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Pressure-driven gas flow in viscously deformable porous media: application to lava domes

Published online by Cambridge University Press:  18 April 2019

David M. Hyman Open the ORCID record for David M. Hyman [Opens in a new window] ,
M. I. Bursik  and
E. B. Pitman
David M. Hyman*
Affiliation:
Cooperative Institute for Meteorological Satellite Studies (CIMSS), University of Wisconsin - Madison, WI, USA Department of Geology, University at Buffalo, Buffalo, NY, USA
M. I. Bursik
Affiliation:
Department of Geology, University at Buffalo, Buffalo, NY, USA
E. B. Pitman
Affiliation:
Department of Materials Design and Innovation, University at Buffalo, Buffalo, NY, USA
*
†Email address for correspondence: davidhym@buffalo.edu
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Abstract

The behaviour of low-viscosity, pressure-driven compressible pore fluid flows in viscously deformable porous media is studied here with specific application to gas flow in lava domes. The combined flow of gas and lava is shown to be governed by a two-equation set of nonlinear mixed hyperbolic–parabolic type partial differential equations describing the evolution of gas pore pressure and lava porosity. Steady state solution of this system is achieved when the gas pore pressure is magmastatic and the porosity profile accommodates the magmastatic pressure condition by increased compaction of the medium with depth. A one-dimensional (vertical) numerical linear stability analysis (LSA) is presented here. As a consequence of the pore-fluid compressibility and the presence of gravitation compaction, the gradients present in the steady-state solution cause variable coefficients in the linearized equations which generate instability in the LSA despite the diffusion-like and dissipative terms in the original system. The onset of this instability is shown to be strongly controlled by the thickness of the flow and the maximum porosity, itself a function of the mass flow rate of gas. Numerical solutions of the fully nonlinear system are also presented and exhibit nonlinear wave propagation features such as shock formation. As applied to gas flow within lava domes, the details of this dynamics help explain observations of cyclic lava dome extrusion and explosion episodes. Because the instability is stronger in thicker flows, the continued extrusion and thickening of a lava dome constitutes an increasing likelihood of instability onset, pressure wave growth and ultimately explosion.

JFM classification

Geophysical and Geological Flows: Magma and lava flow Low-Reynolds-number flows: Porous media
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 869 , 25 June 2019 , pp. 85 - 109
Copyright
© 2019 Cambridge University Press 

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