Permeability of polydisperse magma foam

Jérémie Vasseur,Donald B Dingwell,Fabian B Wadsworth

doi:10.1130/g47094.1

Jérémie Vasseur, Donald B Dingwell + Show 1 more

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https://doi.org/10.1130/g47094.1

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Abstract

AbstractEffective 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.

Highlights

Permeability can exert a first-order control on the explosive potential of magmas rising through the crust (e.g., Mueller et al, 2008; Degruyter et al, 2012; Cassidy et al, 2018)
No theoretical treatment of permeability exists for polydisperse bubble sizes that is valid from the lower limit of the percolation threshold to the upper limit of foam at high porosity
We use a combination of collated published experimental data and novel numerical simulation results to test and validate a scaling for permeability that fully accounts for polydisperse bubble sizes

Summary

INTRODUCTION

Permeability can exert a first-order control on the explosive potential of magmas rising through the crust (e.g., Mueller et al, 2008; Degruyter et al, 2012; Cassidy et al, 2018). Collations of measured vesicle size distributions in erupted pyroclasts of pumice or scoria, and conversion of them to S via Equation 1, demonstrate that for all natural volcanic products, the vesicle sizes are highly polydisperse (Fig. 1) Despite this fact, no theoretical treatment of permeability exists for polydisperse bubble sizes that is valid from the lower limit of the percolation threshold (i.e., the point at which a cluster of bubbles first spans the system edge to edge) to the upper limit of foam at high porosity. No theoretical treatment of permeability exists for polydisperse bubble sizes that is valid from the lower limit of the percolation threshold (i.e., the point at which a cluster of bubbles first spans the system edge to edge) to the upper limit of foam at high porosity In this contribution, we use a combination of collated published experimental data and novel numerical simulation results to test and validate a scaling for permeability that fully accounts for polydisperse bubble sizes. We focus on the prograde path of bubble growth, in which the porosity is an increasing function of time

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CONCLUSIONS