1. CONDUIT4 A computer code for the simulation of magma ascent through volcanic conduits and fissures Paolo Papale and Margherita Polacci Istituto Nazionale di Geofisica e Vulcanologia - Pisa

2. Dobran (JVGR 1992): DUCT Steady, isothermal, two-phase non-equilibrium flow Steady, isothermal, two-phase non-equilibrium flow Volcanic conduit or fissure Volcanic conduit or fissure Homogeneous flow, bubbly flow, and gas-particle/droplet flow regimes Homogeneous flow, bubbly flow, and gas-particle/droplet flow regimes Fragmentation at critical volume fraction (0.75) Fragmentation at critical volume fraction (0.75) Constant liquid density Constant liquid density Simple relationships for liquid viscosity and water solubility Simple relationships for liquid viscosity and water solubility Ideal gas properties Ideal gas properties

3. P/Po, and gas volume fraction liquid velocity (m/s) log [  mixt (Pa s)] non-dimensional conduit coordinate, z/L 0 1 pressure gas volume fraction lithostatic pressure mixture viscosity liquid velocity By making no assumption on pressure distribution, DUCT first revealed the existence of a region below magma fragmentation where large gradients of all flow variables and magma properties do occur

4. Papale and Dobran (JVGR 1993, JGR 1994): CONDUIT2 Magma properties on the basis of magma composition (10 major oxides + water) Magma properties on the basis of magma composition (10 major oxides + water) Multiphase (gas phase, and homogeneous liquid+crystal phase) Multiphase (gas phase, and homogeneous liquid+crystal phase) Real gas properties Real gas properties Applications to the AD 79 Vesuvius and May 18, 1980 Mount St. Helens eruptions Applications to the AD 79 Vesuvius and May 18, 1980 Mount St. Helens eruptions Applications to hazard forecasting at Vesuvius, with coupled simulations of conduit flow and atmospheric dispersion dynamics (Dobran et al., Nature 1993) Applications to hazard forecasting at Vesuvius, with coupled simulations of conduit flow and atmospheric dispersion dynamics (Dobran et al., Nature 1993)

5. Papale (FMTT 1998), Papale et al. (JVGR 1998), Papale and Polacci (BV 1999): CONDUIT3 Inclusion of carbon dioxide as an additional volatile component Inclusion of carbon dioxide as an additional volatile component Inclusion of separately developed (Papale, CMP 1997, AM 1999) modeling for water, carbon dioxide, and water+carbon dioxide saturation as a function of liquid magma composition Inclusion of separately developed (Papale, CMP 1997, AM 1999) modeling for water, carbon dioxide, and water+carbon dioxide saturation as a function of liquid magma composition Applications to parametric studies on the role of magma composition, water content, carbon dioxide content, and crystal content on the magma ascent dynamics (also Polacci et al., submitted) Applications to parametric studies on the role of magma composition, water content, carbon dioxide content, and crystal content on the magma ascent dynamics (also Polacci et al., submitted) Coupling with atmospheric dispersion and pyroclastic flow modeling, for parametric studies and hazard forecasting (Neri et al., JVGR 1998, JVGR in press; Todesco et al., BV 2002) Coupling with atmospheric dispersion and pyroclastic flow modeling, for parametric studies and hazard forecasting (Neri et al., JVGR 1998, JVGR in press; Todesco et al., BV 2002)

6. After Papale, 1997 Water solubility in silicate liquids with natural magmatic composition

7. CONDUIT4 – Multicomponent volatile saturation modeling 12 oxide components specified (10 major oxides and two volatiles H 2 O and CO 2 ) 12 oxide components specified (10 major oxides and two volatiles H 2 O and CO 2 ) non-ideal, non-Henrian, non-Henrian analogue non-ideal, non-Henrian, non-Henrian analogue calibrated on about 1,000 experimental data calibrated on about 1,000 experimental data P-T range of application: P-T range of application: H 2 O only:P atm < P < 1 GPa 900 < T < 1900 °C CO 2 only: P atm < P < 0.5 – 3 GPa 800 < T < 1900 °C H 2 O+CO 2 : P atm < P < 0.5 - 1 Gpa 900 < T < 1900 °C 900 < T < 1900 °C

