Parameters in modeling explosive volcanic eruptions

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:

ln = A+B/(T-C) where C ranges from 0 to 700 K or ln = 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

Non-Arrhenian behavior of viscosity

-2

0

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12

14

0.4 0.5 0.6 0.7 0.8 0.9 1

LGB (6 ppm H2O)AOQ (0.025 wt% H2O)HPG8 (0.018 wt% H2O)Anorthite

log (

)in Pa·s

1000/T

Viscosity of magma

• Models for hydrous rhyolitic melts: Shaw (1972)Much improved by Hess and Dingwell (1996)

• The 2 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 depends on H2O:

1/ = 1/dry + bXn , where X is mole frac of H2OUsing this formulation, Zhang et al. develop a new model.

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.

logη=−log{exp(18.561−49584/T)+

exp[1.0389−(1518/8/T)2.1969X1+(1829/T)2}

1/ = 1/dry + bXn

Viscosity of hydrous rhyolitic melt

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10

12

14

16

0.0001 0.001 0.01 0.1 1 10

AOQShaw 1963Stevenson et al. 1995Neuville et al. 1993Zhang et al. 1997, 2000Liu and Zhang 2000HPG8Fit

log (

)in Pa·s

H2Ot ( %)wt

773-1173 Using data of K

973 K

B&H D

2

4

6

8

10

12

14

16

2 4 6 8 10 12 14 16

AOQ & rhyoliteShaw 1963HPG8

Calculated log

(

)in Pa·s

Measured log ( )in Pa·s

This work A

2

4

6

8

10

12

14

16

2 4 6 8 10 12 14 16

AOQ & rhyoliteShaw 1963HPG8

Calculated log

(

)in Pa·s

Measured log ( )in Pa·s

B Hess and

Dingwell

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 availableGeneral model by Shaw (1972), not accurate

H2O solubility and diffusivity

Water in magmaTwo hydrous species in melt1.92

1.78

1.64

1.50

1.36

1.22

1.08

0.94

6000 5750 5500 5250 5000 4750 4500 4250 4000 3750

Wavenumbers

Absorbance

OHH 2 O m

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

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0 1000 2000 3000 4000 5000

Basalt (Dixon et al., 1995)Rhyolite

Total H

2

O solubility (wt%)

P (bar)

1200 °C

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

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0 1000 2000 3000 4000 5000

500 °C

600 °C

700 °C

800 °C

900 °C

1000 °C

H

2

O

t

solubility (wt%)

PH2O

(bars)

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 = (-13.869+0.0002474P) + (3890.3-0.3948P)/T, K2 = 6.53exp(-3110/T)where T is in K and P is in bar.

X =K1f +K1K2f(1−K1f)

K1K2 f + (K1K2 f)2 +4K1K2 f(1−K1f)

X =Xm+0.5XOH

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

------------------------------------------------------------------

DH2Ot=Xexp(m){1+exp[X(−34.1+

44620T

+57.3PT

)

+56+m− X(0.091+4.77×106

T2 )]}

where m = -20.79 -5030/T -1.4P/T

Diffusivity of H2O in magma

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0 1 2 3 4 5 6 7 8

ln(DH2Ot/X)

H2Ot (wt%)

400°C

500°C

600°C

800°C

1000°C

P = 500 MPa

1200°C

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 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

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 recommendationsFor 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

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0 500 1000 1500 2000 2500 3000 3500

Bubble radius (µm)

Time (seconds)

2B-2C-5 (2.03wt% H2Ot) at 575°C

Viscosity reduced by a factor of 2.2

Beer Fizzics

Bubble growth in Budweiser

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0.25

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0.35

0.4

0 0.5 1 1.5 2 2.5 3 3.5 4

Shafer and Zare, 1991

Calculated

Radius (mm)

Time (s)

P=1.51 bar; T=4°C

Bubble rise in Budweiser

0

0.05

0.1

0.15

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0 0.5 1 1.5 2 2.5 3 3.5 4

Shafer & Zare, 1991

Calculated, drag for rigid sph

Height (m)

Time (s)

T=4°C

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.

