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