a numerical program for steady flow through volcanic conduits

1
a numerical program for steady flow through
volcanic conduits

• Larry G. Mastin
• U.S. Geological Survey

2
Assumptions and simplifications

• Steady-state
• Vertical conduit
• 1-dimensional
• homogeneous flow
• Equilibrium degassing (distributed version)
• No heat or mass flow through conduit walls

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Main features

• User-friendly, visual interface
• Publicly-documented, open-source code
• See http//vulcan.wr.usgs.gov/Projects/Mastin
• Calculates solubility thermodynamics using
• Full MELTS equations (Ghiorso Sack, 1995) for
  melts
• Full equation of state for gas (H2O)
• Uses viscosity of bubbly melts formulation based
  on Capillary number.
• Fragmentation criterion based either on volume
  fraction gas or strain rate.

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Weaknesses of this model (and others)

• Poorly characterized rheology
• Kinetics of degassing, crystallization
• Magma-host rock interaction
• Conduit geometry
• Difficulty in comparing results with observations

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ODE for 1-D flow

• Option 1 specify conduit geometry, solve for
  pressure

Ax-sectional area rradius ffriction
factor rdensity MMach uvelocity
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ODE for 1D flow

• Option 2 Specify pressure gradient and calculate
  conduit geometry

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Friction Factor
1
f
.001
2
7
Log Re
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Viscosity

• Melt viscosity
• SiO2gt70 wt Hess Dingwell (1996)
• SiO2lt70 wt Shaw (1972)
• Effect of Crystals
• lt40 Roscoe-Einstein (Marsh calibration)

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Viscosity (contd)

• Effect of bubbles

-1ltnlt1
Depending on Capillary number
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Relationship between n and Ca
n
Log10(Ca)
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Calculating Capillary number

• gSurface tension0.34 N/m
• ravg. bubble radius (3vg/(4pNvm))1/3 , where
• Vg, vm are volume fractions gas and melt,
  respectively
• Nnuclei per unit volume log(N) 0.2wtSiO2
• eavg. shear-strain rate4u/3D under laminar flow

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Demo of the program
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Ongoing future work

• Kinetics of magma degassing (with M. Mangan)
• Calculating bubble-size distributions
• Improved fragmentation criterion
• Improved rheology of bubbly magmas
• Elastic coupling of fluid host rock
• 2-D, transient flow (with R. Denlinger)
• Etc. etc.

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Kinetics of magma degassing

• In collaboration with Margaret Mangan, Tom Sisson

Data from Mangan Sisson (2001)
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SampleResults

• Depend significantly on fragmentation criterion
  (vg.75 or strain-rate)