P R E P R I N T – ICPWS XV
Berlin, September 8–11, 2008
Explosive Properties of Water in Volcanic and Hydrothermal Systems
Régis Thiérya and Lionel Mercuryb
a
: Laboratoire Magmas et Volcans, UMR 6524, CNRS/Clermont Université
Email: [email protected]
b
: Institut des Sciences de la Terre d'Orléans, UMR 6113, CNRS/Université d'Orléans
Email: [email protected]
Water is the main explosive agent on Earth. Terrestrial volcanism is mainly produced by two
end-member processes, where water plays an important role: (1) first, the depressurization of a
H2O-rich magma, followed by its violent water exsolution and expansion of a steam-pyroclasts
mixture (plinian volcanism), and, (2) the explosive interaction of cold liquid water with hot
magma (phreato-magmatism). Thus, volcanological models requires a good assessment of the
energetic properties of water and physico-chemical processes. The energetic balance of volcanic
eruptions has been reassessed here with the help of the Wagner and Pruss equation of state [1]
and by taking into account the irreversibility of steam expansion into the atmosphere. Next, it is
shown how other aspects of water explosivity in volcanic and hydrothermal environments can be
linked fruitfully to recent concepts about water metastability.
Introduction
Magmatic, volcanic and hydrothermal processes
are associated with the explosive release of energy
that is produced essentially by the mechanical work
of exsolution and expansion of fluids, mainly
composed of water. In particular, most explosive
volcanism is typically produced by two types of
situations [2]: (1) plinian volcanism and (2)
phreato-magmatism. The former is caused by the
violent decompression of pressurized gases, which
exsolve from a fluid-rich and viscous magma
during its ascent through the crust; the latter is
produced by the explosive boiling of large
quantities of liquid water at the contact of hot
magma. Besides these cataclysmic phenomena, one
can also mention other eruptive manifestations, less
violent, but which are also produced by water:
geysering, hydrothermal eruptions [3] and other
types of volcanism [2] (strombolian volcanism, ...).
Thus, water is the main explosive agent on Earth.
Therefore, the assessment of the energy released by
volcanic eruptions is one of the primary goals of
volcanology. The rate of energy release, i.e. the
power of explosions, is another important
parameter to tackle, and there is a strong need to
understand the factors, which control the
explosivity of water. For this reason, the energetic
properties of water have been already the subject of
numerous studies in volcanology and magmatology,
both through experimentation and modeling [4-9].
The present contribution tries to address these
questions by thermodynamic modeling with the
recent reference equation of Wagner and Pruss [1]
for water. In the first part, we present the different
processes, which transform water into an explosive
substance. In particular, we will show how the
explosive transformations of water can be linked to
its metastability degree. In the second part, the
energetic contributions of the different physical
transformations of water are quantified. Finally, in
the third part, we will give some application
examples of our approach to geological problems.
What Makes Water an Explosive?
An explosion is always the response of a system
to a physico-chemical perturbation, which has left it
in an energetic, metastable or unstable state. As a
consequence, the characterization of water
metastability can give us some indications about the
explosive nature of these transformations. This
work follows a phenomenological approach [10],
based on classical thermodynamics and equations
of state. Indeed, it is well known that the stability of
a fluid is ruled by important relations, which are the
consequences of the second law of thermodynamics
that are:
- the thermal stability criterion:
(∂S/∂T)v > 0,
- and the mechanical stability criterion:
(∂P/∂v)T > 0.
to more or less vigorous boiling. In the case of a
transient decompression, the stretched and
superheated liquid relaxes rapidly to equilibrium by
the collapse of microscopic gas cavities, giving rise
to the well-known process of cavitation. The
concentration of mechanical energy on these
imploding bubbles has important consequences: the
pressure reequilibration inside the bubbles (see the
upward arrow in Figure 1) shifts the gas into the
field of supercooled gases and leads to phenomena,
like sonolumininescence, sonochemistry and
cleansing of solid surfaces [15].
