Transport in Porous Media

, Volume 94, Issue 1, pp 19–46 | Cite as

On the Initiation of a Hydrothermal Eruption Using the Shock-Tube Model

Article

Abstract

In this work, the authors introduce the shock-tube model for a hydrothermal eruption in a geothermal reservoir. The governing equations, based on the multiphase Euler equations and a Darcy-type law, are solved using a three-phase weighted sub-system numerical solver. Results are then presented which show the importance of the geometry of the geothermal reservoir in predicting the initiation of a hydrothermal eruption. In particular, the porosity, permeability, and cohesion of the reservoir are shown to significantly affect the pressure difference required to initiate an eruption. Finally, the authors show the importance of the initial liquid water/water vapour volume fractions in determining the size of an eruption, and further show boiling to be of major importance.

Keywords

Hydrothermal eruption Porous medium Boiling Euler equations Shock-tube 

List of Symbols

ρ

Density (kg/m3)

u

Fluid velocity (m/s)

P

Pressure (Pa)

s

Entropy (J/K)

e

Internal energy (J)

T

Temperature (K)

μ

Dynamic viscosity (Pa s)

R

Specific gas constant (J/kg/K)

VI

Interface velocity (m/s)

PI

Interface pressure (Pa)

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

Volume fraction of phase of water

χa,w

Volume fraction of fluid

\({\epsilon}\)

Porosity of the porous medium

k

Permeability of the porous medium

Cpm

Cohesion of porous medium (Pa/m)

cF

Ergun coefficient

ν

Specific volume (m3/kg)

t

Time (s)

z

Vertical coordinate (m)

dp

Particle diameter (m)

g

Acceleration due to gravity (m/s2)

ω

Interaction weight

Ω

Border length

S

Wave speed (m/s)

U

Vector of conserved variables

F

Vector of fluxes

Subscripts

f

Fluid

v

Vapour phase

l

Liquid phase

a

Air

w

Water

s

Solid

0

Pertaining to time t = 0

F

Flashing front

E

Eruption jet

*

Middle

L

Left

R

Right

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Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  1. 1.Institute of Fundamental SciencesMassey UniversityPalmerston NorthNew Zealand

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