Permeability of polydisperse magma foam

Abstract

Effective models for the evolution of magma permeability are key to understanding shallow magma ascent and eruption dynamics. Models are generally empirical constructs, commonly focused on monodisperse systems, and unable to cope with the foam limit at high porosity. Here, we confirm that bubble size distributions in high-porosity pyroclasts are highly polydisperse. We combine collated experimental data and numerical simulations to test and validate a theoretically grounded percolation model for isotropic magma permeability, which accounts for the effect of polydispersivity of bubble sizes. We find that the polydispersivity controls the percolation threshold. It also serves as essential input into the scaling of permeability that is required to achieve universality in the description of permeability. Our model performs well against collated published data for the permeability of high-porosity volcanic rocks. We then extend this model to predict the viscous and inertial contributions to fluid flow that are required to model magma outgassing in all regimes. Our scaling relationship holds across the full range of porosity, from the percolation threshold to the open-foam limit.

Predicting permeability via statistical learning on higher-order microstructural information

“…The permeability is independent of the fluid and the pressure difference and a property solely of the microstructure provided that the Reynolds number is sufficiently small ( Re < 0.01 ), which also ensures that the velocity is proportional to the pressure difference. The computed permeabilities have units voxels 2 , where the voxels have unit length.…”

“…Specifically, understanding how fluid transport properties are related to the microstructure of a porous medium is crucial in a wide range of areas e.g. geological events 2 , polymeric composites for packaging materials 3 , catalysis, filtration and separation 4 , energy, fuels, and electrochemistry 5 , fiber and textile materials for health care and hygiene 6 , and porous, biodegradable polymer films for controlled release of medical compounds 7 . Numerous efforts in determining the physical properties of complex materials have been made since the early work of Maxwell 1 , 8 – 11 , and such investigations have been enhanced due to the availability of high-resolution 3D images of various types of materials microstructures using X-ray nanotomography 12 , 13 or focused ion beam scanning electron microscopy 14 , and nuclear magnetic resonance as well 15 , 16 .…”

A model for the kinetics of high-temperature reactions between polydisperse volcanic ash and SO2 gas

“…In general, the polydispersivity of a distribution of spheres is captured by = 〈 〉〈 〉/〈 3 〉 where 〈 〉 is the nth moment of the distribution (Torquato 2013;Wadsworth et al 2017a;Vasseur et al 2020). Here = is the monodisperse end member and = is infinitely polydisperse.…”

CO2 favours the accumulation of excess fluids in felsic magmas

“…Progressive magma crystallization increases the relative volume of excess fluids until their fraction reaches a critical volume at which bubbles interconnect through the magma edge to edge. This critical volume or percolation threshold determines the release of excess fluids from the magma (Stauffer and Abarov, 1994;Walsh and Saar, 2008), modulated by magma crystallinity (Belien et al, 2010;Oppenheimer et al, 2015), deformation (Okumura et al, 2006;Caricchi et al, 2011), style of bubble nucleation in melts (Hurwitz and Navon, 1994; Mangan and Sisson, 2000), and bubble size polydispersivity (Vasseur et al, 2020). However, the influence of the excess fluid composition on the percolation threshold has never been tested.…”