CONDUIT4CONDUIT4

A computer code for the simulation of magma ascentA computer code for the simulation of magma ascent

through volcanic conduits and fissuresthrough volcanic conduits and fissures

  

Paolo Papale and Margherita PolacciPaolo Papale and Margherita Polacci

Istituto Nazionale di Geofisica e Vulcanologia - PisaIstituto Nazionale di Geofisica e Vulcanologia - Pisa

Dobran (Dobran (JVGR 1992JVGR 1992): ): DUCTDUCT

• Steady, isothermal, two-phase non-equilibrium flowSteady, isothermal, two-phase non-equilibrium flow

• Volcanic conduit or fissureVolcanic conduit or fissure

• Homogeneous flow, bubbly flow, and gas-particle/droplet flow Homogeneous flow, bubbly flow, and gas-particle/droplet flow regimesregimes

• Fragmentation at critical volume fraction (0.75)Fragmentation at critical volume fraction (0.75)

• Constant liquid densityConstant liquid density

• Simple relationships for liquid viscosity and water solubilitySimple relationships for liquid viscosity and water solubility

• Ideal gas propertiesIdeal gas properties

0.0

0.2

0.4

0.6

0.8

1.0

0

50

100

150

200

-5

0

5

10

P/P

o, a

nd g

a s v

olum

e f r

acti

onli

quid

ve l

oci t

y (m

/ s)

log

[m

ixt (

Pa

s)]

non-dimensional conduit coordinate, z/L0 1

pressure

gas volume fraction

lithostatic pressure

mixture viscosity

liquid velocity

By making By making no assumption on no assumption on pressure distribution,pressure distribution, DUCT first DUCT first revealed the existence of a region revealed the existence of a region below magma fragmentation below magma fragmentation where where large gradientslarge gradients of all flow of all flow variables and magma properties do variables and magma properties do occuroccur

Papale and Dobran (Papale and Dobran (JVGR 1993, JGR 1994JVGR 1993, JGR 1994): ): CONDUIT2CONDUIT2

• Magma properties on the basis of magma composition (10 Magma properties on the basis of magma composition (10 major oxides + water)major oxides + water)

• Multiphase (gas phase, and homogeneous liquid+crystal phase)Multiphase (gas phase, and homogeneous liquid+crystal phase)

• Real gas propertiesReal gas properties

• Applications to the AD 79 Vesuvius and May 18, 1980 Mount Applications to the AD 79 Vesuvius and May 18, 1980 Mount St. Helens eruptionsSt. Helens eruptions

• Applications to hazard forecasting at Vesuvius, with coupled Applications to hazard forecasting at Vesuvius, with coupled simulations of conduit flow and atmospheric dispersion dynamics simulations of conduit flow and atmospheric dispersion dynamics ((Dobran et al., Nature 1993Dobran et al., Nature 1993) )

Papale (Papale (FMTT 1998FMTT 1998), Papale et al. (), Papale et al. (JVGR 1998JVGR 1998), Papale ), Papale and Polacci (and Polacci (BV 1999BV 1999): ): CONDUIT3CONDUIT3

• Inclusion of carbon dioxide as an additional volatile component Inclusion of carbon dioxide as an additional volatile component

• Inclusion of separately developed (Inclusion of separately developed (Papale, CMP 1997, AM Papale, CMP 1997, AM 19991999) modeling for water, carbon dioxide, and water+carbon ) modeling for water, carbon dioxide, and water+carbon dioxide saturation as a function of liquid magma compositiondioxide saturation as a function of liquid magma composition

• Applications to parametric studies on the role of magma Applications to parametric studies on the role of magma composition, water content, carbon dioxide content, and crystal composition, water content, carbon dioxide content, and crystal content on the magma ascent dynamics (also content on the magma ascent dynamics (also Polacci et al., Polacci et al., submittedsubmitted))

