Parameters in modeling explosive volcanic eruptions

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Parameters in modeling explosive volcanic
eruptions
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Primary parameters must be determined before
each eruption

• Melt composition, esp. initial H2O content
• Initial temperature
• Initial pressure (degree of saturation) and
  exsolved gas content
• Conduit geometry and wall rock property
• All other parameters should in principle be
  calculatable

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Magma properties and theories needed

• Viscosity of magma A function of T,
  composition (esp. H2O)
• Solubility of H2O (and other gases) in magma
• Diffusivity of H2O (and other gases) in magma
• Fragmentation criterion
• Bubble growth experiments
• Enthalpy of H2O exsolution from magma
• Tensile strength, surface tension, heat capacity,
  density

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Viscosity of magma

• Viscosity decreases with increasing temperature,
  non-Arrhenian lnh AB/(T-C) where C ranges
  from 0 to 700 K or lnh A(B/T)n where n ranges
  from 1 to 3
• Viscosity increases with the concentration of
  SiO2 and other network formersincreases from
  basaltic to rhyolitic melt
• Viscosity decreases with the concentration of
  network modifiers, esp. H2O
• Viscosity is also affected by the presence of
  crystals and bubbles

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Non-Arrhenian behavior of viscosity
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Viscosity of magma

• Models for hydrous rhyolitic melts Shaw
  (1972) Much improved by Hess and Dingwell (1996)
• The 2s uncertainty in viscosity of the Hess and
  Dingwell model is a factor of 8. The model
  cannot be extrapolated to dry melt.
• Zhang et al. (submitted) propose a new empirical
  relation on how h depends on H2O 1/h 1/hdry
  bXn , where X is mole frac of H2OUsing this
  formulation, Zhang et al. develop a new model.

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1/h 1/hdry bXn

• where T is in K and X is the mole fraction of
  total H2O on a single oxygen basis.
• The viscosity of hydrous high-SiO2 rhyolitic melt
  can be calculated within a factor of 2.4.

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Viscosity of hydrous rhyolitic melt
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Summary Viscosity of hydrous melts

• Hydrous rhyolite (high-SiO2 rhyolite with 76 to
  77 wt SiO2) Best known and modeled.
• Hydrous andesite Richet et al. (1996)
• Other hydrous melts of natural compositions
  Not available General model by Shaw (1972),
  not accurate

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H2O solubility and diffusivity
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Water in magmaTwo hydrous species in melt
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Solubility of H2O in magma

• Pressure Solubility of H2O increases with
  pressure but not simply proportional to pressure.
  This complexity is due to the presence of at
  least two hydrous species in melt.
• Temperature At the same pressure, solubility of
  H2O decreases slightly with increasing
  temperature, at least when the pressure is below
  2 kb.
• Composition The dry melt composition has a small
  effect.
• For volcanic eruption models, accurate H2O
  solubility at low pressure is critical since most
  expansion occurs in this stage (Blower et al.,
  2001)

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Solubility of H2O in basalt and rhyolite
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Solubility models

• Most solubility models predict H2O solubility at
  intermediate pressures (a few hundred to a few
  thousand bars) well.
• Many models fail at high pressures (e.g., 5 kb).
  Most models fail under low pressures (e.g., 1
  bar).

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Comparison of different models

• Predicted H2O Solubility at 1 bar and 850C
  Papale (1997) 0.012 wtMoore et al. (1998)
  0.071 wtYamashita (1999) 0.074Zhang (1999)
  0.099 wtBurnham (1975) 0.104 wt
• Experimental data (Liu and Zhang, 1999, Eos)
  0.10 wt
• Liu et al. obtained more data at low P and are
  working on a refined model

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Solubility of H2O in rhyolite
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• Solubility model of Zhang (1999)

where X, Xm, and XOH are mole fractions of total,
molecular and hydroxyl H2O on a single oxygen
basis, f is H2O fugacity, K1 and K2 are two
equilibrium constants and are given below lnK1
(-13.8690.0002474P) (3890.3-0.3948P)/T, K2
6.53exp(-3110/T)where T is in K and P is in
bar.
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Diffusion of H2O in magma

