Transport in Porous Media

, Volume 92, Issue 1, pp 15–28 | Cite as

The Effect of Cracks and a Steam Cap on Hydrothermal Eruptions

Article

Abstract

The shock-tube model for a hydrothermal eruption in a geothermal reservoir (Fullard and Lynch, Trans Porous Med, 2011) is used to simulate eruptions that have a steam phase present near the surface in the form of a steam cap or a large crack. Simulations are performed with various steam cap/crack depths and it is shown that the presence of a steam phase greatly reduces the size of an eruption. We show that a steam cap type eruption is physically unlikely because of the large pressure differences required, but conclude that rock cracking is potentially a viable initiation mechanism for a hydrothermal eruption.

Keywords

Hydrothermal eruption Boiling Porous medium Shock tube Multiphase flow Steam cap Rock cracking 

List of symbols

ρ

Density (kg m−3)

u

Fluid velocity (ms−1)

P

Pressure (Pa)

s

Entropy (JK−1)

T

Temperature (K)

μ

Dynamic viscosity (Pa s)

R

Specific gas constant (J kg−1 K−1)

VI

Interface velocity (ms−1)

PI

Interface pressure (Pa)

\({\phi_{\rm v,l,a}}\)

Volume fraction of phase (vapour/steam, liquid, air)

\({\epsilon}\)

Porosity of the porous medium

k

Permeability of the porous medium

Cpm

Cohesion of porous medium (Pa m−1)

cF

Ergun coefficient

t

Time (s)

z

Vertical coordinate (m)

dp

Particle diameter (m)

Dj

Drag term (kg m−2 s−2)

Lj

Lift term (kg m−2 s−2)

δ

Solid profile constant

g

Acceleration due to gravity (m s−2)

Subscripts

f

Fluid

v

Vapour phase

l

Liquid phase

a

Air

s

Solid

0

Pertaining to time t = 0

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Andrianov N., Saurel R., Warnecke G.: A simple method for compressible multiphase mixtures and interfaces. Int. J. Numer. Methods Fluids 41, 109–131 (2003)CrossRefGoogle Scholar
  2. Bdzil J.B., Menikoff R., Son S.F., Kapila A.K., Stewart D.S.: Two-phase modeling of deflagration-to-detonation transition in granular materials: a critical examination of modeling issues. Phys. Fluids 11(2), 378–402 (1999)CrossRefGoogle Scholar
  3. Bercich, B.J.: Mathematical modelling of natural hydrothermal eruptions. Report, Department of Engineering Science, School of Engineering, University of Auckland (1992)Google Scholar
  4. Browne, P.R.L., Lawless, J.V.: Characteristics of hydrothermal eruptions, with examples from New Zealand and elsewhere. In Earth-Science Reviews, pp. 299–331. Elsevier Science B.V, Amsterdam (2001)Google Scholar
  5. Chang C.H., Liou M.S.: A robust and accurate approach to computing compressible multiphase flow: stratified flow model and AUSM+ -up scheme. J. Comp. Phys. 225, 840–873 (2007)CrossRefGoogle Scholar
  6. Chapman C.J.: High speed flow. Cambridge University Press, Cambridge (2000)Google Scholar
  7. Drew D.A.: Mathematical modeling of two-phase flow. Annu. Rev. Fluid Mech. 15, 261–291 (1983)CrossRefGoogle Scholar
  8. Fowler A. C., Bettina Scheu., Lee W. T., McGuinness M. J.: A theoretical model of the explosive fragmentation of vesicular magma. Proc. R. Soc. A 466, 731–752 (2009)CrossRefGoogle Scholar
  9. Fullard, L. A., Lynch, T. A.: On the initiation of a hydrothermal eruption using the shock-tube model. Trans. Porous Med. (2011) (in press)Google Scholar
  10. McKibbin, R.: An attempt at modelling hydrothermal eruptions. In: Proceedings of the 11th New Zealand Geothermal Workshop 1989, pp. 267–273. University of Auckland, Auckland (1989)Google Scholar
  11. McKibbin, R.: Could non-condensible gases affect hydrothermal eruptions? In: Conference proceedings: 18th New Zealand geothermal workshop, 1996. University of Auckland, Auckland (1996)Google Scholar
  12. Powers J.M.: Two-phase viscous modeling of compaction of granular materials. Phys. Fluids 16(8), 2975–2990 (2004)CrossRefGoogle Scholar
  13. Rogers G.F.C., Mayhew Y.R.: Thermodynamic and transport properties of fluids Technical report. Basil Blackwell Publisher, Oxford (1983)Google Scholar
  14. Saurel R., Abgrall R.: A multiphase Godunov method for compressible multifluid and multiphase flows. J. Comput. Phys. 150, 425–467 (1999)CrossRefGoogle Scholar
  15. Smith, T.A.: Mathematical modelling of underground flow processes in hydrothermal eruptions. PhD thesis, Massey University, Palmerston North (2000)Google Scholar
  16. Smith, T.A., McKibbin, R.: An investigation of boiling processes in hydrothermal eruptions. In: Proceedings of the 21st New Zealand Geothermal Workshop 1999, pp. 699–704. University of Auckland, Auckland (1999)Google Scholar
  17. Toro E.F.: Riemann solvers and numerical methods for fluid dynamics: a practical introduction. Springer-Verlag Telos, Santa Clara (1997)Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.Institute of Fundamental SciencesMassey UniversityPalmerston NorthNew Zealand

Personalised recommendations