• Coupling with atmospheric dispersion and pyroclastic flow Coupling with atmospheric dispersion and pyroclastic flow modeling, for parametric studies and hazard forecasting (modeling, for parametric studies and hazard forecasting (Neri et Neri et al., JVGR 1998, JVGR in press; Todesco et al., BV 2002al., JVGR 1998, JVGR in press; Todesco et al., BV 2002))

30020010000

2

4

6

8

Pressure (MPa)

diss

olve

d H

2O (

wt%

)

rhyolite, T = 1100 K

Agnano Monte Spina trachyte,T = 1100 K

Campanian Ignimbrite trachyte,T = 1150 K

Monte Nuovo trachyte,T = 1150 K

Vesuvius AD79 phonolite (W),T = 1150 K

Vesuvius AD79 phonolite (G),T = 1170 K

After Papale, 1997

Water solubility in silicate liquids with natural magmatic compositionWater solubility in silicate liquids with natural magmatic composition

CONDUIT4 – Multicomponent volatile saturation CONDUIT4 – Multicomponent volatile saturation modelingmodeling

• 12 oxide components specified (10 major oxides and 12 oxide components specified (10 major oxides and two volatiles Htwo volatiles H22O and COO and CO22))

• non-ideal, non-Henrian, non-Henrian analoguenon-ideal, non-Henrian, non-Henrian analogue

• calibrated on about 1,000 experimental datacalibrated on about 1,000 experimental data

• P-T range of application:P-T range of application:

HH22O only:O only: PPatmatm < P < 1 GPa < P < 1 GPa

900 < T < 1900 °C900 < T < 1900 °C

COCO22 only: only: P Patmatm < P < 0.5 – 3 GPa < P < 0.5 – 3 GPa

800 < T < 1900 °C800 < T < 1900 °C

HH22O+COO+CO22:: P Patmatm < P < 0.5 - 1 Gpa < P < 0.5 - 1 Gpa

900 < T < 1900 °C900 < T < 1900 °C

Equilibrium equations

22

22

22

22

221

COCO

COTCO

OHOH

OHT

OH

COOH

xy

xx

xy

xx

yy

oLCOCOCOCOCO

LCO

GCO

oLOHOHOHOHOH

LOH

GOH

LG

LG

fxPyff

fxPyff

TTT

PPP

2222222

2222222

Mass balance equations

Multicomponent volatile saturation modeling

dPdTT

vTv

RT

dPRT

vTPfTPf

P

PP

oio

i

T

T

P

P

oioooL

ioL

i

oo

o

2

1

),(ln),(ln

31098

22765

34

2321, 22

PaTaaPTaTaaP

TaTaTaavoCOOHi

Reference fugacity of dissolved volatiles

where

)0(

1

'

2

2

22222222)1)(1()1(ln OiH

n

COiiCOOHOHOCOHCOOHOH wxxxxwxxRT

n

OHiiCOio

n

OHiiCOiCOOHCO wx

P

Pwxxxx

1

)1('

1

)0('

2

2

2

2222ln)1(

1

1, 1,

''2

22 22

22)1(

n

COOHi

n

iCOOHjijjiCOOH wxxxx

)0(

1

'

2

2

22222222)1()1(ln OiH

n

COiiCOOHOHOCOHOHCOCO wxxxxwxxRT

n

OHiiCOio

n

OHiiCOiCOOHCO wx

P

Pwxxxx

1

)1('

1

)0('

2

2

2

2222ln)1)(1(

1

1, 1,

''2

22 22

22)1(

n

COOHi

n

iCOOHjijjiCOOH wxxxx

Activity coefficient of dissolved volatiles

Water:

Carbon dioxide:

0

10

20

30

3020100

experimental H2O (wt%)

calc

ulated

H2O

(wt%

) 492 data

201000

10

20

experimental CO2 (wt%)

calcul

ated

CO

2 (w

t%)

94 group 1 data (squares)169 group 2 data (points)

Water

Carbon dioxide

Comparison between Comparison between calculated and experimental calculated and experimental water and carbon dioxide water and carbon dioxide solubilities.solubilities.

