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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All other parameters should in principle be calculatable
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.
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
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.
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
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
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
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.
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
Bubble growth in Budweiser Zhang (2000)
Bubble rise in Budweiser Zhang (2000)
Unzen, Japan, 1991 Zhang (2000)
Unzen lava dome Zhang (2000)
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% H2O), no fragmentation would occur.
From Camp and Sale case (0.7% H
Mount Pinatubo eruption, July 1991 case (0.7% H
Kilauea, caldera case (0.7% H
Mayon Volcano, pyroclastic flow, 2001 case (0.7% H
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.
CH case (0.7% H4 flow
Methane hydrate crystals CH4(H2O)n
Distribution of volcanos on Earth case (0.7% H
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 above the clouds; it is erupting currently
Mount Pinatubo eruption, July 1991, the big one: killed more than 900 people, devastated US Clark Air Force Base
Lake Nyos, Cameroon than 900 people, devastated US Clark Air Force Base
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).
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.
Maximum velocity; from Zhang, 1996 (Cameroon, Africa).
Degassing Lake Nyos (Cameroon, Africa).
Future work: more realistic bubble plume eruption models, and the role of disequilibrium in lake eruptions