• Numerous studies, starting from Shaw (1973)
• Because of two hydrous species, the diffusion of
  H2O in magma differs from that of other
  components. The diffusivity of the H2O component
  depends strongly on H2O content. This is a
  practically important and yet theoretically
  interesting problem.
• Diffusion of H2O in silicate melt can be modeled
  as follows Molecular H2O is the diffusion
  species, and the diffusivity of molecular H2O
  increases exponentially with total H2O content.
  OH species is basically immobile.

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Diffusion of H2O in magma (Zhang and Behrens,
2000)

• DH2Om exp(14.08-13128/T-2.796P/T)
  (-27.2136892/T57.23P/T)X,
• DH2Ot DH2OmdXm/X,
• where T is in K, P is in MPa (not mPa), and X
  and Xm are the mole fractions of total and
  molecular H2O on a single oxygen basis
• --------------------------------------------------
  ----------------

where m -20.79 -5030/T -1.4P/T
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Diffusivity of H2O in magma
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Magma fragmentation

• Two recent models Papale (1999) Strain-rate
  based Zhang (1999) If tensile stress at bubble
  walls exceed the the tensile strength of the
  magma, there would be fragmentation

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Differences between Papale (1999) and Zhang (1999)

• 1. Papale (1999) strain-rate based Zhang
  (1999) stress basedFor Newtonian melt, stress
  and strain rate are proportional (equivalent).
  For more complicated melt, they are not. After
  years of debate, the engineering literature
  concluded that stress-based model is applicable
• 2. Papale (1999) liquid with or without bubbles
  would fragment in the same wayZhang (1999)
  bubbles play a critical role because tensile
  stress on bubble wall causes bubble explosion

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Bubble growth experiments

• Experiments by Liu and Zhang (2000) show that
  bubble growth can be modeled well with the model
  of Proussevitch and Sahagian (1998) as long as
  viscosity, diffusivity and solubility are known.

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My biased recommendations

• For H2O diffusivity in rhyolitic melt, use the
  model of Zhang and Behrens (2000)
• For H2O solubility in rhyolitic melt, use the
  model of Zhang (1999) (we will have an updated
  model soon)For basaltic melts Dixon et al.
  (1995), For other (general) melts Moore et al.
  (1998)
• For viscosity of crystal- and bubble-free hydrous
  rhyolitic melt, use the model of Zhang et al.
  (submitted)
• For magma fragmentation criterion, use the model
  of Zhang (1999)
• Papers/manuscript are available

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Our work on explosive volcanic eruptions

• Experimental simulation of conduit fluid flow
  processes
• Dynamics of lake eruptions
• Bubble growth in magma and in beer
• Modeling the fragmentation process (current)
• Experimental investigation of magma properties
  viscosity, H2O diffusivity, H2O solubility, etc.
• Developing geospeedometers to study temperature
  and cooling rate in the erupting column

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Bubble growth
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Bubbles in glass in a bubble growth experiment,
from Liu and Zhang (2000)
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Predicting bubble growth
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Beer Fizzics
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Bubble growth in Budweiser
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Bubble rise in Budweiser
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Magma fragmentation

1. Magma fragmentation defines explosive eruption
2. Before 1997, it is thought that fragmentation
   occurs at 74 vesicularity. Recent experimental
   and field studies show that vesicularity at
   fragmentation can range from 50 to 97.
3. Slowly growing lava dome or slowly advancing lava
   flows can suddenly fragment into pyroclastic
   flow.

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Unzen, Japan, 1991
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Unzen lava dome
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Unzen, 1991 34 people died of the pyroclastic
eruption
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Why did a slowly growing dome suddenly collapse
into a pyroclastic flow?

• Zhang (1999) published a first-order model based
  on brittle failure theory.

