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Reaction-infiltration instability in a compacting porous medium

Published online by Cambridge University Press:  02 August 2018

David W. Rees Jones Open the ORCID record for David W. Rees Jones [Opens in a new window]  and
Richard F. Katz Open the ORCID record for Richard F. Katz [Opens in a new window]
David W. Rees Jones*
Affiliation:
Department of Earth Sciences, University of Oxford, South Parks Road, Oxford OX1 3AN, UK
Richard F. Katz
Affiliation:
Department of Earth Sciences, University of Oxford, South Parks Road, Oxford OX1 3AN, UK
*
†Email address for correspondence: [email protected]
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Abstract

Certain geological features have been interpreted as evidence of channelized magma flow in the mantle, which is a compacting porous medium. Aharonov et al. (J. Geophys. Res., vol. 100 (B10), 1995, pp. 20433–20450) developed a simple model of reactive porous flow and numerically analysed its instability to channels. The instability relies on magma advection against a chemical solubility gradient and the porosity-dependent permeability of the porous host rock. We extend the previous analysis by systematically mapping out the parameter space. Crucially, we augment numerical solutions with asymptotic analysis to better understand the physical controls on the instability. We derive scalings for the critical conditions of the instability and analyse the associated bifurcation structure. We also determine scalings for the wavelengths and growth rates of the channel structures that emerge. We obtain quantitative theories for and a physical understanding of, first, how advection or diffusion over the reactive time scale sets the horizontal length scale of channels and, second, the role of viscous compaction of the host rock, which also affects the vertical extent of channelized flow. These scalings allow us to derive estimates of the dimensions of emergent channels that are consistent with the geologic record.

JFM classification

Geophysical and Geological Flows: Geophysical and Geological Flows Low-Reynolds-number flows: Porous media Multiphase and Particle-laden Flows: Reacting multiphase flow
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 852 , 10 October 2018 , pp. 5 - 36
Copyright
© 2018 Cambridge University Press 