8. Equilibrium equations Mass balance equations Multicomponent volatile saturation modeling

9. Reference fugacity of dissolved volatiles where

10. Activity coefficient of dissolved volatiles Water: Carbon dioxide:

11. Water Carbon dioxide Comparison between calculated and experimental water and carbon dioxide solubilities. Volatile-free compositions range from synthetic two- components to natural (10 components). Group 2 data for carbon dioxide were produced during the seventies with obsolete techniques, and are known to be poorly consistent with the more recent FTIR- and NMR- based group 1 data.

12. Solid symbols: leucitite Open symbols: tholeiite The volatile saturation model allows to account for large as well as small compositional differences Solid symbols: experimental Open symbols: calculated

13. symbols: calculations from Gerlach, 1986 lines: present modeling H2OH2O CO 2 Dissolved volatiles (wt%) Gas phase (wt%) Dissolved CO 2, calculated (wt%) Rhyolite, 1173 K Tholeiite, 1473 K Gerlach, 1986 Holloway and Blank, 1994

14. (after Papale, CMP 1997) experimental for rhyolite (Liu and Zhang, 1999) ??? this model as quoted by Zhang (2002)

15. Application of the volatile saturation model to the definition of conditions in the magma chamber of Vulcano, Eolian Islands. From the reconstruction of the composition of volatiles leaving the chamber, and assumed magma composition and T, the model allows: 1) to fix, for any chamber pressure, the amount of dissolved H 2 O and CO 2 2) to fix, for any chamber pressure, consistent pairs of total H 2 O and CO 2 in magma.

16. After Romano et al., 2002, and Giordano et al., 2002 Viscosity of silicate liquids with natural magmatic composition (with D. Dingwell and others) 01234 0 2 4 6 8 10 12 IGC MNV log 10 [  ( Pa · s)] H 2 Owt% 01234 0 2 4 6 8 10 12 log 10 [  ( Pa · s)] H 2 Owt% rhyolite Etna basalt trachytes phonolites T = 1100 K

17. CONDUIT4 - Multiphase non-Newtonian magma viscosity Effect of solid particles (crystals, xenoliths, etc.) by the Einstein-Roscoe equation with Marsh (1981) calibration up to about 40 vol.% (not known above) Effect of solid particles (crystals, xenoliths, etc.) by the Einstein-Roscoe equation with Marsh (1981) calibration up to about 40 vol.% (not known above) Role of gas bubbles by the Ishii and Zuber (1979) equation (assumes undeformable bubbles)Role of gas bubbles by the Ishii and Zuber (1979) equation (assumes undeformable bubbles) Liquid pseudo-plasticity (or viscous thinning) by the Bottinga (1994) model calibrated on data from Webb and Dingwell (1990)Liquid pseudo-plasticity (or viscous thinning) by the Bottinga (1994) model calibrated on data from Webb and Dingwell (1990) Magma viscoelasticity forming the base of the fragmentation criterion.Magma viscoelasticity forming the base of the fragmentation criterion.