If the tensile stress on the bubble wall exceeds
the tensile strength of magma, there will be
fragmentation
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If the tensile strength of magma is 60 bar, for
the above case, when vesicularity reaches 60,
magma would fragment into a pyroclastic flow.
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If the tensile strength of magma is 60 bar, for
the above case (0.7 H2O), no fragmentation would
occur.
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More realistic modeling is needed
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Our work on explosive volcanic eruptions

• Experimental simulation of conduit fluid flow
  processes
• Dynamics of lake eruptions (current)
• Bubble growth in magma ad in beer
• Modeling the fragmentation process
• Experimental investigation of magma properties
  viscosity, H2O diffusivity, H2O solubility, etc.
• Developing geospeedometers to study temperature
  and cooling rate in the erupting column

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Our work on explosive volcanic eruptions

• Experimental simulation of conduit fluid flow
  processes
• Experimental investigation of bubble growth in
  magma
• Modeling the fragmentation process (current)
• Experimental investigation of magma properties
  viscosity, H2O diffusivity, H2O solubility, etc.
• Developing geospeedometers to study temperature
  and cooling rate in the erupting column

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Eruption column Cooling rateTemperatureDynami
cs
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Hydrous species geospeedometer

• Measure the IR band intensities of different
  dissolved H2O species in rhyolitic glass
• From the band intensities, cooling rate can be
  inferred.
• The principle of the geospeedometer reaction
  rate increases with temperature. If cooling rate
  is high, then there is a shorter time at each
  temperature, the species equilibrium would
  reflect that at high temperature. And vice
  versa.

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Why did pyroclasts cool slower than in air?

• Cooling rate depends on ambient temperature in
  the erupting column. Hence we can turn the
  geospeedometer to a thermometer.

• For cooling rate to be 1/2 of that in air, the
  ambient temperature (i.e., average temperature in
  the erupting column) can be estimated to be about
  300 C.
• Systematic investigation of different pyroclastic
  beds
• Inference of erupting column dynamics

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Some current research directions on gas-driven
eruptions

1. Experimental investigation of magma properties
   Viscosity, diffusion, etc.
2. Trigger mechanism for explosive volcanic
   eruptions, fragmentation, and conditions for
   non-explosive and explosive eruptions.
3. Dynamics of bubble plume eruptions
4. Understanding volcanic eruption columns
5. Methane-driven water eruptions

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Some other current research directions

1. Geochemical evolution of Earth, Venus, and Mars
   Atmospheric age, formation, and
   evolutionVarious ages and events of planetary
   formation
2. Kinetics related to methane hydrate in marine
   sediment (experimental and theoretical)
3. Experimental work on D/H fractionation
4. Experimental investigation of phase stability and
   kinetics under high pressure (mantle)

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From Camp and Sale
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Mount Pinatubo eruption, July 1991
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Kilauea, caldera
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Mayon Volcano, pyroclastic flow, 2001
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Phase diagram of H2O
According to the phase diagram, the pressure on
the water pipe is P-94T where T is in C and P
is in bar. For example, at -15C, P is 1400 bar,
or 1.4 ton/cm2. Usually a water pipe would
fracture at several hundred bars.
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Different types of gas-driven eruptions

• Explosive volcanic eruptions Conduit
  processes Fragmentation Erupting column
• Lake eruptions (limnic eruptions)
• Possible CH4-driven water eruptions

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Types of gas-driven eruptions

• Eruption of Champagne, beer, or soft drinks,
  especially after heating, disturbance, or
  addition of impurities as nucleation sites
• Explosive volcanic eruptions
• Lake eruptions
• Possible methane-driven water eruptions in oceans
  
• Cryovolcanism on Jovian satellites

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Types of gas-driven eruptions

• Eruption of Champagne, beer, or soft drinks,
  especially after heating, disturbance, or
  addition of impurities as nucleation sites
• Explosive volcanic eruptions
• Lake eruptions
• Possible methane-driven water eruptions in oceans
  