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References

Aharonov, E., Whitehead, J. A., Kelemen, P. B. & Spiegelman, M. 1995 Channeling instability of upwelling melt in the mantle. J. Geophys. Res. 100 (B10), 20433–20450.Google Scholar
Asimow, P. D., Hirschmann, M. M. & Stolper, E. M. 1997 An analysis of variations in isentropic melt productivity. Phil. Trans. R. Soc. Lond. A 355, 255–281.Google Scholar
von Bargen, N. & Waff, H. S. 1986 Permeabilities, interfacial-areas and curvatures of partially molten systems – results of numerical computation of equilibrium microstructures. J. Geophys. Res. 91, 9261–9276.Google Scholar
Braun, M. G. & Kelemen, P. B. 2002 Dunite distribution in the Oman ophiolite: implications for melt flux through porous dunite conduits. Geochem. Geophys. Geosyst. 3 (11), 8603.Google Scholar
Elthon, D. & Scarfe, C. M. 1984 High-pressure phase equilibria of a high-magnesia basalt and the genesis of primary oceanic basalts. Am. Mineral. 69 (1), 1–15.Google Scholar
Hesse, M. A., Schiemenz, A. R., Liang, Y. & Parmentier, E. M. 2011 Compaction–dissolution waves in an upwelling mantle column. Geophys. J. Intl 187 (3), 1057–1075.Google Scholar
Hewitt, I. J. 2010 Modelling melting rates in upwelling mantle. Earth Planet. Sci. Lett. 300, 264–274.Google Scholar
Hinch, E. J. & Bhatt, B. S. 1990 Stability of an acid front moving through porous rock. J. Fluid Mech. 212, 279–288.Google Scholar
Hoefner, M. L. & Fogler, H. S. 1988 Pore evolution and channel formation during flow and reaction in porous media. AIChE J. 34 (1), 45–54.Google Scholar
Holtzman, B. K., Groebner, N. J., Zimmerman, M. E., Ginsberg, S. B. & Kohlstedt, D. L. 2003 Stress-driven melt segregation in partially molten rocks. Geochem. Geophys. Geosyst. 4, 8607.Google Scholar
Katz, R. F. & Weatherley, S. M. 2012 Consequences of mantle heterogeneity for melt extraction at mid-ocean ridges. Earth Planet. Sci. Lett. 335–336, 226–237.Google Scholar
Kelemen, P. B. 1990 Reaction between ultramafic rock and fractionating basaltic magma I. Phase relations, the origin of calc-alkaline magma series, and the formation of discordant dunite. J. Petrol. 31 (1), 51–98.Google Scholar
Kelemen, P. B., Braun, M. & Hirth, G. 2000 Spatial distribution of melt conduits in the mantle beneath oceanic spreading ridges: observations from the Ingalls and Oman ophiolites. Geochem. Geophys. Geosyst. 1, 1005.Google Scholar
Kelemen, P. B., Dick, H. J. B. & Quick, J. E. 1992 Formation of hartzburgite by pervasive melt rock reaction in the upper mantle. Nature 358 (6388), 635–641.Google Scholar
Kelemen, P. B., Shimizu, N. & Salters, V. J. M. 1995a Extraction of mid-ocean-ridge basalt from the upwelling mantle by focused flow of melt in dunite channels. Nature 375 (6534), 747–753.Google Scholar
Kelemen, P. B., Whitehead, J. A., Aharonov, E. & Jordahl, K. A. 1995b Experiments on flow focusing in soluble porous-media, with applications to melt extraction from the mantle. J. Geophys. Res. 100, 475–496.Google Scholar
Keller, T. & Katz, R. F. 2016 The role of volatiles in reactive melt transport in the asthenosphere. J. Petrol. 57 (6), 1073–1108.Google Scholar
Liang, Y., Schiemenz, A., Hesse, M. A., Parmentier, E. M. & Hesthaven, J. S. 2010 High-porosity channels for melt migration in the mantle: top is the dunite and bottom is the harzburgite and lherzolite. Geophys. Res. Lett. 37, L15306.Google Scholar
Longhi, J. 2002 Some phase equilibrium systematics of lherzolite melting: I. Geochem. Geophys. Geosyst. 3 (3), 1–33.Google Scholar
McKenzie, D. 1984 The generation and compaction of partially molten rock. J. Petrol. 25 (3), 713–765.Google Scholar
Miller, K. J., Zhu, W., Montési, L. G. J. & Gaetani, G. A. 2014 Experimental quantification of permeability of partially molten mantle rock. Earth Planet. Sci. Lett. 388, 273–282.Google Scholar
O’Hara, M. J. 1965 Primary magmas and the origin of basalts. Scott. J. Geol. 1 (1), 19–40.Google Scholar
Ortoleva, P. J. 1994 Geochemical Self-organization. Oxford University Press.Google Scholar
Pec, M., Holtzman, B. K., Zimmerman, M. E. & Kohlstedt, D. L. 2015 Reaction infiltration instabilities in experiments on partially molten mantle rocks. Geology 43 (7), 575–578.Google Scholar
Pec, M., Holtzman, B. K., Zimmerman, M. E. & Kohlstedt, D. L. 2017 Reaction infiltration instabilities in mantle rocks: an experimental investigation. J. Petrol. 58 (5), 979–1003.Google Scholar
Quick, J. E. 1982 The origin and significance of large, tabular dunite bodies in the Trinity peridotite, northern California. Contrib. Mineral. Petrol. 78 (4), 413–422.Google Scholar
Ramberg, H. 1972 Mantle diapirism and its tectonic and magmagenetic consequences. Phys. Earth Planet. Inter. 5, 45–60.Google Scholar
Rees Jones, D. W., Katz, R. F., Tian, M. & Rudge, J. F. 2018 Thermal impact of magmatism in subduction zones. Earth Planet. Sci. Lett. 481, 73–79.Google Scholar
Rudge, J. F.2017 Microscale models of partially molten rocks and their macroscale physical properties. Presented at Fall Meeting, AGU 2017 (DI51B-0314).Google Scholar
Rudge, J. F. 2018 Textural equilibrium melt geometries around tetrakaidecahedral grains. Proc. R. Soc. Lond. A 474, 20170639.Google Scholar
Schiemenz, A., Liang, Y. & Parmentier, E. M. 2011 A high-order numerical study of reactive dissolution in an upwelling heterogeneous mantle – I. Channelization, channel lithology and channel geometry. Geophys. J. Intl 186 (2), 641–664.Google Scholar
Sleep, N. H. 1988 Tapping of melt by veins and dikes. J. Geophys. Res. 93 (B9), 10255–10272.Google Scholar
Spiegelman, M. 1993 Flow in deformable porous-media. Part 1. Simple analysis. J. Fluid Mech. 247, 17–38.Google Scholar
Spiegelman, M. & Kelemen, P. B. 2003 Extreme chemical variability as a consequence of channelized melt transport. Geochem. Geophys. Geosyst. 4 (7), 1055.Google Scholar
Spiegelman, M., Kelemen, P. B. & Aharonov, E. 2001 Causes and consequences of flow organization during melt transport: the reaction infiltration instability in compactible media. J. Geophys. Res. 106 (B2), 2061–2077.Google Scholar
Stevenson, D. J. 1989 Spontaneous small-scale melt segregation in partial melts undergoing deformation. Geophys. Res. Lett. 16 (9), 1067–1070.Google Scholar
Stolper, E. 1980 A phase diagram for mid-ocean ridge basalts: preliminary results and implications for petrogenesis. Contrib. Mineral. Petrol. 74 (1), 13–27.Google Scholar
Szymczak, P. & Ladd, A. J. C. 2012 Reactive-infiltration instabilities in rocks. Fracture dissolution. J. Fluid Mech. 702, 239–264.Google Scholar
Szymczak, P. & Ladd, A. J. C. 2013 Interacting length scales in the reactive-infiltration instability. Geophys. Res. Lett. 40 (12), 3036–3041.Google Scholar
Szymczak, P. & Ladd, A. J. C. 2014 Reactive-infiltration instabilities in rocks. Part 2. Dissolution of a porous matrix. J. Fluid Mech. 738, 591–630.Google Scholar
Weatherley, S. M. & Katz, R. F. 2012 Melting and channelized magmatic flow in chemically heterogeneous, upwelling mantle. Geochem. Geophys. Geosyst. 13, Q0AC18.Google Scholar