Parameters in modeling explosive volcanic eruptions

1. Parameters in modeling explosive volcanic eruptions

2. 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

3. 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

4. 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

5. Non-Arrhenian behavior of viscosity

6. 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.

7. 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.

8. Viscosity of hydrous rhyolitic melt

10. 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

11. H2O solubility and diffusivity

12. Water in magmaTwo hydrous species in melt

13. 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)

14. Solubility of H2O in basalt and rhyolite

15. 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).

16. 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

17. Solubility of H2O in rhyolite

18. 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.

19. 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.

20. 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

21. Diffusivity of H2O in magma

22. 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

23. 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

24. 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.

25. 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

27. 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

28. Bubble growth

29. Bubbles in glass in a bubble growth experiment, from Liu and Zhang (2000)

30. Predicting bubble growth

31. Beer Fizzics

32. Bubble growth in Budweiser

33. Bubble rise in Budweiser

34. Magma fragmentation • 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.

35. Unzen, Japan, 1991

36. Unzen lava dome

37. Unzen, 1991: 34 people died of the pyroclastic eruption

38. 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

39. If the tensile strength of magma is 60 bar, for the above case, when vesicularity reaches 60%, magma would fragment into a pyroclastic flow.

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

41. More realistic modeling is needed

42. 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

43. 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

44. Eruption column: Cooling rateTemperatureDynamics

47. 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.

50. 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