• Cryovolcanism on Jovian satellites

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Speculation on a possible type of gas-driven
eruption Methane-driven water eruption in
oceans (yet unknown)
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CH4 flow
Methane bubbles
Methane hydrate crystals CH4(H2O)n
Marine sediment
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Research directions
Youxue Zhang Department of Geological
Sciences University of Michigan Ann Arbor, MI
48109-1063 youxue_at_umich.edu
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Experimental petrology lab

• Ultra-high pressure (multi-anvil apparatus)
  4-20 GPa (40-200 kb, 100-600 km depth) To 2500
  C
• Intermediate pressure (piston-cylinder
  apparatus) 0.5-3.5 GPa, up to 1800C
• Hydrothermal conditions (cold-seal bombs)
  10-300 MPa, up to 900C
• One-atmosphere furnaces
• Infrared spectroscopy

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Research directions

• Gas-driven eruptions experimental and
  theoretical
• Experimental studies (including models and
  theory) Volatiles (mostly H2O) in magma
  Speciation, solubility, diffusion Reaction
  kinetics Geospeedometry (cooling rate) Magma
  viscosity High pressure phase equilibria Isotopi
  c fractionation Diffusion and kinetics
• Geochemical evolution of the earth and planets
  models Noble gases and their isotopes Earth,
  Venus, and Mars

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Gas-driven eruptions
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Distribution of volcanos on Earth Some eruptions
Santorini, Vesuvius, Tambora, Pelee
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Mayon Volcano (Philippines), beautiful cone shape
with sumit above the clouds it is erupting
currently
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Mount St. Helens, pyroclastic flow, 1980
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Mount Pinatubo eruption, July 1991, the big one
killed more than 900 people, devastated US Clark
Air Force Base
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Lake Nyos, Cameroon
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Lake Nyos (Cameroon, Africa) after the August
1986 eruption, killing 1700 people, and thousands
of cows, birds, and other animals.
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A cow killed by the August 1986 eruption of Lake
Nyos (Cameroon, Africa).
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OverviewMechanism of gas-driven eruptions

• When dissolved gas in a liquid reaches
  oversaturation, bubbles nucleate and grow (that
  is, the gas exsolves), leading to volume
  expansion, and ascent
• Liquid can be either magma, water, or other
  liquid
• Gas can be either steam, CO2, CH4 or other gas
• Types of gas-driven eruptions 1. Explosive
  volcanic eruptions2. Lake eruptions

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Overview of the eruption dynamics From Camp
and Sale
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Our work on gas-driven eruptions

• Experimental simulation of conduit fluid flow
  processes and demonstration of CO2-driven lake
  eruptions
• Dynamics of lake eruptions
• Experimental investigation of bubble growth in
  magma
• Modeling the fragmentation process
• Experimental investigation of magma properties
  viscosity, H2O diffusivity, H2O solubility, etc.
• Developing geospeedometers to study temperature
  and cooling rate in the erupting column

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Experimental simulations of gas-driven eruptions
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Experimental simulation, Exp89
Zhang et al., 1997
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Dynamics of Lake eruptions CO2 from magma at
depth percolates throught the rocks and into lake
bottom. Dissolution of CO2 increases the density
of water. Hence CO2 concentrates in lake bottom.
When saturation is reached (or if unsaturated but
disturbed), the sudden exsolution of CO2 can lead
to lake eruption. The eruption dynamics can be
modeled semi-quantitatively using the Bernoulli
equation. The erupted CO2 gas with water droplets
is denser than air, and hence would eventually
collapse down to form a density flow along
valleys, coined as ambioructic flow by Zhang
(1996), which is similar to a pyroclastic flow.
The flow would choke people and animal along its
way.
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Maximum velocity from Zhang, 1996
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Degassing Lake Nyos
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Future work more realistic bubble plume
eruption models, and the role of disequilibrium
in lake eruptions