Parameters in modeling explosive volcanic eruptions
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Parameters in modeling explosive volcanic eruptions. Primary parameters: must be determined before each eruption . Melt composition, esp. initial H 2 O content Initial temperature Initial pressure (degree of saturation) and exsolved gas content Conduit geometry and wall rock property

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Primary parameters must be determined before each eruption l.jpg
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 = 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 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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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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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 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


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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 = (-13.869+0.0002474P) + (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) + (-27.21+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

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

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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Beer Fizzics Zhang (2000)




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Magma fragmentation Zhang (2000)

  • Magma fragmentation defines explosive eruption

  • 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%.

  • Slowly growing lava dome or slowly advancing lava flows can suddenly fragment into pyroclastic flow.


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Unzen, Japan, 1991 Zhang (2000)


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Unzen lava dome Zhang (2000)



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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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Our work on explosive volcanic eruptions case (0.7% H

  • 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 case (0.7% H

  • 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: case (0.7% HCooling rateTemperatureDynamics


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Hydrous species geospeedometer case (0.7% H

  • 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? case (0.7% H

  • 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 case (0.7% H

  • Experimental investigation of magma properties: Viscosity, diffusion, etc.

  • Trigger mechanism for explosive volcanic eruptions, fragmentation, and conditions for non-explosive and explosive eruptions.

  • Dynamics of bubble plume eruptions

  • Understanding volcanic eruption columns

  • Methane-driven water eruptions


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Some other current research directions case (0.7% H

  • Geochemical evolution of Earth, Venus, and Mars: Atmospheric age, formation, and evolutionVarious ages and events of planetary formation

  • Kinetics related to methane hydrate in marine sediment (experimental and theoretical)

  • Experimental work on D/H fractionation

  • Experimental investigation of phase stability and kinetics under high pressure (mantle)


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From Camp and Sale case (0.7% H



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Kilauea, caldera case (0.7% H



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Phase diagram of H case (0.7% 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.


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Different types of gas-driven eruptions case (0.7% H

  • 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 case (0.7% H

  • 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 case (0.7% H

  • 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 case (0.7% HMethane-driven water eruption in oceans (yet unknown)


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CH case (0.7% H4 flow

Methane bubbles

Methane hydrate crystals CH4(H2O)n

Marine sediment


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Research directions case (0.7% H

Youxue Zhang

Department of Geological Sciences

University of Michigan

Ann Arbor, MI 48109-1063

[email protected]


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Experimental petrology lab case (0.7% H

  • 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


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Research directions case (0.7% H

  • 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


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Gas-driven eruptions case (0.7% H


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Distribution of volcanos on Earth case (0.7% H

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 above the clouds; it is erupting currently


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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 than 900 people, devastated US Clark Air Force Base


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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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Overview (Cameroon, Africa). 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

  • 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 (Cameroon, Africa). From Camp and Sale


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Our work on gas-driven eruptions (Cameroon, Africa).

  • 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 simulation, Exp#89 (Cameroon, Africa).

Zhang et

al., 1997


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Dynamics of Lake eruptions (Cameroon, Africa).

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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Degassing Lake Nyos (Cameroon, Africa).


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


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