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

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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
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• Papale and Dobran (JVGR 1993, JGR 1994) CONDUIT2
• Magma properties on the basis of magma
  composition (10 major oxides water)
• Multiphase (gas phase, and homogeneous
  liquidcrystal phase)
• Real gas properties
• 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)

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• 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 separately developed (Papale, CMP
  1997, AM 1999) modeling for water, carbon
  dioxide, and watercarbon 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)
• 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)

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Water solubility in silicate liquids with natural
magmatic composition
After Papale, 1997
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CONDUIT4 Multicomponent volatile saturation
modeling

• 12 oxide components specified (10 major oxides
  and two volatiles H2O and CO2)
• non-ideal, non-Henrian, non-Henrian analogue
• calibrated on about 1,000 experimental data
• P-T range of application

H2O only Patm lt P lt 1 GPa 900 lt T lt 1900
C CO2 only Patm lt P lt 0.5 3 GPa 800 lt T lt
1900 C H2OCO2 Patm lt P lt 0.5 - 1 Gpa 900 lt
T lt 1900 C
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Multicomponent volatile saturation modeling
Equilibrium equations
Mass balance equations
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Reference fugacity of dissolved volatiles
where
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Activity coefficient of dissolved volatiles
Water
Carbon dioxide
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Comparison between calculated and experimental
water and carbon dioxide solubilities. Volatile-fr
ee 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.
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The volatile saturation model allows to account
for large as well as small compositional
differences
Solid symbols experimental Open symbols
calculated
Solid symbols leucitite Open symbols tholeiite
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Gerlach, 1986
Holloway and Blank, 1994
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(after Papale, CMP 1997)
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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
H2O and CO2 2) to fix, for any chamber pressure,
consistent pairs of total H2O and CO2 in magma.
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Viscosity of silicate liquids with natural
magmatic composition (with D. Dingwell and others)
After Romano et al., 2002, and Giordano et al.,
2002
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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)
• 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)
• Magma viscoelasticity forming the base of the
  fragmentation criterion.

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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)
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Calculated mass flow-rates and conduit exit
conditions for a variety of cases involving
calcalkaline magmas (after Papale et al., JVGR
1998)
Gas volume fraction
Mass flow-rate (kg/s)
Gas velocity (m/s)
Particle velocity (m/s)
Pressure (MPa)
Mixture density (kg/s)
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Effect of carbon dioxide on water saturation
Composition rhyolite, Temperature 1100 K
after Papale, AM 1999
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Effect of carbon dioxide on water saturation
After Papale and Polacci, 1999
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S1 total vol. content is constant s2 total
water content is constant
Mass flow-rate (kg/s x 10-8)
Fragmentation depth (m)
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
Gas volume fraction
Pressure (MPa)
Mixture density (kg/m3)
Velocity (m/s)
CH
CH
After Papale and Polacci, BV 1999
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• 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)

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Strain-rate -induced magma fragmentation
after Dingwell, Science 1996
Time-scale of strain lt structural relaxation time
of magma
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Both strain-rate-induced and gas bubble
overpressure-induced fragmentation mechanisms
predict that fragmentation occurs when
or
The way viscosity and strain-rate evolve in
volcanic conduits is critical for the achievement
of fragmentation conditions
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Sketch of main processes and their relationships
within volcanic conduits
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General distribution of flow variables along a
volcanic conduit
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Calculated conditions at fragmentation
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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)
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• Papale (JGR 2001) CONDUIT4
• Inclusion of different kinds of particles formed
  at fragmentation pumice (three-phase
  liquid/glasscrystalgas 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
• Inclusion of a pumice non-equilibrium degassing
  parameter

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Fragmentation efficiency
Or
formed at fragmentation
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Pumice non-equilibrium degassing parameter
k 1 equilibrium degassing k 0 no degassing
from pumice 0 lt k lt 1 variable extents of
non-equilibrium pumice degassing
Post-processing analysis based on Darcys 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
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Natural pumice shows a large variability of
vesicle textures, and largely different degrees
of vesicle coalescence
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Distribution of gas volume fraction along the
volcanic conduit. Black lines total gas volume
fraction, and wf 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
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Volume fraction of particles at the level where
magma fragmentation occurs
Particle volume fraction at fragmentation
the amount of pumice increases
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
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• 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 continuous gas volume fraction always
  decreases with increasing pumice content
• The extent of changes strongly depends on the
  eruptive conditions

Exit total gas volume fraction
Exit continuous gas volume fraction
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Mechanical energy content of the magmatic mixture
at the conduit exit
Previous investigations with wf 1 (Papale,
Neri, and Macedonio, JVGR 1998a,b)
Exit mechanical energy (m2/s2 x 10-4)
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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)
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• 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
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Input data

• magma temperature
• stagnation (magma chamber) pressure
• conduit or fissure length
• volatile-free magma composition (10 major
  oxides)
• total amounts of H2O and CO2
• 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

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Coupled numerical simulations of conduit flow and
pyroclast dispersal
with Augusto Neri and co-workers
Volcanic plume
Pyroclastic flow
Flow choking
Magma fragmentation
Magma chamber
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Constitutive equations for mass balance
Bubbly flow region
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Constitutive equations for mass balance
At fragmentation
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Constitutive equations for mass balance
Gas-particle/droplet flow region
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Constitutive equations for mass balance
Gas-particle/droplet flow region (continued)
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Constitutive equations for momentum balance
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Constitutive equations for momentum balance
Bubbly flow region
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Constitutive equations for momentum balance
Gas-particle/droplet flow region