1 bar 1 bar

Pin PinPin

Plateau borderFilm

A

If the tensile stress on the bubble wall exceeds the tensile strength of magma, there will be fragmentation

PoutBPin

R1

R2

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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0 0.2 0.4 0.6 0.8 1

Pressure or stress (bar)

Vesicularity

Dynamic pressure

Tensile stress at bubble wall

700°C, H 2Ot,i=1%

Pout=3 bars

C

Pout=1 bar

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Pressure or stress (bar)

Vesicularity

Tensile stress at bubble wall

B

Pout=1 bar, H 2Ot,i=0.7%

700°C

600°C

If the tensile strength of magma is 60 bar, for the above case (0.7% H2O), no fragmentation would occur.

More realistic modeling is needed1 bar 1 bar

Pin PinPin

Plateau borderFilm

A

PoutBPin

R1

R2



• 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.




• 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 rateTemperature

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.

0.1

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40004500500055006000

Absorbance

Wavenumber (cm -1)

H2O OH

Near infrared spectrum

1

10

100

0.1 1 10

bed 2bed 7air quench

q (K/s)

V/A (mm)

Pyroclasts from Mono Craters

Quench in air

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

q=(T −Tambient)

hρCpL

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 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)

QuickTime™ and aSorenson Video decompressorare needed to see this picture.

From Camp and Sale

Mount Pinatubo eruption, July 1991

Kilauea, caldera

Mayon Volcano, pyroclastic flow, 2001

-35

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-10

-5

0

5

0 500 1000 1500 2000 2500 3000

T (°C)

P (bar)

Ice I

Liquid water

Ice III

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 bars.

Different types of gas-driven eruptions

• Explosive volcanic eruptionsConduit processesFragmentationErupting 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, disturbance, or addition of impurities as nucleation sites

• Explosive volcanic eruptions

• Lake eruptions

• Possible methane-driven water eruptions in oceans

• Cryovolcanism on Jovian satellites

Liq with dissolved gas

High-P

Fragmen-tation

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


High-P

Fragmen-tation

Speculation on a possible type of gas-driven eruption

Methane-driven water eruption in oceans (yet unknown)

seafloor

methane hydrate rises

released CH4 gas reacts with seawater to form hydrate

methane hydrate dissociates into gas

bubbly water rises, eruption

Methane hydrate crystals CH4(H2O)n

Marine sediment

CH4 flow

Methane bubbles

Research directions

Youxue Zhang

Department of Geological SciencesUniversity of Michigan

Ann Arbor, MI [email protected]

mailto:[email protected]





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, diffusionReaction kineticsGeospeedometry (cooling rate)Magma viscosity

High pressure phase equilibriaIsotopic fractionation Diffusion and kinetics

• Geochemical evolution of the earth and planets: models Noble gases and their isotopesEarth, Venus, and Mars

Gas-driven eruptions

Distribution of volcanos on EarthSome 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).

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


High-P

Fragmen-tation

Overview of the

eruption dynamics

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.


Experimental simulations of gas-driven eruptions

DiaphragmCutter

Low-Pressure Tank

Diaphragm

Test Cell

Experimental simulation, Exp#89

Zhang et al., 1997


Dynamics of Lake eruptionsCO2 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.

15001400130012001000900800700

1100 Lake Nyos

S N80m

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Depth (m)

Saturation depth = 208 m

A

u

(m/s)

Maximum velocity; from Zhang, 1996

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uexit

(m/s)

Saturation depth (m)

Nyos

Monoun

B

Degassing Lake Nyos

Future work: more realistic bubble plume eruption models, and the role of disequilibrium in lake eruptions

Documents

Parameters in modeling explosive volcanic eruptions