Volatile-free compositions Volatile-free compositions range from synthetic two-range from synthetic two-components to natural (10 components to natural (10 components).components).

Group 2 data for carbon Group 2 data for carbon dioxide were produced during dioxide were produced during the seventies with obsolete the seventies with obsolete techniques, and are known to techniques, and are known to be poorly consistent with the be poorly consistent with the more recent FTIR- and NMR-more recent FTIR- and NMR-based group 1 data.based group 1 data.

2

4

6

8

10

12

P = 0.05 GPaT = 1273 K

P = 0.1 GPaT = 1123 K

P = 0.2 GPaT = 1173 K

P = 0.5 GPaT = 1173 K

Experimental

Calculated

diss

olve

d H

2O (w

t%)

different haplogranitic compositions(from Holtz et al., 1995)

20001800160014000

2

4

6

8

0.1 11.50.5

1

1.5

2

temperature (K)

diss

olve

d CO

2 (w

t%)

Solid symbols: leucitite Open symbols: tholeiite

The volatile saturation The volatile saturation model allows to account for model allows to account for large as well as small large as well as small compositional differencescompositional differences

Solid symbols: experimental Open symbols: calculated

0

0.1

0.2

0.3

H2O

CO2

10864200

0.1

0.2

0.3

0.4

pressure (MPa)

Composition: kilauean tholeiiteT = 1420 K

Symbols: calculations from Gerlach, 1986lines: present modeling

symbols: calculations from Gerlach, 1986

lines: present modeling

H2O

CO2Dis

solv

ed v

olat

iles

(w

t%)

Gas

pha

se (

wt%

)

0.2

0.4

0.6

0.8

0.5

0.4

0.3

0.2

0.1

0.1

0.2

0.3

0.2

0.4

0.6

0.8

0.50.4

0.3

0.2

0.1

86420

0.1

0.2

0.3

rhyolite, T = 1173 K

tholeiite, T = 1473 K

0.2

dissolved H2O, calculated (wt%)

Dis

solv

ed C

O2,

calc

ulat

ed (

wt%

)D

isso

lved

CO

2, ca

lcul

ated

(w

t%)

Rhyolite, 1173 K

Tholeiite, 1473 K

Gerlach, 1986Gerlach, 1986 Holloway and Blank, 1994Holloway and Blank, 1994

(after Papale, CMP 1997)

experimental for rhyolite (Liu and Zhang, 1999)

??? this model as quoted by Zhang (2002)

1601401201008060400

10

20

30

40

H O2

CO2

diss

olve

d H

2 O (wt%

) an

d CO

2 (p

pm)

pressure (MPa)

1086420

1

2

3

4

5

0.05 0.1 0.15

total C

O2 in

sys

tem

(wt%

)

total H2O in system (wt%)

P (GPa) =

Application of the volatile Application of the volatile saturation model to the saturation model to the definition of conditions in definition of conditions in the magma chamber of the magma chamber of Vulcano, Eolian Islands.Vulcano, Eolian Islands.

From the reconstruction of the From the reconstruction of the composition of volatiles composition of volatiles leaving the chamber, and leaving the chamber, and assumed magma composition assumed magma composition and T, the model allows:and T, the model allows:

1) to fix, for any chamber 1) to fix, for any chamber pressure, the amount of pressure, the amount of dissolved Hdissolved H22O and COO and CO22

2) to fix, for any chamber 2) to fix, for any chamber pressure, consistent pairs of pressure, consistent pairs of total Htotal H22O and COO and CO22 in magma. in magma.