As a result, the phase diagram of water is
subdivided into three main regions:
- (1) the instability region, where the stability
criteria are not respected by the equation of state of
the fluid. Thus, the fluid demixes spontaneously by
the rapid phase-separation process of spinodal
decomposition [11].
- and the metastable (2) and stable (3) fields,
where stability criteria are obeyed. However, in the
metastability field, a biphasic liquid-gas association
is found to be more stable, and a monophasic fluid
is expected to demix by the process of nucleation
and phase growth [11].
These three regions are represented in Figure 1
for water in a pressure-temperature diagram. The
most interesting elements for our concerns are the
two spinodal curves, which delimit the boundaries
between the metastable and the unstable regions.
The liquid spinodal curve, noted Sp(L), marks the
ultimate theoretical limit where a liquid can subsist
in a superheated state without boiling. The gas
spinodal curve, noted Sp(G), delimits the stability
field of metastable supercooled gas, which should
relax to equilibrium by condensation. One
important point is that the violence of a physical
transformation can be linked to its proximity degree
to spinodal curves: a system is expected to react all
the more explosively when it approaches a spinodal
curve.
Figure 1: The P-T phase diagram of water
illustrating the different perturbation
processes that shift water into
metastable or unstable states.
The different physical transformations leading
to explosive phenomena are displayed in Figure 1.
The first case is illustrated by rapid heating of
liquid water at the contact of a magma, which can
trigger explosive boiling, when the liquid
temperature is abruptly shifted above the spinodal
temperature (Tsp=320.45°C at 1 bar) up to the
unstable field. The second case is represented by
the sudden decompression of a pressurized
reservoir under earth. Depending upon the initial
temperature of the fluid, the decompression can
perturb the system up to unstable conditions. This is
effectively the case of water depressurizations
occurring between 320°C and 374°C, where the
decompression path cuts the liquid spinodal curve,
producing a violent and explosive boiling. Such
phenomena are well feared by safety engineers of
the chemical industry, where they are known as
BLEVE [12,13] (Boiling Liquid Expansion Vapour
Explosion). The violence of the reaction can be
attributed to spinodal decompositions of liquid
water [11]. Cooler liquid reservoirs show a higher
resilience to sudden depressurizations and can even
bear negative pressures [14]. A pressure drop leads
The Explosive Energy of Water
The energy of volcanic eruptions is provided
essentially by three contributions: (1) the exsolution
work of water from magma, (2) the expansion work
of pressurized steam, and (3) the vaporization work
of boiling liquids. The first contribution is an
important energy source [16], but is not considered
here, as no equation of state has been yet developed
for water-magma systems. The second one is
always present, and the third one is important only
for phreato-magmatic eruptions.
One arguable point is related to the assessment
of the expansion work of steam, which is always
estimated by current volcanological models [2,5]
under the hypothesis of reversible transformations.
In other words, the decompression energy is
calculated by a difference of the internal energy (U)
between initial (i) and final (f) states:
W = U f − Ui ,
2
(curve G(L)) or saturated liquids (curve
L(G)), as a function of the initial saturation
temperature Tsat. The mechanical energy is
calculated either under the reversibility
assumption
(solid
line)
or
the
irreversibility one (dashed line). CP refers
to the critical point.
for an adiabatic and reversible process. However, it
is well accepted that this formula overestimates
strongly the expansion work. A better solution is to
take irreversibility into account through the
following relation:
W = −Patm v f − v i ,
(
)
where vi and vf are the molar volumes of water at
initial and final states, and the expansion work is
calculated against the atmospheric pressure Patm.
This is what has been done in this work, where
energies have been calculated with the Wagner and
Pruss equation of state [1] by using a general
package for thermodynamic calculations [17].
Calculated values (in J/g of water) are given
respectively for a monophasic gas system (Figure 2)
and a biphasic liquid-gas mixture (Figure 3). These
values amount to 25% - 30% of those yielded by
the reversibility hypothesis, and provide more
realistic estimations of eruptive impacts (e.g. mass
and velocities of ejecta).
