Perple_X
generic hybrid molecular fluid equation-of-state solution models (GFSM)
Contents
Thermodynamic
data file modifications for GFSM
Adding/Removing species from a GFSM
Example 1
– in17b metabasalt decarbonation
Example
2 – carbon precipitation induced by methane decomposition
Example
3 – kn7, H-O-S fluid composition as a function of log[f(O2)] and
log[f(S2)]
Figures
Figure 1. Metabasalt
decarbonation, simple oxides, binary H2O-CO2 fluid
Figure 2. Metabasalt
decarbonation, redox allowed, GFSM H2O-CO2-CH4-H2
fluid
Figure 3. Modal amount and CH4-content of
the fluid
Figure 4. Excess oxygen content of the solid phase
assemblage
Figure 5. Thermal decomposition of bulk CH4 composition
fluid
Petrologists traditionally have treated molecular fluids by imposing
various simplifying assumptions (e.g., fluid-saturation or binary H2O-CO2
speciation) that are accommodated in Perple_X
by identifying certain volatile chemical components as special components in
the header
section of the thermodynamic data file. Generic hybrid molecular fluid
equation-of-state (EoS)
solution models offer an effective alternative to this treatment for systems in
which fluid-saturation is not assumed. In Perple_X,
hybrid designates any mixed-volatile
equation of state that combines different pure species EoS
(Connolly 1995).
Generic hybrid molecular fluid EoS
solution models (GFSM) are
ordinary solution models that allow hybridization, but, more importantly, do
not require the existence of internal functions to compute the equilibrium
speciation of the fluid. This page describes how to
use and modify GFSM.
In
case you’re not convinced, a few petrological examples of why GFSM are useful:
Phase-saturation (as opposed to
component-saturation) is a strong (i.e., bad) assumption, both because the bulk
chemistry necessary to validate the assumption is a function of physical
conditions and because it is assumed that all possible compositions of the
fluid are stable at all conditions. These assumptions become limiting at low
temperature when the fluid may freeze or become immiscible and at high
temperature where fluid–saturation implies implausible silicate liquid
compositions or the fluid may be entirely miscible with a silicate liquid. It
is possible to emulate fluid-saturation calculations using GFSM by computing
phase diagram sections with a bulk compositional variable(s) that are closely
related to fluid composition. E.g., a section in which the bulk composition of
the system varies from 100 mole H2O + 0.1 mole non-volatile
components to 100 mole CO2 + 0.1 mole non-volatile components, will
effectively reproduce the phase relations of the classical metamorphic P-T-XCO2
projection with none of the limiting assumptions of that construction.
The assumption that COH-fluids can be approximated
by binary CO2-H2O mixtures is bad practice in systems
where redox processes, e.g., the oxidation or reduction of carbon and iron, are
possible, because it masks the fact that in most natural systems the exchange
of oxygen between fluid and solid phases dictate redox state (Connolly &
Cesare 1993, Connolly
1995). And, in the absence of interactions with a mobile fluid/melt phase,
it is much more probable that redox state of natural system is determined by
its bulk oxygen content than it is by some arbitrary oxygen fugacity buffer
such as QFM.
In calculation of phase equilibria as a function of
volatile fugacities (or chemical potentials or
activities), say, oxygen and sulfur fugacity, a common practice is to assume
that a pure, or nearly pure, H2O fluid is present. In reality, the
speciation of the fluid is dependent on f(O2) and f(S2)
and the pure water assumption is reasonable for only a limited f(O2)-f(S2)
range. A GFSM allows the user to monitor the speciation of the fluid as a
function of f(O2) and f(S2) and identify implausible
conditions (Fig 6).
GFSM are required for the treatment of
electrolytic-fluids by the lagged speciation
method.
The
pros and cons of GFSM:
The pro arguments for GFSM are flexibility and
absence of implicit phase equilibrium assumptions. Because GFSM associate a
compositional degree of freedom with each molecular species, they are
computationally costly for fluids with > 10 molecular species. The
alternative is to use special solution models (solution model types 0, 40, and 41)
that associate an internal speciation routine with the solution model so that
the compositional variables of the solution model correspond to the bulk
compositional variables of the fluid. In consequence, the use of internal
speciation routines offers better resolution and is less costly than GFSM. The
number of species that can be treated by internal speciation routines is
unlimited, but the addition and removal of species generally requires
modification of the program. Additionally, internal speciation routines
generally cannot be used in calculations with independent
fugacity/activity/chemical potential constraints on a component of the fluid.
Thermodynamic Data File Modifications
for GFSM
Many of the thermodynamic files included with Perple_X are configured for fluid-saturation
constraints rather than GFSM. To be certain that the thermodynamic file you
want to use is appropriate for GFSM calculations:
1)
Verify that the EoS flag is set appropriately in the
thermodynamic data for every molecular fluid species that is to be included in
the GFSM. Appropriately in this context means that EoS flag is set to the value that identifies the species.