After Romano et al., 2002, and Giordano et al., 2002

Viscosity of silicate liquids with natural magmatic compositionViscosity of silicate liquids with natural magmatic composition

(with D. Dingwell and others)(with D. Dingwell and others)

0 1 2 3 4

0

2

4

6

8

10

12IGC MNV

log 1

0[

(Pa·

s)]

H 2O wt %0 1 2 3 4

0

2

4

6

8

10

12

log 1

0[

(Pa·

s)]

H 2O wt %

rhyolite

Etna basalt

trachytes

phonolites

T = 1100 K

CONDUIT4 - Multiphase non-Newtonian magma viscosityCONDUIT4 - Multiphase non-Newtonian magma viscosity

• Effect of Effect of solid particlessolid particles (crystals, xenoliths, etc.) by (crystals, xenoliths, etc.) by the Einstein-Roscoe equation with Marsh (1981) the Einstein-Roscoe equation with Marsh (1981) calibration up to about 40 vol.% (not known above)calibration up to about 40 vol.% (not known above)

•Role of Role of gas bubblesgas bubbles by the Ishii and Zuber (1979) by the Ishii and Zuber (1979) equation (assumes undeformable bubbles)equation (assumes undeformable bubbles)

•Liquid Liquid pseudo-plasticitypseudo-plasticity (or viscous thinning) by the (or viscous thinning) by the Bottinga (1994) model calibrated on data from Webb Bottinga (1994) model calibrated on data from Webb and Dingwell (1990)and Dingwell (1990)

•Magma Magma viscoelasticityviscoelasticity forming the base of the forming the base of the fragmentation criterion.fragmentation criterion.

0.0

0.2

0.4

0.6

0.8

1.0

non-dimensional vertical coordinate, z/L

non-

dim

ensi

onal

pre

ssur

e, P

/Po,

and

gas

volu

me

frac

tion

rhyolite trachyte

gas volumefraction

pressure

0

100

200

liqu

id o

r pa

rtic

le v

eloc

ity

(m/s

)

rhyolite trachyte

velocity

1.21.00.80.60.40.20.0-5-4-3-2-1012345678

log

[mix

ture

vis

cosi

ty (

Pa

s)]

rhyolitetrachyte

mixtureviscosity

At equal other conditions, trachitic At equal other conditions, trachitic magma magma fragmentsfragments higher in the higher in the conduitconduit compared to rhyolitic compared to rhyolitic magma, due to lower viscosity and magma, due to lower viscosity and larger water solubilitylarger water solubility

(after (after Polacci et al., submittedPolacci et al., submitted))

76543210

10

20

total water content (wt%)

mas

s fl

ow-r

ate

(kg/

s x

10-7

)

D = 30 m

D = 60 m

D = 90 m

rhyolite

trachyteMass flow-rate

0

2

4

8

1 0

RHYOLITE

RHYODACITE

DACITE

0 .8 5

0 .9 0

0 .9 5

1 .0 0

RHYOLITE

RHYODACITE

DACITE

1 20

1 40

1 60

1 80

2 00

2 20

RHYOLITE

RHYODACITE

DACITE

1 00

1 20

1 40

1 60

1 80

2 00

2 20

RHYOLITE

RHYODACITEDACITE

76543210

2

4

6

8

1 0

1 2

RHYOLITE

RHYODACITE

DACITE

76543210

1 00

2 00

3 00

4 00

RHYOLITE

RHYODACITE

DACITE

H O con ten t (w t% )2H O con ten t (w t% )2

a)

c)

e ) f)

d )

b )

DACITE+CR.

DACITE+CR.

DACITE+CR.

DACITE+CR.

DACITE+CR.

DACITE+CR.

Mas

s fl

ow-r

ate

(kg/

s)

Gas

vol

ume

frac

tion

Gas

vel

ocit

y (m

/s)

Par

ticl

e v e

l oc i

t y (

m/s

)

Pre

ssur

e (M

Pa)

Mix

ture

den

sity

(kg

/s)

Calculated mass Calculated mass flow-rates and flow-rates and conduit exit conduit exit conditions for a conditions for a variety of cases variety of cases involving involving calcalkaline calcalkaline magmasmagmas(after (after Papale et al., JVGR Papale et al., JVGR 19981998))

Effect of carbon dioxide on water saturationEffect of carbon dioxide on water saturation

