Hostname: page-component-7479d7b7d-68ccn Total loading time: 0 Render date: 2024-07-11T06:30:26.799Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Blower, J. 2001 Factors controlling permeability-porosity relationships in magma. Bull. Volcanol. 63 (7), 497–504.Google Scholar
Boudon, G., Balcone-Boissard, H., Villemant, B. & Morgan, D. J. 2015 What factors control superficial lava dome explosivity? Nature Sci. Rep. 5 (14551).Google Scholar
Costa, A., Melnik, O., Sparks, R. & Voight, B. 2007 Control of magma flow in dykes on cyclic lava dome extrusion. Geophys. Res. Lett. 34, L02303.10.1029/2006GL027466Google Scholar
Delgado-Granados, H., Cardenas-Gonzalez, L. & Piedad-Sanchez, N. 2001 Sulfur dioxide emissions from Popocatepetl Volcano (Mexico); case study of a high-emission rate, passively degassing erupting volcano. J. Volcanol. Geotherm. Res. 108 (1–4), 107–120.10.1016/S0377-0273(00)00280-8Google Scholar
Girona, T., Costa, F., Taisne, B., Aggangan, B. & Ildefonso, S. 2015 Fractal Degassing from Erebus and Mayon volcanoes revealed by a new method to monitor H20 emission cycles. J. Geophys. Res. 120, 2988–3002.10.1002/2014JB011797Google Scholar
Gómez-Vazquez, A., De la Cruz-Reyna, S. & Mendoza-Rosas, A. T. 2016 The ongoing dome emplacement and destruction cyclic process at Popocatépetl volcano, Central Mexico. Bull. Volcanol. 78 (9), 1–15.10.1007/s00445-016-1054-zGoogle Scholar
Holland, A. S. P., Watson, I. M., Phillips, J. C., Caricchi, L. & Dalton, M. P. 2011 Degassing processes during lava dome growth: insights from Santiaguito lava dome, Guatemala. J. Volcanol. Geotherm. Res. 202 (1), 153–166.10.1016/j.jvolgeores.2011.02.004Google Scholar
Huyakorn, P. S. & Pinder, G. F. 1983 Computational Methods in Subsurface Flow. Academic Press.Google Scholar
Hyman, D. M., Bursik, M. I. & Legorreta Paulin, G. 2018 Time dependence of passive degassing at Volcán Popocatépetl, Mexico, from infrared measurements: implications for gas pressure distribution and lava dome stability. J. Geophys. Res. 123, 8527–8547.10.1029/2018JB015674Google Scholar
Jellinek, A. M. & Bercovici, D. 2011 Seismic tremors and magma wagging during explosive volcanism. Nature 470 (7335), 522–526.10.1038/nature09828Google Scholar
Kozono, T. & Koyaguchi, T. 2010 A simple formula for calculating porosity of magma in volcanic conduits during dome-forming eruptions. Earth Planets Space 62 (5), 483–488.10.5047/eps.2010.02.005Google Scholar
Lowman, N. K. & Hoefer, M. A. 2013 Dispersive shock waves in viscously deformable media. J. Fluid Mech. 718, 524–557.10.1017/jfm.2012.628Google Scholar
Manga, M. 1996 Waves of bubbles in basaltic magmas and lavas. J. Geophys. Res. 101 (B8), 17457–17465.10.1029/96JB01504Google Scholar
McKenzie, D. 1984 The generation and compaction of partially molten rock. J. Petrol. 25, 713–765.10.1093/petrology/25.3.713Google Scholar
Melnik, O. & Sparks, S. J. 1999 Nonlinear dynamics of lava dome extrusion. Nature 402 (6757), 37–41.10.1038/46950Google Scholar
Michaut, C., Ricard, Y., Bercovici, D. & Sparks, R. J. 2013 Eruption cyclicity at silicic volcanoes potentially caused by magmatic gas waves. Nature Geosci. 6 (10), 856–860.10.1038/ngeo1928Google Scholar