The energy produced by isobaric vaporization and
heating of initial liquid water, which is an important
energetic source in phreato-magmatic and
hydrothermal eruptions, can be estimated from:
W = (H f −U f ) − (H i − U i ) .
Corresponding mechanical work can be estimated
graphically from Figure 4. For instance, the
maximal vaporization work (almost 200 J/g) is
produced by the boiling of liquid water at 222°C
and 24 bar.
Figure 4: A T-(H-U) diagram to calculate the
energy produced by isobaric vaporization
and heating of liquid water. The isobaric
mechanical work between initial state (A)
and final state (B) is given by: W=WB-WA.
Figure 2: A P-T diagram showing: (1) the energy
produced by the steam expansion (solid
curves), and (2) the mass liquid fraction
after expansion (dashed curves).
Geological applications
a) Explosivity of Hydrothermal and Volcanic
Systems
A rough classification of the different types of
hydrothermal and volcanic systems can be done in a
pressure-enthalpy diagram (Figure 5). This
typology is first based on the energetic contents of
these systems. From the left to the right (i.e. from
the less to the more energetic), one can distinguish:
-
Figure 3: The expansion work (W) produced by
the depressurization of saturated steams
3
liquid-dominated geothermal systems (case
A).
-
-
deep geothermal systems (case B), typically
found in the lithocaps of magmatic
chambers [18], or in oceanic hydrothermal
systems (black smokers of oceanic ridges).
vapour-dominated geothermal systems
(case C).
water exsolved by magmas during their
ascent through the crust that is at the origin
of plinian and vulcanian volcanism (case D).
and superficial waters (case E) which have
been heated at the contact of magma
(phreato-magmatism).
Figure 5: An H-P diagram showing the different
types of hydrothermal and volcanic
systems. The thick dotted curves are the
spinodals. The thin dashed curves are
isotherms. The thin solid lines are
isentropic expansion curves and are
labelled by the initial temperature of the
fluid at 1000 bar. The shaded area
indicates
explosive
superspinodal
decompressions.
Besides the intensity of the energy transfer
involved in these systems, another differentiating
point is related to their explosivity degree. This last
feature can be estimated by considering the
intersections of the expansion pathways followed
by water with the spinodal curves and the unstable
fields of the phase diagram. Decompression paths,
approximated by isentropic expansions, have been
drawn in Figure 5. Depending upon the incursion or
not of these pathways into the instability field, two
contrasted situations can be recognized:
subspinodal decompressions and superspinodal
ones. Superspinodal decompressions differ from the
former by liquid boiling up to the unstable field. As
a result, they are featured by explosive boiling (like
BLEVE). It can be observed in Figure 5 that most
liquid-dominated geothermal systems will exhibit
subspinodal decompressions (case A), whereas
deeper geothermal ones (case B) will be
characterized by explosive superspinodal eruptions.
Another explosive situation is represented by
phreato-magmatism, where water is brutally shifted
from point A to point E through the instability field
of water. Case D is also characterized by an
explosive exsolution of water from magma (but this
phenomenon cannot be featured in Figure 5).
b) Global Thermodynamic Analysis of
Hydromagmatism
Another diagram [2,5,6] of interest in
volcanology is given in Figure 6. These curves give
the amount of mechanical energy produced by the
interaction of one gram of magma with a mass m
(in grams) of cold liquid water. Such curves point
out the key control played by the amount of water
in phreato-magmatic (or hydromagmatic) processes.
Most explosive conditions are encountered for m
between 0.1 and 0.5. Below this optimal range,
water is shifted to explosive conditions, but is not
abundant enough to drive a large explosion. Above
this range, water is not heated strongly enough to
behave in an explosive way. Figure 6 presents
revised curves, which have been recalculated under
the hypothesis of irreversibility with the equation of
state of Wagner and Pruss [1]. Again, the explosive
character of the magma-water interaction can be
assessed from the theoretical peak temperature (Tp)
reached by water: when this temperature exceeds
the liquid spinodal temperature (Tsp=320.45°C at 1
bar), a most explosive boiling process can be
expected.