Composition: rhyolite, Temperature: 1100 K

1

2

3

4

5 CH = 0CH = 0 .0 2

CH = 0 .0 8

CH = 0 .1 7

CH = 0.3 3

CH = 0.5 0

0.20.10

CH = 0CH = 0 .0 2

CH = 0 .0 9CH = 0 .1 7

CH = 0 .3 3

0.20.10

CH = 0 .5 0

diss

olve

d H

2O (

wt%

)

p ressure (G P a) p ressure (G P a)

to tal vo lat ile co ntent = 6 w t% = co nst to tal w ater co ntent = 5 w t% = co nst

a) b)

after Papale, AM 1999

TT

T

COOH

CO

mm

mCH

22

2

After Papale and Polacci, 1999

Effect of carbon dioxide on water saturationEffect of carbon dioxide on water saturation

1.00.80.60.40.20.00.0

0.2

0.4

0.6

0.8

1.0

CH = 0.50CH = 0.33CH = 0.17CH = 0.08CH = 0

LITHOSTATIC

1.00.80.60.40.20.0

CH = 0.50CH = 0.33CH = 0.17CH = 0.09CH = 0

LITHOSTATIC

a) b)

volatiles = 6 wt%s1: total H2O = 5 wt%s2: total

non-dimensional vertical coordinate non-dimensional vertical coordinate

non-

dim

ensi

onal

pre

ssur

e

0

1

2

3

x

0 .9 3

0 .9 4

0 .9 5

0 .9 6

0 .9 7

0 .9 8

c)

f)

1 70

1 80

1 90

2 00

2 10

2 20

2 30

2 40

1

2

3

4

5

d)

0 .60 .50 .40 .30 .20 .10 .0

C H

e)

6 0

8 0

1 00

1 20

1 40

1 60

1 80

b)

1 00 0

2 00 0

4 00 0

5 00 0a)

s1

s2

0 .60 .50 .40 .30 .20 .10 .0

C H

s1

s2

s1

s2

s1

s2

s1

s2

s1

s2, gas, liqu id

Ma s

s f l

ow- r

a te

( kg /

s x

1 0-8)

Ga s

vo l

ume

f ra c

tion

Fra

gme n

t at i

o n d

ept h

(m

)P

res s

u re

( MP

a )

Mi x

t ure

de n

s it y

(k g

/m3 )

Ve l

o cit

y ( m

/ s)

CH CH

S1: total vol. content is constant

s2: total water content is constant

An increase of carbon An increase of carbon dioxide produces a decrease dioxide produces a decrease of the mass flow-rate, and of the mass flow-rate, and changes in the conduit exit changes in the conduit exit quantities which are for the quantities which are for the most part opposite to those most part opposite to those produced by increase of produced by increase of waterwater

Different roles of Different roles of water and carbon water and carbon dioxide on the dioxide on the eruption dynamicseruption dynamics

After Papale and Polacci, BV 1999

Papale (Papale (Nature 1999Nature 1999): ): CONDUIT3CONDUIT3

• Inclusion of a dynamic fragmentation criterion based on rate-Inclusion of a dynamic fragmentation criterion based on rate-induced viscous to elastic transition of magma (based on induced viscous to elastic transition of magma (based on Maxwell equation and experimental work by Maxwell equation and experimental work by Dingwell and Webb Dingwell and Webb 19901990))

Strain-rate -induced magma fragmentationStrain-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)

XG

kkdz

dvs

s

z

:or , 1

after Dingwell, Science 1996

Time-scale of strain < structural relaxation time of magma

Both Both strain-ratestrain-rate-induced and -induced and gas bubble overpressuregas bubble overpressure--induced fragmentation mechanisms predict thatinduced fragmentation mechanisms predict that fragmentation occurs whenfragmentation occurs when

kG

d

dT

4

3(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:or: stress > strength

Pressure Pressure decreasedecrease

Gas volume Gas volume fraction increasefraction increase

Dissolved water Dissolved water decreasedecrease

Viscosity Viscosity increaseincrease

Friction Friction increaseincrease

Density Density decreasedecrease

Velocity Velocity increaseincrease

Magma fragmentation:

Sketch of main processes and their relationships within volcanic conduits

Strain-rate Strain-rate increaseincrease

0.0

0.2

0.4

0.6

0.8

1.0

0

50

100

150

200

-5

0

5

10

P/P

o, a

nd g

a s v

olum

e f r

acti

onli

quid

ve l

oci t

y (m

/ s)

log

[m

ixt (

Pa

s)]

non-dimensional conduit coordinate, z/L0 1

pressure

gas volume fraction

lithostatic pressure

mixture viscosity

liquid velocity

General distribution of flow General distribution of flow variables along a volcanic variables along a volcanic conduitconduit

DACITE

RHYOLITE

0.90.80.70.6

0

4

3

2

1WATERDECREASES

WATERDECREASES

CRYSTALSINCREASE

CARBON DIOXIDEINCREASES ATCONSTANT VOLATILECONTENT

CARBON DIOXIDEINCREASES ATCONSTANT WATERCONTENT

vesicularity at fragmentation

frag

men

tation

dep

th (km

)

Calculated conditions at fragmentationCalculated conditions at fragmentation

The strain-rate induced fragmentation mechanism, although very The strain-rate induced fragmentation mechanism, although very simple in its formulation, produces an inverse trend between simple in its formulation, produces an inverse trend between pumice vesicularitypumice vesicularity and magma viscosity at fragmentation, and magma viscosity at fragmentation, according to previous results (according to previous results (Thomas et al., 1994Thomas et al., 1994))

8.58.07.57.06.50.6

0.7

0.8

0.9

1.0

log10 [viscosity at fragmentation (Pa s)]

calc

ulat

ed g

as v

olum

efr

acti

on a

t fr

agm

enta

tion

Basalt, arbitrarily increased by 4 orders of magnitude

Papale (Papale (JGR 2001JGR 2001): ): CONDUIT4CONDUIT4

• Inclusion of different kinds of particles formed at Inclusion of different kinds of particles formed at fragmentation: pumice (three-phase liquid/glass+crystal+gas fragmentation: pumice (three-phase liquid/glass+crystal+gas bubble particles), ash (one-phase liquid/glass particles), and free bubble particles), ash (one-phase liquid/glass particles), and free crystalscrystals

• New constitutive equations for mechanical gas-particle and New constitutive equations for mechanical gas-particle and particle-particle interactions covering conditions from dilute to particle-particle interactions covering conditions from dilute to dense gas-particle mixturesdense gas-particle mixtures

• Inclusion of a pumice non-equilibrium degassing parameterInclusion of a pumice non-equilibrium degassing parameter

Fragmentation efficiencyFragmentation efficiency::

SfPf

Sff ww

ww

Or:Or:

ash pumice of mass

ash of mass

formed at fragmentationformed at fragmentation

GfGGP kk 1

Pumice non-equilibrium degassing parameterPumice non-equilibrium degassing parameter::

kk = 1: equilibrium degassing = 1: equilibrium degassing

kk = 0: no degassing from pumice = 0: no degassing from pumice

0 < 0 < kk < 1: variable extents of non-equilibrium < 1: variable extents of non-equilibrium pumice degassingpumice 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

Natural pumice shows a large variability of vesicle Natural pumice shows a large variability of vesicle textures, and largely different degrees of vesicle textures, and largely different degrees of vesicle coalescencecoalescence

0.0

0.2

0.4

0.6

0.8

1.0

wf = 1

wf = .85

wf = .70

wf = .55

wf = .40

wf = .15

Rhyolite, H2O = 4 wt%

1.00.80.60.40.20.00.0

0.2

0.4

0.6

0.8

1.0

z/L

wf = 1

wf = .85

wf = .70

wf = .55

wf = .40

wf = .15

Rhyolite, H2O = 4 wt%

k = 1

k = 0

a

b

Distribution of gas volume Distribution of gas volume fraction along the volcanic fraction along the volcanic conduit.conduit.