Mueller, S., Melnik, O., Spieler, O., Scheu, B. & Dingwell, D. B. 2005 Permeability and degassing of dome lavas undergoing rapid decompression: an experimental determination. Bull. Volcanol. 67, 526–538.10.1007/s00445-004-0392-4Google Scholar
Scott, D. R. & Stevenson, D. J. 1984 Magma solitons. Geophys. Res. Lett. 11, 1161–1164.10.1029/GL011i011p01161Google Scholar
Scott, D. R. & Stevenson, D. J. 1986 Magma ascent by porous flow. J. Geophys. Res. 91 (B9), 9283–9296.10.1029/JB091iB09p09283Google Scholar
Sheldrake, T. E., Sparks, R. S. J., Cashman, K. V., Wadge, G. & Aspinall, W. P. 2016 Similarities and differences in the historical records of lava dome-building volcanoes: implications for understanding magmatic processes and eruption forecasting. Earth-Sci. Rev. 160, 240–263.10.1016/j.earscirev.2016.07.013Google Scholar
Sparks, R. S. J. 1978 The dynamics of bubble formation and growth in magmas: a review and analysis. J. Volcanol. Geotherm. Res. 28, 257–274.10.1016/0377-0273(86)90026-0Google Scholar
Sparks, R. S. J., Barclay, J., Jaupart, C., Mader, H. M. & Phillips, J. C. 1994 Physical aspects of magma degassing: I. Experimental and theoretical constraints on vesiculation. Rev. Miner. 30, 414–445.Google Scholar
Spiegelman, M. 1993a Flow in deformable porous media. I. Simple analysis. J. Fluid Mech. 247 (17–38).10.1017/S0022112093000369Google Scholar
Spiegelman, M. 1993b Flow in deformable porous media. 2. Numerical analysis-the relationship between shock waves and solitary waves. J. Fluid Mech. 247 (39–63).10.1017/S0022112093000370Google Scholar
Spieler, O., Kennedy, B., Kueppers, U., Dingwell, D. B., Scheu, B. & Taddeucci, J. 2004 The fragmentation threshold of pyroclastic rocks. Earth Planet Sci. Lett. 226 (1), 139–148.10.1016/j.epsl.2004.07.016Google Scholar
Sweeney, D., Kyle, P. R. & Oppenheimer, C. 2008 Sulfur dioxide emissions and degassing behaviour of Erebus volcano, Antarctica. J. Volcanol. Geotherm. Res. 177 (3), 725–733.10.1016/j.jvolgeores.2008.01.024Google Scholar
Tamburello, G., Aiuppa, A., McGonigle, A. J. S., Allard, P., Cannata, A., Giudice, G., Kantzas, E. P. & Pering, T. D. 2013 Periodic volcanic degassing behaviour: the Mount Etna example. Geophys. Res. Lett. 40 (18), 4818–4822.10.1002/grl.50924Google Scholar
Vasseur, J. & Wadsworth, F. B. 2017 Sphere models for pore geometry and fluid permeability in heterogeneous magmas. Bull. Volcanol. 79 (11), 1–15.10.1007/s00445-017-1165-1Google Scholar
Vazquez, J. L. 2007 The Porous Medium Equation: Mathematical Theory. Clarendon Press.Google Scholar
Whitaker, S. 1999 The Method of Volume Averaging. Springer.10.1007/978-94-017-3389-2Google Scholar
Yarushina, V. M., Bercovici, D. & Michaut, C. 2015 Two-phase dynamics of volcanic eruptions: particle size distribution and the conditions for choking. J. Geophys. Res. Solid Earth 120, 1503–1522.10.1002/2014JB011195Google Scholar
Yokoyama, I. 2005 Growth rates of lava domes with respect to viscosity of magmas. Ann. Geophys. 48 (6), 957–971.Google Scholar