Parameters in modeling explosive volcanic eruptions - PowerPoint

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					Parameters in modeling explosive
      volcanic eruptions
   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
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
            Viscosity of magma
• Viscosity decreases with increasing temperature, non-
  Arrhenian:
      lnh = A+B/(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 formers
  increases 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
Non-Arrhenian behavior of viscosity
            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 H2O
  Using this formulation, Zhang et al. develop a new
  model.
      1/h = 1/hdry + bXn
log h   log{exp(18.561 49584 / T) 
                                                    2
                             2.1969 1(1829 / T )
 exp[1.0389  (1518/ 8 / T )       X                    }

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.
Viscosity of hydrous rhyolitic melt
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
H2O solubility and diffusivity
                  Water in magma
             Two hydrous species in melt
             1.92


             1.78

                                     H 2Om                 OH
Absorbance




             1.64


             1.50


             1.36


             1.22


             1.08


             0.94
                6000   5750   5500   5250    5000   4750   4500   4250   4000   3750
                                       W avenumbers
     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)
Solubility of H2O in basalt and rhyolite
           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).
 Comparison of different models
Predicted H2O Solubility at 1 bar and 850°C:
  Papale (1997): 0.012 wt%
  Moore et al. (1998): 0.071 wt%
  Yamashita (1999): 0.074%
  Zhang (1999): 0.099 wt%
  Burnham (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
Solubility of H2O in rhyolite
 Solubility model of Zhang (1999)
           X  Xm  0.5XOH
                           K1K 2 f (1  K1 f )
  X  K1 f 
               K1K2 f  (K1K2 f )2  4K1K2 f (1  K1 f )

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 = (-13.869+0.0002474P) + (3890.3-0.3948P)/T,
 K2 = 6.53exp(-3110/T)
 where T is in K and P is in bar.
      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.
            Diffusion of H2O in magma
            (Zhang and Behrens, 2000)
DH2Om = exp[(14.08-13128/T-2.796P/T)
 + (-27.21+36892/T+57.23P/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
------------------------------------------------------------------
                                      44620 57.3P
 DH 2 Ot  X exp(m){1  exp[X(34.1             )
                                         T    T
                             4.77  106
        56  m  X(0.091        2     )]}
                                T
  where m = -20.79 -5030/T -1.4P/T
Diffusivity of H2O in magma
        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
    Differences between Papale
     (1999) and Zhang (1999)
1. Papale (1999): strain-rate based
   Zhang (1999): stress based
  For 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 way
  Zhang (1999): bubbles play a critical role because
  tensile stress on bubble wall causes bubble
  explosion
   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.
      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
 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
Bubble growth
Bubbles in glass in a bubble growth experiment,
from Liu and Zhang (2000)
Predicting bubble growth
Beer Fizzics
Bubble growth in Budweiser
Bubble rise in Budweiser
       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.
Unzen, Japan,
1991
Unzen lava dome
Unzen, 1991: 34 people died of the pyroclastic eruption
    Why did a slowly growing dome suddenly
       collapse into a pyroclastic flow?
    Zhang (1999) published a first-order model based on
     brittle failure theory.                            Pout
                                       B         R1
                                                     Pin
                    1 bar         1 bar                         R2
A
              Pin
                            Pin
                                          Pin   If the tensile stress
                                                on the bubble wall
                                                exceeds the tensile
                                                strength of magma,
                                  Film          there will be
        Plateau border                          fragmentation
If the tensile strength of magma is 60 bar, for the above
case, when vesicularity reaches 60%, magma would
fragment into a pyroclastic flow.
If the tensile strength of magma is 60 bar, for the above
case (0.7% H2O), no fragmentation would occur.
More realistic modeling is needed
                  1 bar         1 bar
 A
            Pin                         Pin
                          Pin




                                Film
      Plateau border


                                   Pout
      B                 R1
                  Pin
                                   R2
 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
 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
Eruption column:

   Cooling rate
   Temperature
    Dynamics
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.
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.