Black linesBlack lines: total gas volume : total gas volume fraction, and wfraction, and wff = 1 = 1

Blue linesBlue lines: continuous gas : continuous gas volume fractionvolume fraction

The presence of pumice The presence of pumice results in a much lower gas results in a much lower gas volume fraction above volume fraction above fragmentation than previously fragmentation than previously supposed.supposed.

after Papale, JGR 2001

0.0

0.2

0.4

0.6

0.8

1.0

1.0 0.8 0.6 0.4 0.2 0.0fragmentation efficiency, w f

Par

ticl

e vo

lum

e fr

acti

on a

t fr

agm

enta

tion

the amount of pumice increases

Volume fraction of Volume fraction of particles at the level where particles at the level where magma fragmentation magma fragmentation occursoccurs

Large possible volume fractions of particles in the volcanic Large possible volume fractions of particles in the volcanic conduit require the introduction of a normal stress term due to conduit require the introduction of a normal stress term due to particle-particle interactions in the particle momentum equationparticle-particle interactions in the particle momentum equation

1.0 0.8 0.6 0.4 0.2 0.0fragmentation efficiency, wf

0.86

0.88

0.90

0.92

0.94

0.96

0.98

0.45

0.55

0.65

0.75

0.85

0.95

a

b

Exi

t tot

al g

as v

olum

e fr

acti

onE

xit c

onti

nuou

s ga

s vo

lum

e fr

acti

on

Total and continuous gas Total and continuous gas volume fractions at the volume fractions at the conduit exit.conduit exit.

Black linesBlack lines: k = 1 (equilibrium : k = 1 (equilibrium pumice degassing)pumice degassing)

Blue linesBlue lines: k = 0 (maximum : k = 0 (maximum nonequilibrium pumice degassing)nonequilibrium pumice degassing)

• The total gas volume fraction The total gas volume fraction only changes for noneq. only changes for noneq. pumice degassingpumice degassing

• The continuous gas volume The continuous gas volume fraction always decreases with fraction always decreases with increasing pumice contentincreasing pumice content

• The extent of changes The extent of changes strongly depends on the strongly depends on the eruptive conditionseruptive conditions

D1150/4

R1100/2

R1100/4/30

R1100/4_2

R1100/4

R1100/6

k = 1k = 0

Mechanical energy content of Mechanical energy content of the magmatic mixture at the the magmatic mixture at the

conduit exitconduit exit

atm

eGe

eTe P

PRTw

uE ln

2

2

76543210

4

8

12

16

water content (wt%)

Dacite, D = 127 mDacite, D = 80 m

Rhyodacite, D = 127 mRhyolite, D = 127 m

Rhyolite, D = 80 m

Collapsing

Transit ional

Plinian

Previous investigations with wf = 1 (Papale, Neri, and

Macedonio, JVGR 1998a,b)

Exi

t mec

hani

cal e

nerg

y (m

2 /s2 x

10-4

)

0

5

10

15

fragmentation efficiency, w f

k = 0

a

b

1.0 0.8 0.6 0.4 0.2 0.00.2

0.4

0.6

0.8

1.0

1.2

CONDUIT4:

Exi

t mec

hani

cal e

nerg

y (m

2 /s2 x

10-4

)N

orm

aliz

ed e

xit m

echa

nica

l ene

rgy

k = 1

k = 0

CONDUIT4CONDUIT4::

Particularly suitable to account for compositional effects in Particularly suitable to account for compositional effects in the dynamic of sustained eruptionsthe dynamic of sustained eruptions

Detailed studies on sustained phases of explosive eruptions Detailed studies on sustained phases of explosive eruptions can be donecan be done

Powerful tool to get insights into the large-scale dynamics of Powerful tool to get insights into the large-scale dynamics of explosive eruptions, especially when coupled to atmospheric explosive eruptions, especially when coupled to atmospheric dispersion modeling (e.g., PDAC-2D, dispersion modeling (e.g., PDAC-2D, Neri et alNeri et al., in press)., in press)

