# 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
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
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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Jun Wang Dr
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