18. At equal other conditions, trachitic magma fragments higher in the conduit compared to rhyolitic magma, due to lower viscosity and larger water solubility (after Polacci et al., submitted) Mass flow- rate

19. Mass flow-rate (kg/s) Gas volume fraction Gas velocity (m/s) Particle velocity (m/s) Pressure (MPa) Mixture density (kg/s) Calculated mass flow-rates and conduit exit conditions for a variety of cases involving calcalkaline magmas (after Papale et al., JVGR 1998)

20. Effect of carbon dioxide on water saturation Composition: rhyolite, Temperature: 1100 K after Papale, AM 1999

21. After Papale and Polacci, 1999 Effect of carbon dioxide on water saturation non-dimensional pressure

22. Mass flow-rate (kg/s x 10 -8 ) Gas volume fraction Fragmentation depth (m) Pressure (MPa) Mixture density (kg/m 3 ) Velocity (m/s) CH S1: total vol. content is constant s2: total water content is constant An increase of carbon dioxide produces a decrease of the mass flow-rate, and changes in the conduit exit quantities which are for the most part opposite to those produced by increase of water Different roles of water and carbon dioxide on the eruption dynamics After Papale and Polacci, BV 1999

23. Papale (Nature 1999): CONDUIT3 Inclusion of a dynamic fragmentation criterion based on rate- induced viscous to elastic transition of magma (based on Maxwell equation and experimental work by Dingwell and Webb 1990) Inclusion of a dynamic fragmentation criterion based on rate- induced viscous to elastic transition of magma (based on Maxwell equation and experimental work by Dingwell and Webb 1990)

24. Strain-rate -induced magma fragmentation The glass transition in time-reciprocal temperature space. Deformations slower than the structural relaxation time generated a relaxed, viscous liquid response of the melt. When the time scale of deformation approaches that of the glass transition t, the result is elastic storage of strain energy for low strains and shear thinning and brittle failure for high strains. The glass transition may be crossed many times during the formation of volcanic glasses. The first crossing may be the prymary fragmentation event in explosive volcanism. Variations in water and silica contents can drastically shift the temperature at which the transition in mechanical behavior is experienced. Thus, magmatic differentiation and degassing are important processes influencing the melt’s mechanical behavior during volcanic eruptions. (From Dingwell – Science) after Dingwell, Science 1996 Time-scale of strain < structural relaxation time of magma

25. Both strain-rate-induced and gas bubble overpressure- induced fragmentation mechanisms predict that fragmentation occurs when (gas bubble overpressure, Melnik 2001) (strain-rate) The way viscosity and strain-rate evolve in volcanic conduits is critical for the achievement of fragmentation conditions or: stress > strength

26. Pressure decrease Gas volume fraction increase Dissolved water decrease Viscosity increase Friction increase Density decrease Velocity increase Magma fragmentation: Sketch of main processes and their relationships within volcanic conduits Strain-rate increase

27. P/Po, and gas volume fraction liquid velocity (m/s) log [  mixt (Pa s)] non-dimensional conduit coordinate, z/L 0 1 pressure gas volume fraction lithostatic pressure mixture viscosity liquid velocity General distribution of flow variables along a volcanic conduit

28. Calculated conditions at fragmentation

29. The strain-rate induced fragmentation mechanism, although very simple in its formulation, produces an inverse trend between pumice vesicularity and magma viscosity at fragmentation, according to previous results (Thomas et al., 1994) Basalt,  arbitrarily increased by 4 orders of magnitude

30. Papale (JGR 2001): CONDUIT4 Inclusion of different kinds of particles formed at fragmentation: pumice (three-phase liquid/glass+crystal+gas bubble particles), ash (one-phase liquid/glass particles), and free crystals Inclusion of different kinds of particles formed at fragmentation: pumice (three-phase liquid/glass+crystal+gas bubble particles), ash (one-phase liquid/glass particles), and free crystals New constitutive equations for mechanical gas-particle and particle-particle interactions covering conditions from dilute to dense gas-particle mixtures New constitutive equations for mechanical gas-particle and particle-particle interactions covering conditions from dilute to dense gas-particle mixtures Inclusion of a pumice non-equilibrium degassing parameter Inclusion of a pumice non-equilibrium degassing parameter