4
eruptive phenomena are influenced by numerous
parameters, the influence of the porosity is a
question which merits further investigations.
Figure 6: The mechanical energy Em (J/g of magma)
produced by the interaction of one gram of
magma and m grams of water. Solid
curves are calculated for different magma
temperatures (from 400°C to 1500°C).
Dotted curves indicate the equilibrium
temperature (Tp) of magma and water after
a first interaction step. The shaded area
indicates explosive conditions.
Figure 7: The boiling curves of water in finely
porous media. The solid line is the
saturation curve, whereas the dotted curves
indicate the pressure of liquid. The
numbers indicate the bubble radius.
d) Instabilities of Supercooled Steams along WaterMagma Interfaces
The thin film of vapour, which develops at the
interface between magma and liquid water, is
known to be affected by numerous fluid instabilities
[5,6], like periodic film collapses, Taylor-Rayleigh
instabilities and other instabilities (Figure 8).
Therefore, such a system is in a strong state of
disequilibrium. Moreover, the frequent oscillations
of the film thickness (δ) prevents the development
of steady heat fluxes from the magma (Qin) and to
the liquid (Qout). Thus, the system is both anisobaric
(Pliq≠Pvap)
and
anisothermal
(Tliq≠Tvap).
Nevertheless, an approximate thermodynamic
description can be made at the liquid-gas interface
from
T vap = T liq + ΔT ,
c) Boiling of Superheated Liquids in Finely Porous
Formations
The occurrences of geysers and other
hydrothermal eruptions are closely linked to the
formation of superheated liquids, either by a
temperature increase or a pressure drop. The
important superheating degree is a key parameter to
create a large destabilization of the system. Thus, it
is necessary to consider any factor, which is
susceptible to generate superheat in the nature.
Interestingly, there are strong evidences that
phreato-magmatic eruptions are influenced by the
lithology of host rocks: in particular, rocks of low
porosity and permeability, like shales and siltstones,
tend to favour hydromagmatic eruptions in contrast
to highly porous formations, like sandstones [19].
For this reason, it is worthwhile to consider the
effect of small pores on the boiling properties of
water. This is done by considering (1) the Laplace
law and (2) the equality of chemical potentials (µ)
of H2O between a liquid and a vapour:
2σ
Pvap = Pliq +
,
r
(
)
(
where ΔT is a positive parameter accounting for the
thermal disequilibria between gas and liquid, and
from the equality of chemical potentials between
both phases:
μ liq (T liq , Pliq ) = μ vap (T vap , Pvap ) .
The resulting P-T conditions for the steam are given
in Figure 9. Calculations have been made for a
constant liquid temperature. This shows that the
steam is in a metastable supercooled state, which
can approach gaseous spinodal conditions under
extreme conditions. As a consequence, the film
collapse is a phenomenon, which could be ascribed
to spinodal conditions. Like cavitation, this creates
visible damage [4,5] at the solid surface (distortion
and fragmentation of magma and sediments), which
)
μ liq T , Pliq = μ vap T , Pvap ,
where σ is the liquid-gas surface tension coefficient
and r is the bubble radius. The corresponding
boiling curves calculated in Figure 7 for different
bubble radii confirm that a fine porosity can
contribute to important superheating. While natural
5
are of importance in geological formations, called
“peperites” [20].
Acknowledgements
This work has benefited from the financial support
from the ANR (Agence Nationale de la Recherche)
for the project SURCHAUF-JC05-48942.
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Conclusion
This contribution gives a brief summary of
energetic properties of water in hydrothermal and
volcanic systems. It provides a phenomenological
point of view, based on metastability concepts, to
assess the explosivity of water transformations.
While this approach can be fruitful, there remains a
lot to do, in particular: (1) to determine the spinodal
boundaries in water-gas-salts-magma systems, and
(2) to gain a more detailed and comprehensive
knowledge of destabilization processes of magmawater systems in eruptive phenomena from the
molecular scale up to the crustal scale.
6
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