• 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

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

Coupled numerical simulations of conduit Coupled numerical simulations of conduit flow and pyroclast dispersalflow 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-workerswith Augusto Neri and co-workers

M a s s B a l a n c e :

G A S P H A S E ( b u b b l e s b e l o w f r a g m e n t a t i o n , c o n t i n u o u s a b o v e i t )

D E N S E P H A S E ( l i q u i d + c r y s t a l s b e l o w f r a g m e n t a t i o n , p a r t i c l e s / d r o p l e t s a b o v e i t )

M o m e n t u m B a l a n c e :

G A S P H A S E ( b u b b l e s b e l o w f r a g m e n t a t i o n , c o n t i n u o u s a b o v e i t )

D E N S E P H A S E ( l i q u i d + c r y s t a l s b e l o w f r a g m e n t a t i o n , p a r t i c l e s / d r o p l e t s a b o v e i t )

dz

dwmu

dz

d GAGG

dz

dwmu

dz

d GADD 1

dz

dwmuuuuFg

dz

dP

dz

duu G

ADGDGwGGG

GG

dz

d

dz

dwmuu

uuFgdz

dP

dz

duu

sGADG

DGwDDD

DD

1

111

TPLDVL

DVCC

DV

C

CiC

CiCiLCD

DV

DV

oVTCG

wwdw

d

dz

dw

w

ww

dz

dw

,

2

1

1

11

1

1

11

Constitutive equations for mass balance

Bubbly flow region:

const

wwww

www

ww

ww

w

w

ww

ww

CiCiC

CCf

LfSf

DffGffmf

mfPf

GfCfSfPf

PfTCCf

TCmf

GffPf

Gfff

fTC

f

mf

Gff

TCGf

SfPf

Sff

1

1

1

1

1

11

1

1

11

Constitutive equations for mass balance

At fragmentation:

Constitutive equations for mass balance

Gas-particle/droplet flow region:

1

,

,

,2

,

,

,

,

11

11

1

1

1

11

1

P

GPfPDV

PDVDVfCTCPf

GffDVfPfP

SDV

SDV

fDVSf

S

GP

GP

P

PDV

GPPDV

CPGPPP

SPG

G

w

wwwwwww

dz

dw

w

ww

dz

dw

dz

dw

w

w

dz

dw

ww

www

dz

dwdz

dw

dz

dw

dz

dw

Constitutive equations for mass balance

Gas-particle/droplet flow region

(continued):

1

1

1

1

1

1

CC

C

SS

S

PP

P

D

GD

C

C

S

S

P

PGD

GP

PGf

G

d

w

d

w

d

wwd

wwww

w

w

LS

GfGGP

DPfGPfP

P

GPfGP

CfC

CSPG

SDV

DVfSfS

kk

w

constww

wwww

w

www

1

1

1

1

1

,

Constitutive equations for momentum balance

5.2,,

21

2

,

2

,,

,

2/1

; 1

1 , 0

Re ; Re

12

2,

0

||2

GGPFmD

BFm

s

GPFBF

m

A

DDsGPFwD

m

AGPFwGBFwD

BFwG

DGGfr

dz

dG

dz

d

DmB

Bf

D

ufF

D

mfFF

F

uuD

C

Constitutive equations for momentum balance

Bubbly flow region:

3/1

7.4687.0

2/13

6

||1Re

1Re15.01Re

24

18

3

Nd

uud

C

d

DCC

b

m

DGbDb

bb

D

bG

DDfr

Constitutive equations for momentum balance

Gas-particle/droplet flow region:

m

DGDGD

D

Ds

D

DD

D

DD

fr

uud

G

u

gdf

C

Cd

DC

||Re

43.576.8log

0285.0

2

Relog5.1exp65.07.3

Re15.01Re

24

1

8

3

2/1

2

687.0

2/1