                  (T  Tambient )
               q
                     hCp L
• 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
  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
     Some other current research
             directions
1. Geochemical evolution of Earth, Venus, and
   Mars:
   Atmospheric age, formation, and evolution
   Various 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)
                                   From
                                   Camp
                                   and Sale


       QuickTime™ and a
Sore nson Video decompressor
are need ed to see this picture.
Mount Pinatubo
eruption, July 1991
Kilauea, caldera
Mayon Volcano, pyroclastic
flow, 2001
                                            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 -15°C, P is 1400 bar, or 1.4 ton/cm2.
Usually a water pipe would fracture at several hundred
   Different types of gas-driven
             eruptions
• Explosive volcanic eruptions
    Conduit processes
    Fragmentation
    Erupting column
• Lake eruptions (limnic eruptions)
• Possible CH4-driven water eruptions
   Types of gas-driven eruptions
• Eruption of Champagne,
  beer, or soft drinks,
  especially after heating,                    Fragmen-
                                               tation
  disturbance, or addition of      High-P
  impurities as nucleation sites
• Explosive volcanic eruptions     Liq with
                                   dissolved
• Lake eruptions                   gas


• Possible methane-driven
  water eruptions in oceans
• Cryovolcanism on Jovian
  satellites
    Types of gas-driven eruptions
• Eruption of Champagne, beer, or
  soft drinks, especially after
  heating, disturbance, or addition of               Fragmen-
  impurities as nucleation sites                     tation
                                         High-P
• Explosive volcanic eruptions
• Lake eruptions
                                         Liq with
• Possible methane-driven                dissolved
                                         gas
  water eruptions in oceans
• Cryovolcanism on Jovian
  satellites
Speculation on a possible type of
      gas-driven eruption

Methane-driven water eruption in
    oceans (yet unknown)
                                                                                CH4 flow

                                  bubbly water rises, eruption                  Methane
                                  methane hydrate dissociates into gas
                                                                                bubbles


                                                                                Methane
                                    methane hydrate rises                       hydrate crystals
                                                                                CH4(H2O)n



seafloor   re le ase d CH4
                             ga s rea cts wit
                                              h   s eaw ater to fo
                                                                  rm hy drate

                                                                                Marine sediment
Research directions


         Youxue Zhang
Department of Geological Sciences
     University of Michigan
   Ann Arbor, MI 48109-1063
      youxue@umich.edu
     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 1800°C
• Hydrothermal conditions (cold-seal bombs)
   10-300 MPa, up to 900°C
• One-atmosphere furnaces
• Infrared spectroscopy
             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
     Isotopic fractionation
     Diffusion and kinetics
• Geochemical evolution of the earth and planets: models
     Noble gases and their isotopes
     Earth, Venus, and Mars
Gas-driven eruptions
      Distribution of volcanos on Earth
Some eruptions: Santorini, Vesuvius, Tambora, Pelee
Mayon Volcano (Philippines), beautiful cone shape with
sumit above the clouds; it is erupting currently
Mount St. Helens,
pyroclastic flow,
1980
Mount Pinatubo eruption, July 1991, the big one: killed more than
900 people, devastated US Clark Air Force Base
Lake Nyos, Cameroon
Lake Nyos (Cameroon, Africa) after the August 1986 eruption,
killing 1700 people, and thousands of cows, birds, and other
animals.
A cow killed by the August
1986 eruption of Lake Nyos
(Cameroon, Africa).
            Overview
  Mechanism 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                         Fragmen-
• Liquid can be either magma, water, or                   tation
  other liquid                                High-P

• Gas can be either steam, CO2, CH4 or
  other gas
                                              Liq with
• Types of gas-driven eruptions:              dissolved
  1. Explosive volcanic eruptions             gas

  2. Lake eruptions
                                   Overview
                                     of the
                                    eruption
                                   dynamics
       QuickTime™ and a
Sore nson Video decompressor
are need ed to see this picture.
                                     From
                                    Camp
                                   and Sale
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
Experimental simulations of gas-driven
              eruptions


Low-Pressure Tank    Diaphragm
                     Cutter



   Diaphragm
      Test Cell
Experimental simulation, Exp#89
                                     Zhang et
                                     al., 1997



         QuickTime™ and a
  Sore nson Video decompressor
  are neede d to see this picture.
      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.
        100


                              Saturation depth = 208 m
            80


            60
  u (m/s)



            40


            20
                     A
            0
                 0       50         100       150        200
                                Depth (m)

Maximum velocity; from Zhang, 1996
Degassing
Lake Nyos
Future work: more realistic bubble plume eruption
models, and the role of disequilibrium in lake eruptions

				
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