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 All other parameters should in principle be calculatable

Magma properties and theories needed Viscosity of magma A function of T, composition (esp. H 2 O) Solubility of H 2 O (and other gases) in magma Diffusivity of H 2 O (and other gases) in magma Fragmentation criterion Bubble growth experiments Enthalpy of H 2 O 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 orln  = A+(B/T) n where n ranges from 1 to 3 Viscosity increases with the concentration of SiO 2 and other network formers increases from basaltic to rhyolitic melt Viscosity decreases with the concentration of network modifiers, esp. H 2 O 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 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 H 2 O: 1/  = 1/  dry + bX n, where X is mole frac of H 2 O Using this formulation, Zhang et al. develop a new model.

where T is in K and X is the mole fraction of total H 2 O on a single oxygen basis. The viscosity of hydrous high-SiO 2 rhyolitic melt can be calculated within a factor of /  = 1/  dry + bX n

Viscosity of hydrous rhyolitic melt

Summary: Viscosity of hydrous melts Hydrous rhyolite (high-SiO 2 rhyolite with 76 to 77 wt% SiO 2 ) 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

H 2 O solubility and diffusivity

Water in magma Two hydrous species in melt

Solubility of H 2 O in magma Pressure: Solubility of H 2 O 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 H 2 O 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 H 2 O solubility at low pressure is critical since most expansion occurs in this stage (Blower et al., 2001)

Solubility of H 2 O in basalt and rhyolite

Solubility models Most solubility models predict H 2 O 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 H 2 O Solubility at 1 bar and 850°C: Papale (1997): wt% Moore et al. (1998): wt% Yamashita (1999): 0.074% Zhang (1999): wt% Burnham (1975): 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 H 2 O in rhyolite

Solubility model of Zhang (1999) where X, X m, and X OH are mole fractions of total, molecular and hydroxyl H 2 O on a single oxygen basis, f is H 2 O fugacity, K 1 and K 2 are two equilibrium constants and are given below: lnK 1 = ( P) + ( P)/T, K 2 = 6.53exp(-3110/T) where T is in K and P is in bar.

Diffusion of H 2 O in magma Numerous studies, starting from Shaw (1973) Because of two hydrous species, the diffusion of H 2 O in magma differs from that of other components. The diffusivity of the H 2 O component depends strongly on H 2 O content. This is a practically important and yet theoretically interesting problem. Diffusion of H 2 O in silicate melt can be modeled as follows: Molecular H 2 O is the diffusion species, and the diffusivity of molecular H 2 O increases exponentially with total H 2 O content. OH species is basically immobile.

Diffusion of H 2 O in magma (Zhang and Behrens, 2000) D H2Om = exp[( /T-2.796P/T) + ( /T+57.23P/T)X], D H2Ot = D H2Om dX m /X, where T is in K, P is in MPa (not mPa), and X and X m are the mole fractions of total and molecular H 2 O on a single oxygen basis where m = /T -1.4P/T

Diffusivity of H 2 O 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 H 2 O diffusivity in rhyolitic melt, use the model of Zhang and Behrens (2000) For H 2 O 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, H 2 O diffusivity, H 2 O 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. If the tensile stress on the bubble wall exceeds the tensile strength of magma, there will be 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% H 2 O), no fragmentation would occur.

More realistic modeling is needed

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, H 2 O diffusivity, H 2 O 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, H 2 O diffusivity, H 2 O 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 H 2 O 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. 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

Mount Pinatubo eruption, July 1991

Kilauea, caldera

Mayon Volcano, pyroclastic flow, 2001

Phase diagram of H 2 O 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 eruptions Conduit processes Fragmentation Erupting column Lake eruptions (limnic eruptions) Possible CH 4 -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

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

Speculation on a possible type of gas-driven eruption Methane-driven water eruption in oceans (yet unknown)

Methane hydrate crystals CH 4 (H 2 O) n Marine sediment CH 4 flow Methane bubbles

Research directions Youxue Zhang Department of Geological Sciences University of Michigan Ann Arbor, MI

Experimental petrology lab Ultra-high pressure ( multi-anvil apparatus ): 4-20 GPa ( kb, km depth) To 2500 °C Intermediate pressure (piston-cylinder apparatus) GPa, up to 1800°C Hydrothermal conditions (cold-seal bombs) 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 H 2 O) 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 Liquid can be either magma, water, or other liquid Gas can be either steam, CO 2, CH 4 or other gas Types of gas-driven eruptions: 1. Explosive volcanic eruptions 2. Lake eruptions

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 CO 2 -driven lake eruptions Dynamics of lake eruptions Experimental investigation of bubble growth in magma Modeling the fragmentation process Experimental investigation of magma properties: viscosity, H 2 O diffusivity, H 2 O solubility, etc. Developing geospeedometers to study temperature and cooling rate in the erupting column

Experimental simulations of gas-driven eruptions

Experimental simulation, Exp#89 Zhang et al., 1997

Dynamics of Lake eruptions CO 2 from magma at depth percolates throught the rocks and into lake bottom. Dissolution of CO 2 increases the density of water. Hence CO 2 concentrates in lake bottom. When saturation is reached (or if unsaturated but disturbed), the sudden exsolution of CO 2 can lead to lake eruption. The eruption dynamics can be modeled semi- quantitatively using the Bernoulli equation. The erupted CO 2 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.

Maximum velocity; from Zhang, 1996

Degassing Lake Nyos

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