parameter space applicable to real magma mush. Furthermore, we propose and validate innovative solutions for permeability that can be found using only 2D data (for example, using a thin section scan), which is useful for common situations where full 3D information may not be available for analysis. In general, our results show that if we consider melt percolation in magma mush akin to fluid flow through porous media, the complexity and anisotropy are well represented by the specific surface area of the crystals. Knowledge of the crystal shape and size are essential variables in our proposed permeability model, unless the mush displays overgrowth textures at low melt fraction, in which case the effect of shape becomes less important. Our results have key implications for melt extraction timescales and cumulate textures as well as for crustal melt segregation processes and reactive flow on the scale of mush reservoirs.