31. Fragmentation efficiency: Or: formed at fragmentation

32. Pumice non-equilibrium degassing parameter: k = 1: equilibrium degassing k = 0: no degassing from pumice 0 < k < 1: variable extents of non-equilibrium pumice degassing Post-processing analysis based on Darcy’s flow of gas through the interconnected network of gas bubbles in pumice, together with the results of previous gas bubble growth modeling during magma flow in volcanic conduits (Proussevitch and Sahagian, JGR 1998), shows that the adopted pumice non- equilibrium degassing parameter coincides in most cases involving highly viscous magma with the degree of gas bubble coalescence in pumice

33. Natural pumice shows a large variability of vesicle textures, and largely different degrees of vesicle coalescence

34. Distribution of gas volume fraction along the volcanic conduit. Black lines: total gas volume fraction, and w f = 1 Blue lines: continuous gas volume fraction The presence of pumice results in a much lower gas volume fraction above fragmentation than previously supposed. after Papale, JGR 2001

35. Particle volume fraction at fragmentation the amount of pumice increases Volume fraction of particles at the level where magma fragmentation occurs Large possible volume fractions of particles in the volcanic conduit require the introduction of a normal stress term due to particle-particle interactions in the particle momentum equation

36. Exit total gas volume fraction Exit continuous gas volume fraction Total and continuous gas volume fractions at the conduit exit. Black lines: k = 1 (equilibrium pumice degassing) Blue lines: k = 0 (maximum nonequilibrium pumice degassing) The total gas volume fraction only changes for noneq. pumice degassing The total gas volume fraction only changes for noneq. pumice degassing The continuous gas volume fraction always decreases with increasing pumice content The continuous gas volume fraction always decreases with increasing pumice content The extent of changes strongly depends on the eruptive conditions The extent of changes strongly depends on the eruptive conditions D1150/4 R1100/2 R1100/4/30 R1100/4_2 R1100/4 R1100/6 k = 1 k = 0

37. Mechanical energy content of the magmatic mixture at the conduit exit Previous investigations with w f = 1 (Papale, Neri, and Macedonio, JVGR 1998a,b) Exit mechanical energy (m 2 /s 2 x 10 -4 ) CONDUIT4: Exit mechanical energy (m 2 /s 2 x 10 -4 ) Normalized exit mechanical energy k = 1 k = 0

38. CONDUIT4: Particularly suitable to account for compositional effects in the dynamic of sustained eruptions Detailed studies on sustained phases of explosive eruptions can be done Powerful tool to get insights into the large-scale dynamics of explosive eruptions, especially when coupled to atmospheric dispersion modeling (e.g., PDAC-2D, Neri et al., in press)

39. Steady magma flow: Two point boundary value problem Up-flow (conduit base) boundary condition: Magma chamber pressure Magma composition Down-flow (conduit exit) boundary condition: Choking (sonic condition), or Atmospheric pressure

40. Input data: magma temperature stagnation (magma chamber) pressure conduit or fissure length volatile-free magma composition (10 major oxides) total amounts of H 2 O and CO 2 crystal volume and density distribution fragmentation efficiency representative diameters of each kind of magmatic particle extent of non-equilibrium degassing from pumice one among conduit diameter (or fissure width) and mass flow-rate

41. Coupled numerical simulations of conduit flow and pyroclast dispersal Magma chamber Magma fragmentation Volcanic plume Pyroclastic flow Flow choking One-way coupling is sufficient for modeling the coupled conduit flow and pyroclast dispersion dynamics. Choked conduit flow in explosive eruptions ensures that the dynamics in the atmosphere do not affect the conduit flow dynamics with Augusto Neri and co-workers

43. Constitutive equations for mass balance Bubbly flow region:

44. Constitutive equations for mass balance At fragmentation:

45. Constitutive equations for mass balance Gas-particle/droplet flow region:

46. Constitutive equations for mass balance Gas-particle/droplet flow region (continued):

47. Constitutive equations for momentum balance

48. Bubbly flow region:

49. Constitutive equations for momentum balance Gas-particle/droplet flow region: