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Governing equations In FEHM, the governing partial differential

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1
Governing equations
2
In FEHM, the governing partial differential equations for mass and heat transfer are
3
discretized into a system of nonlinear algebraic equations, which are then solved using the
4
Newton-Raphson iteration method (a way to find successively better approximations to the roots
5
or zeroes of a real-valued function from an initial guess). In FEHM (as opposed to some other
6
multi-physics computer codes like TOUGH2 (Pruess et al. 2012), the Newton-Raphson
7
derivatives of the thermodynamic functions with respect to pressure and temperature are formed
8
analytically rather than numerically in order to achieve faster convergence of the nonlinear
9
system of equations (Zyvoloski 2007). FEHM equations of state are nonlinear because the
10
porosity, permeability, density, enthalpy and viscosity are strong functions of pressure and
11
temperature; in addition, relative permeabilities and capillary pressure can also be strong
12
functions of saturation, which varies significantly with temperature and pressure. Pressure and
13
temperature dependent behavior of density, enthalpy and viscosity are represented by rational
14
polynomials derived from National Bureau of Standards (NBS) steam table data (Zyvoloski et al.
15
1991).
16
All variables referenced in these equations are defined in Table 5. A more detailed
17
breakdown of the equation derivation may be found in Zyvoloski et al. (1999) and Keating (
18
(2000).
19
20
21
22
23
Table 5. Variables used in FEHM governing equations
Energy/mass/noncondensible gas accumulation
terms (kg m-1 s-2)/ (kg m-3) / (kg m-3)
Specific heat (m2 s-2 °C-1)
R
S
Relative
permeability
Saturation
T
Temperature
g
flux vectors for energy/mass/noncondensible gas
equation (kg s-3)/ (kg m-2 s-1)/ (kg m-2 s-1)
gravitational acceleration (m s-2)
t
time
h
enthalpy (m2 s-2)
v
Velocity (m s-1)
k
intrinsic rock permeability (m2)
Ο•
Porosity
K
Thermal conductivity (kg m T-1 s-3)
ηvap,liq
P
Pressure (kg m-1 s-2)
μ
Mass fraction of
vapor/liquid
Viscosity (kg m-1 s1
)
Density
Ae,m,
gas
Cp
fe,m,gas
Energy/mass/noncondensible gas source term (kg m- ρ
1 -3
s )/ (kg m-3 s-1)/ (kg m-3 s-1)
Subscripts: gas = noncondensible gas, vap = vapor, liq = liquid, f = fracture, r = rock
qe
24
25
Conservation of mass for water is
πœ•π΄π‘š
26
πœ•π‘‘
Μ… ⋅ π‘“π‘šΜ… + π‘žπ‘š = 0
+∇
(1)
27
where the mass per unit volume Am (a mass accumulation term) is a function of the porosity, the
28
saturation and the mass fraction of each phase:
29
30
31
π΄π‘š = πœ™(π‘†π‘£π‘Žπ‘ πœŒπ‘£π‘Žπ‘ (1 − πœ‚π‘£π‘Žπ‘ ) + π‘†π‘™π‘–π‘ž πœŒπ‘™π‘–π‘ž (1 − πœ‚π‘™π‘–π‘ž ))
(2)
π‘“π‘šΜ… = (1 − πœ‚π‘£π‘Žπ‘ )πœŒπ‘£π‘Žπ‘ π‘£Μ…π‘£π‘Žπ‘ + (1 − πœ‚π‘™π‘–π‘ž )πœŒπ‘™π‘–π‘ž π‘£Μ…π‘™π‘–π‘ž
(3)
the mass flux is
32
and sources/sinks of mass are contained in the term π‘žπ‘š . The total of all water flux through the
33
system, water accumulated in the system, and sources/sinks of water are assumed to equal zero.
34
Conservation of fluid-rock energy is
35
πœ•π΄π‘’
πœ•π‘‘
Μ… ⋅ 𝑓𝑒̅ + π‘žπ‘’ = 0
+∇
(4)
36
where the energy per unit volume (energy accumulation term) Ae is a combination of energy
37
transferred by the rock itself, energy transferred by water vapor and energy transferred by liquid
38
water:
𝐴𝑒 = (1 − πœ™)πœŒπ‘“ πΆπ‘π‘Ÿ 𝑇 + πœ™(π‘†π‘£π‘Žπ‘ πœŒπ‘£π‘Žπ‘ πΆπ‘π‘£π‘Žπ‘ 𝑇 + π‘†π‘™π‘–π‘ž πœŒπ‘™π‘–π‘ž πΆπ‘π‘™π‘–π‘ž 𝑇)
39
(5)
40
The energy flux, 𝑓𝑒̅ , can be stated either as a sum of the products of density, specific enthalpy
41
and velocity of the vapor and liquid, or the product of the thermal conductivity and temperature
42
gradients:
𝑓𝑒̅ = πœŒπ‘£π‘Žπ‘ β„Žπ‘£π‘Žπ‘ π‘£π‘£π‘Žπ‘ + πœŒπ‘™π‘–π‘ž β„Žπ‘™π‘–π‘ž π‘£π‘™π‘–π‘ž = 𝐾𝛻̅𝑇
43
44
The conservation of noncondensible gas is described by
πœ•π΄π‘”π‘Žπ‘ 
45
46
πœ•π‘‘
49
50
51
Μ… + π‘žπ‘”π‘Žπ‘  = 0
Μ… ⋅ π‘“π‘”π‘Žπ‘ 
+∇
(7)
where the accumulation term Agas is
47
48
(6)
π΄π‘”π‘Žπ‘  = πœ™(πœ‚π‘£π‘Žπ‘ π‘†π‘£π‘Žπ‘ πœŒπ‘£π‘Žπ‘ + πœ‚π‘™π‘–π‘ž π‘†π‘™π‘–π‘ž πœŒπ‘™π‘–π‘ž )
(8)
Μ… = πœ‚π‘£π‘Žπ‘ πœŒπ‘£π‘Žπ‘ π‘£Μ…π‘£π‘Žπ‘ + πœ‚π‘™π‘–π‘ž πœŒπ‘™π‘–π‘ž π‘£Μ…π‘™π‘–π‘ž
π‘“π‘”π‘Žπ‘ 
(9)
the gas flux is
and the source and sink term qgas is
π‘žπ‘”π‘Žπ‘  = πœ‚π‘£π‘Žπ‘ π‘žπ‘£π‘Žπ‘ + πœ‚π‘™π‘–π‘ž π‘žπ‘™π‘–π‘ž
(10)
52
It is assumed that Darcy’s law applies to the movement of each phase; in this formulation, the
53
hydraulic conductivity term is replaced by the quotient of the intrinsic and relative permeabilities
54
divided by the viscosity of the phase, and the hydraulic head term is replaced with the difference
55
between the pressure gradient and lithostatic gradient:
56
π‘£Μ…π‘£π‘Žπ‘ = −
57
π‘£Μ…π‘™π‘–π‘ž = −
π‘˜π‘…π‘£π‘Žπ‘
πœ‡π‘£π‘Žπ‘
π‘˜π‘…π‘™π‘–π‘ž
πœ‡π‘™π‘–π‘ž
Μ…π‘ƒπ‘£π‘Žπ‘ − πœŒπ‘£π‘Žπ‘ 𝑔̅ )
(∇
Μ…π‘ƒπ‘™π‘–π‘ž − πœŒπ‘™π‘–π‘ž 𝑔̅ )
(∇
(11)
(12)
58
By combining equations 1 – 10 with Darcy’s law (11 & 12), the full governing equations are
59
derived for mass,
Μ… ⋅ ((1 − πœ‚π‘£π‘Žπ‘ )Θπ‘šπ‘£π‘Žπ‘ ∇
Μ…π‘ƒπ‘£π‘Žπ‘ ) − ∇
Μ… ⋅ ((1 − πœ‚π‘™π‘–π‘ž )π›©π‘šπ‘™π‘–π‘ž ∇
Μ…π‘ƒπ‘™π‘–π‘ž ) + π‘žπ‘š + πœ• 𝑔 ((1 −
−∇
πœ•π‘§
60
πœ‚π‘£π‘Žπ‘ )π›©π‘šπ‘£π‘Žπ‘ πœŒπ‘£π‘Žπ‘ + (1 − πœ‚π‘™π‘–π‘ž )π›©π‘šπ‘™π‘–π‘ž πœŒπ‘™π‘–π‘ž ) +
61
62
63
πœ•π΄π‘š
πœ•π‘‘
=0
(13)
Energy,
Μ… ⋅ (Θπ‘’π‘£π‘Žπ‘ ∇
Μ…π‘ƒπ‘£π‘Žπ‘ ) − ∇
Μ… ⋅ (π›©π‘’π‘™π‘–π‘ž ∇
Μ…π‘ƒπ‘™π‘–π‘ž ) + π‘žπ‘’ + πœ• 𝑔(π›©π‘’π‘£π‘Žπ‘ πœŒπ‘£π‘Žπ‘ + π›©π‘’π‘™π‘–π‘ž πœŒπ‘™π‘–π‘ž ) + πœ•π΄πœ‚π‘”π‘Žπ‘  = 0
−∇
πœ•π‘§
πœ•π‘‘
64
65
66
67
(14)
and noncondensible gas:
Μ… ⋅ (πœ‚π‘£π‘Žπ‘ Θπ‘šπ‘£π‘Žπ‘ ∇
Μ…π‘ƒπ‘£π‘Žπ‘ ) − ∇
Μ… ⋅ (πœ‚π‘™π‘–π‘ž π›©π‘šπ‘™π‘–π‘ž ∇
Μ…π‘ƒπ‘™π‘–π‘ž ) + ∇
Μ… ⋅ (π·π‘£π‘Ž ∇
Μ…πœ‚π‘£π‘Žπ‘ ) + π‘žπœ‚π‘”π‘Žπ‘  +
−∇
πœ•
𝑔(πœ‚π‘£π‘Žπ‘ π›©π‘šπ‘£π‘Žπ‘ πœŒπ‘£π‘Žπ‘ + πœ‚π‘™π‘–π‘ž π›©π‘šπ‘™π‘–π‘ž πœŒπ‘™π‘–π‘ž ) +
πœ•π‘§
πœ•π΄πœ‚π‘”π‘Žπ‘ 
πœ•π‘‘
=0
(15)
68
Transmissibilities, a measure of how easily a given layer transmits water, are represented by Θ in
69
the equations and are given by
π‘˜π‘…π‘£π‘Žπ‘ πœŒπ‘£π‘Žπ‘
70
π›©π‘šπ‘£π‘Žπ‘ =
71
π›©π‘šπ‘™π‘–π‘ž =
72
Θevap = hvap Θmvap
(18)
73
π›©π‘’π‘™π‘–π‘ž = β„Žπ‘™π‘–π‘ž π›©π‘šπ‘™π‘–π‘ž
(19)
74
75
(16)
πœ‡π‘£π‘Žπ‘
π‘˜π‘…π‘™π‘–π‘ž πœŒπ‘™π‘–π‘ž
(17)
πœ‡π‘™π‘–π‘ž
The air/water diffusivity term Dva is given by
0
π·π‘£π‘Ž = πœπœ™π‘†π‘£π‘Žπ‘ π·π‘£π‘Ž
πœŒπ‘£π‘Žπ‘
0.101325 𝑇+273.15 π‘š
𝑃
[
273.15
]
(20)
76
where 𝜏 is the tortuosity factor (for diffusion in porous media, a measure of how circuitous a
77
typical flow path is through a medium), D (standard conditions) = 2.4e-5 m2/s and m = 2.334
78
(Zyvoloski et al. 1997). Transmissibilities are given by
π‘˜π‘…π‘£π‘Žπ‘ πœŒπ‘£π‘Žπ‘
79
π›©π‘šπ‘£π‘Žπ‘ =
80
π›©π‘šπ‘™π‘–π‘ž =
81
π›©π‘’π‘£π‘Žπ‘ = β„Žπ‘£π‘Žπ‘ π›©π‘šπ‘£π‘Žπ‘
(23)
82
π›©π‘’π‘™π‘–π‘ž = β„Žπ‘™π‘–π‘ž π›©π‘šπ‘™π‘–π‘ž
(24)
πœ‡π‘£π‘Žπ‘
π‘˜π‘…π‘™π‘–π‘ž πœŒπ‘™π‘–π‘ž
πœ‡π‘™π‘–π‘ž
(21)
(22)
83
The nonisothermal multiphase transport model in FEHM is formed by equation 13, 14 and 15,
84
setting n = 0 in Equation 13 and leaving out Equation 15 in the pure-water model.
85
86
Relative permeability
87
In cases where the system being modeled in FEHM does not remain fully saturated,
88
FEHM is capable of calculating relative permeability using either a linear, Corey-Brooks
89
(Brooks and Corey 1964), or van Genuchten formulation (van Genuchten 1980). The linear
90
formulation used in this study depends only on the residual liquid and vapor saturations and was
91
chosen for simplicity. Linear functions for relative permeabilities of liquid (the wetting fluid, in
92
this case water) and vapor (the ‘nonwetting fluid’) are defined by the equations
0,
93
94
𝑆𝑙 −π‘†π‘™π‘Ÿ
𝑅𝑙 = {𝑆
π‘™π‘šπ‘Žπ‘₯ −π‘†π‘™π‘Ÿ
𝑅𝑣 = {𝑆
𝑆𝑙 ≤ π‘†π‘™π‘Ÿ
π‘†π‘™π‘Ÿ < 𝑆𝑙 < π‘†π‘™π‘šπ‘Žπ‘₯
1,
𝑆𝑙 ≥ π‘†π‘™π‘šπ‘Žπ‘₯
0,
𝑆𝑣 ≤ π‘†π‘£π‘Ÿ
𝑆𝑣 −π‘†π‘£π‘Ÿ
π‘£π‘šπ‘Žπ‘₯ −π‘†π‘£π‘Ÿ
1,
π‘†π‘£π‘Ÿ < 𝑆𝑣 < π‘†π‘£π‘šπ‘Žπ‘₯
(27)
(28)
𝑆𝑣 ≥ π‘†π‘£π‘šπ‘Žπ‘₯
95
where Sl and Sv are liquid and vapor saturations, Slr and Svr are the residual liquid and vapor
96
saturations, and Slmax and Svmax are the maximum liquid and vapor saturations.
97
98
99
Table 6. Material properties of andesite and dacite lavas and pyroclastic deposits
Reference
Location
Sample
size/type
Rock type
(Aizawa et
al. 2009)
Conceptual
Unknown
(Bartetzko et
al. 2006)
(Bernard et
al. 2007)
Undersea
basin,
PACMANUS
field
Mount Pelée
Density
(kg/m3)
Porosity
(φ)
Permeability
(m2)
Sealing zone
0.01
3.00E-16
Unknown
Basement
0.05
3.00E-16
Unknown
Hydrothermal zone
0.1
3.00E-15
Unknown
0.3
1.00E-13
Unknown
Fractured rock
surrounding
hydrothermal zone
Conduit
0.1
1.00E-12
Unknown
Fresh volcanic rock
0.3
1E-13 - 2E-14
Drill core
Dacite
0.22
1.25E-17
Drill core
Dacite
0.32
2.23E-17
Drill core
Dacite
0.24
4.48E-17
Drill core
Dacite
0.3
1.04E-16
Drill core
Dacite
0.24
4.46E-16
Drill core
Dacite
0.38
7.59E-16
Drill core
Dacite
0.21
1.50E-15
Drill core
Dacite
0.43
2.00E-15
Drill core
Dacite
0.01
1.17E-14
Drill core
Dacite
0.16
Drill core
Dacite
0.17
Drill core
Dacite
0.17
Drill core
Dacite
0.2
Drill core
Dacite
0.21
Drill core
Dacite
0.22
Hand
sample
Hand
sample
Hand
sample
Hand
sample
Hand
sample
Hand
sample
Hand
sample
Hand
sample
Hand
sample
Hand
sample
Hand
sample
Hand
sample
Hand
sample
MB502
2700
0.038
1.00E-16
LPP Calebasse
2850
0.031
1.00E-15
LPP Plume
2890
0.035
1.00E-15
andesite, B&A flows
2780
0.099
1.00E-15
MB501
2740
0.102
1.00E-15
LPP Macouba
2760
0.134
1.00E-15
andesite dome
2720
0.098
2.00E-15
andesite, nuee ardente
flows
andesite, indurated
block and ash flows
andesite, indurated
block and ash flows
andesite, indurated
block and ash flows
andesite dome
2690
0.119
2.90E-15
2720
0.103
3.00E-15
2690
0.146
3.00E-15
2720
0.111
3.90E-15
2740
0.121
3.90E-15
andesite dome
2740
0.154
3.90E-15
Thermal
conductivity
(W/mK)
Specific
heat
(J/kgK)
Hand
sample
Hand
sample
Hand
sample
Hand
sample
Hand
sample
Hand
sample
Hand
sample
Hand
sample
Hand
sample
Hand
sample
Hand
sample
Hand
sample
Hand
sample
Hand
sample
Hand
sample
Hand
sample
Hand
sample
Hand
sample
Hand
sample
Hand
sample
Hand
sample
Hand
sample
Hand
sample
Hand
sample
Hand
sample
Hand
sample
Hand
sample
Hand
sample
Hand
sample
Hand
sample
Hand
sample
Hand
sample
Hand
sample
Hand
sample
Hand
sample
andesite, nuee ardente
flows
andesite, indurated
block and ash flows
andesite, indurated
block and ash flows
andesite, nuee ardente
flows
andesite, indurated
block and ash flows
andesite, nuee ardente
flows
andesite, nuee ardente
flows
andesite, nuee ardente
flows
andesite, indurated
block and ash flows
andesite, nuee ardente
flows
andesite, nuee ardente
flows
andesite, ash-andpumice flows
andesite, nuee ardente
flows
andesite, nuee ardente
flows
andesite, ash-andpumice flows
andesite, indurated
block and ash flows
andesite, indurated
block and ash flows
andesite, ash-andpumice flows
andesite, indurated
block and ash flows
andesite, indurated
block and ash flows
andesite, nuee ardente
flows
andesite, scoria flows
2670
0.157
3.90E-15
2670
0.353
3.90E-15
2770
0.145
4.90E-15
2670
0.169
5.90E-15
2710
0.132
8.90E-15
2670
0.19
1.09E-14
2670
0.099
1.88E-14
2690
0.158
3.85E-14
2720
0.149
5.53E-14
0.312
5.92E-14
2670
0.174
1.09E-13
2650
0.574
1.44E-13
2700
0.197
1.67E-13
2690
0.146
2.04E-13
2630
0.547
2.07E-13
2620
0.213
2.27E-13
2760
0.24
2.54E-13
2650
0.536
4.25E-13
2620
0.232
5.54E-13
2630
0.321
5.70E-13
2670
0.415
6.70E-13
2810
0.28
1.03E-12
andesite, ash-andpumice flows
andesite, nuee ardente
flows
andesite, nuee ardente
flows
andesite, scoria flows
2670
0.574
1.18E-12
2700
0.304
1.18E-12
2670
0.428
1.45E-12
2860
0.363
1.54E-12
andesite, nuee ardente
flows
andesite, indurated
block and ash flows
andesite, ash-andpumice flows
andesite, nuee ardente
flows
andesite, indurated
block and ash flows
andesite, scoria flows
2690
0.251
1.58E-12
2680
0.305
1.77E-12
2670
0.578
2.05E-12
2680
0.274
2.91E-12
2710
0.289
5.06E-12
2840
0.352
5.69E-12
andesite, ash-andpumice flows
andesite, block and ash
flows
andesite, block and ash
flows
2650
0.617
7.66E-12
2710
0.328
1.02E-11
2670
0.408
3.44E-11
(Flint et al.
2006)
Yucca
Mountain
(García et al.
1989)
Los Azufres
(Hicks et al.
2009)
(Hurwitz et
al. 2003)
Soufriere
Hills
Cascades
Hand
sample
Drill core
andesite, ash-andpumice flows
Pyroclastic unit
2670
0.585
1490
0.341
Drill core
Pyroclastic unit
1600
0.322
Drill core
Andesite
2053
0.02
1.05
Drill core
Andesite
2737
0.24
2.34
Hand
sample
Conceptual
Andesite
2600
0.2
2500
0.15
Conceptual
Conduit (numerical
model)
Upper unit (numerical
model)
Basal unit
2500
0.01
Drill core
Volcanic breccia
2400
0.15
Drill core
Lava dike
2500
0.15
Drill core
Lava dike
2600
0.15
Drill core
Volcanic breccia
2500
0.3
Conceptual
Lava flows and domes
younger than 2.3 Ma
Lava flows and minor
pyroclastic rocks from
4-8 Ma
Lava flows from 8 to
17 Ma
Chiefly volcanic and
volcaniclastic strata
from 18-25 Ma
Quartz-bearing ash
flow tuff
Dome rock
Conceptual
(Ikeda et al.
2008)
(Ingebritsen
et al. 1994)
Unzen
Cascades
Conceptual
Conceptual
Conceptual
Conceptual
(Keating
2005)
(Mueller et
al. 2008)
Mount St.
Helens
Unzen
(Platz et al.
2012)
(Reid 2004)
Mt. Taranaki
(Sammel et
al. 1988)
Newberry
Cascades
volcanoes
Hand
sample
Hand
sample
Hand
sample
Hand
sample
Hand
sample
Hand
sample
Hand
sample
Hand
sample
Cores from
clasts
"typical of
volcanic
rocks"
Conceptual
1.00E-10
2
2500
2
2.5
0.15
1.00E-14
1.55
0.1
5.00E-16
1.55
0.05
1.00E-16
1.65
0.05
1.00E-17
2
0.02
2.50E-14
2
2200
0.6
2.10E-14
0.9
1557
2200
0.25
1.00E-15
0.35
2036
2200
0.62
4.66E-14
0.35
2036
0.367
8.90E-14
0.475
1.47E-13
0.343
9.99E-13
Dacite, dome rock
0.349
3.41E-12
Dacite, dome rock
0.412
4.50E-12
14.47
918
2
1000
Pyroclastic flow
deposits (substrate)
Pyroclastic flow
deposits
Dacite, breadcrust
bomb
Dacite, breadcrust
bomb
Dacite, dome rock
andesite dome
2555
Unknown
2650
6.80E-13
Fill
1E-14 - 5E-12
Conceptual
Dikes and pipe
5.00E-15
Conceptual
Flow 1
1E-15 - 1E-13
Conceptual
Flow 2
1E-16 - 1E-14
Conceptual
Flow 3
1E-17 - 1E-15
Conceptual
Flow 4
5E-16 - 1E-13
Conceptual
Flow 5
1E-18 - 1E-16
Conceptual
Magma
1.00E-18
(Scheu et al.
2006)
(Sekioka
1988)
(Smith et al.
2001)
(Watanabe et
al. 2008)
100
101
102
103
104
Unzen
Japanese
geothermal
fields
Japanese
geothermal
fields
Japanese
geothermal
fields
Japanese
geothermal
fields
Japanese
geothermal
fields
Japanese
geothermal
fields
Japanese
geothermal
fields
Mount St.
Helens
Unzen
Hand
sample
Hand
sample
Hand
sample
Hand
sample
Hand
sample
Hand
sample
Calculated
Dacite
2490
0.041
Dacite
2420
0.073
Dacite
2280
0.12
Dacite
2180
0.163
Dacite
2100
0.193
Dacite
1930
0.259
Unknown
1.10E-12
2.04
Calculated
Unknown
3.50E-13
2.33
Calculated
Unknown
1.90E-12
3.43
Calculated
Unknown
2.10E-12
2.87
Calculated
Unknown
2.00E-12
1.49
Calculated
Unknown
5.00E-14
0.93
Calculated
Unknown
1.70E-12
1.65
Cores from
spine
samples
Cores from
spine
samples
Cores from
spine
samples
Cores from
spine
samples
Cores from
spine
samples
Drill core
dacite
2460
0.08
dacite
2390
0.095
dacite
2350
0.103
dacite
2260
0.121
dacite
2040
0.197
2410
0.08
1.00E-19
Drill core
C1-5-7, Brecciated
dacite
C14, Dacite dike
2500
0.16
1.00E-19
Drill core
C12, Volcanic breccia
2400
0.02
1.00E-17
Drill core
C14-2, Dacite dike
2560
0.04
1.00E-17
Drill core
C13, Dacite dike
2570
0.08
1.00E-17
105
106
107
Aizawa K, Ogawa Y, Ishido T (2009) Groundwater flow and hydrothermal systems within
volcanic edifices: Delineation by electric self-potential and magnetotellurics. J Geophys Res
114:1–12. doi: 10.1029/2008JB005910
108
109
110
Bartetzko A, Klitzsch N, Iturrino G, et al (2006) Electrical properties of hydrothermally altered
dacite from the PACMANUS hydrothermal field (ODP Leg 193). J Volcanol Geotherm Res
152:109–120. doi: 10.1016/j.jvolgeores.2005.10.002
111
112
113
Bernard ML, Zamora M, Géraud Y, Boudon G (2007) Transport properties of pyroclastic rocks
from Montagne Pelée volcano (Martinique, Lesser Antilles). J Geophys Res Solid Earth
112:1–16. doi: 10.1029/2006JB004385
114
115
Brooks RH, Corey a T (1964) Hydraulic properties of porous media. Hydrol Pap Fort Collins CO
Colo State Univ 3:27 pgs.
116
117
118
Flint LE, Buesch DC, Flint AL (2006) Characterization of Unsaturated Zone Hydrogeologic
Units using Matrix Properties and Depositional History in a Complex Volcanic
Environment. Vadose Zo J 5:480. doi: 10.2136/vzj2004.0180
119
120
121
García A, Contreras E, Viggiano JC (1989) Establishment of an empirical correlation for
estimating the thermal conductivity of igneous rocks. Int J Thermophys. doi:
10.1007/BF00503174
122
123
124
Hicks PD, Matthews AJ, Cooker MJ (2009) Thermal structure of a gas-permeable lava dome and
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10.1029/2008JB006198
125
126
127
Hurwitz S, Kipp KL, Ingebritsen SE, Reid ME (2003) Groundwater flow, heat transport, and
water table position within volcanic edifices: Implications for volcanic processes in the
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128
129
130
Ikeda R, Kajiwara T, Omura K, Hickman S (2008) Physical rock properties in and around a
conduit zone by well-logging in the Unzen Scientific Drilling Project, Japan. J Volcanol
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131
132
Ingebritsen SE, Mariner RH, Sherrod DR (1994) Hydrothermal systems of the Cascade Range,
north-central Oregon.
133
134
Keating GN (2000) Multiphase thermal modeling in volcanic and contact metamorphic terranes.
242.
135
136
Keating GN (2005) The role of water in cooling ignimbrites. J Volcanol Geotherm Res 142:145–
171. doi: 10.1016/j.jvolgeores.2004.10.019
137
138
Mueller S, Scheu B, Spieler O, Dingwell DB (2008) Permeability control on magma
fragmentation. Geology. doi: 10.1130/G24605A.1
139
140
Platz T, Cronin SJ, Procter JN, et al (2012) Non-explosive, dome-forming eruptions at Mt.
Taranaki, New Zealand. Geomorphology 136:15–30. doi: 10.1016/j.geomorph.2011.06.016
141
142
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143
144
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145
146
Sammel EA, Ingebritsen SE, Mariner RH (1988) The hydrothermal system at Newberry
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147
148
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149
150
151
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152
153
154
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155
156
157
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158
159
160
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161
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168
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