The current list of species flags is: H2O (101), CO2
(102), CO (103), CH4 (104), H2 (105), H2S
(106), O2 (107), SO2 (108), COS (109), N2
(110), NH3 (111), O (112), SiO (113), SiO2
(114), Si (115), C2H6 (116), HF (117). The code must be
modified and recompiled to add new species. The thermodynamic data for these
species should not include volumetric properties and it is assumed that the
calorimetric properties are as described for EoS 1.
For example, if the entry for H2O in the thermodynamic file is:
H2O EoS = 1
H2O(1)
G0 = -228542.3 S0 =
188.8
c1 = 40.1 c2 =
.8656001E-2 c3 = 487500 c5 = -251.2
end
it must be edited to read:
H2O EoS = 101
H2O(1)
G0 = -228542.3 S0 =
188.8
c1 = 40.1 c2 = .8656001E-2
c3 = 487500 c5 = -251.2
end
The association of a molecular EoS
with a particular species is controlled by the hybrid_EoS
option.
WARNING:
setting the hybrid_EoS flag of a
molecular species has the consequence that the FRENDLY thermodynamic calculator program computes the Gibbs
energy of the species at the pressure and temperature of interest rather than
at the reference pressure (P_ref, usually 1 bar) and
temperature of interest when no volumetric EoS is
associated with the species (i.e., when the EoS flag
is 1 and no value for V0 is provided). This has consequences if FRENDLY is to
be used to compute the fugacity of a species determined by a buffer reaction
such as 6 hem = 4 mt + O2. If an EoS has been associated with the oxygen species then the
Gibbs energy change of the reaction, assuming pure mt
and hem, is g = g0 + R T ln[f(O2)/P], whereas if no equation of
state has been associated with oxygen g = g0 + R T ln[f(O2)/Pref]. This issue, which arises because of mixed
reference conventions, is not an issue in other Perple_X
programs because thermodynamic entities without an associated volumetric EoS are automatically excluded from calculations unless the
auto_exclude option has been modified from its default.
2)
Transform any polyatomic components necessary to describe the GFSM to elemental
components (e.g., to describe COH fluids, if the data base has H2O
and CO2 as
components transform them, respectively, to H2 or H and C). To
transform the components use the Perple_X
program CTRANSF,
which takes as input any specified thermodynamic data file and generates a new
file named ctransf.dat with the new components. WARNING: do not use versions of CTRANSF with a time-stamp between
April 2, 2018 and April 13, 2022. Component transformation is not essential,
especially if the GFSM of interest involves only oxide species, e.g., a binary
H2O-CO2 fluid. However, in GFSM where redox is possible,
the use of non-elemental components can lead to complications. In particular: i) Perple_X
will automatically reject any phase/species in which the sum of the components
is less than or equal to zero. Thus, if CO2 and O2 are employed as components,
the composition of graphite is 1 CO2 - 1 O2 and graphite will be rejected from
the calculation. Perple_X writes a warning for each rejected
phase/species, but these are easily overlooked. ii) Perple_X does not allow the amount of a
component in a specified composition to be negative (because it has no way of
testing that this does not cause the mass of one or more elements to be
negative). This has the consequence that if the data base components correspond
to oxides and oxygen, there is no way to specify an oxygen deficient bulk
composition. To circumvent this restriction, use elemental components for any
phase/species that has, or may have, an elemental composition. For example, if
native iron or carbon may
3)
Add and/or set the GFSM option to T (true) in perplex_option.dat or delete the
special component section in the header of the thermodynamic data file.
Setting the GFSM option is preferable, setting the option to T disables phase
saturation constraints and causes Perple_X to
ignore the special component section of the thermodynamic data file. The
alternative is to
open the file in a text-editor and if a special
component section, e.g.:
begin_special_components
H2O
CO2
end_special_components
is present in the header
of the thermodynamic data file delete it, or at least delete any special
components that correspond to the species of the GFSM. Deleting the special
component section will disable phase-saturation constraints.
Adding/removing species from a GFSM
Creating a new GFSM, or adding or removing species
from an existing GFSM, is most easily done using an existing model in the
solution model file (e.g., solution_model.dat).
Open the solution model file in a text editor and locate a suitable model by
searching for the text “fluid”, e.g.,
begin_model
| Fluid, Connolly & Trommsdorff CMP 1991.
F
abbreviation F
full_name fluid
0 | solution
model type: internal EoS. See explanation in the
header of this file for a list of model types
2 | number of
endmembers
CO2
H2O
0 0 | endmember
flags, 1 -> the endmember composition is not considered part of the
solution, otherwise 0
0.0 1.0 0.1 0 | subdivision scheme for
CO2, see commentary in the header of this file
ideal | the ideal tag
indicates excess properties are computed internally
0 | zero
indicates a molecular configurational entropy model
end_of_model
To convert this solution model to GFSM solution
model for geologically relevant C-O-H fluids, change the solution model type to
39, add CH4 and H2 as endmembers, change the endmember
counter, and add a subdivision scheme and endmember flag for each new endmember
as below (changes indicated in red):
begin_model
| my new C-O-H GFSM
my-GFSM
abbreviation F
full_name fluid
39 | solution model
type: internal EoS. See explanation in the header of
this file for a list of model types
4 | number of
endmembers
CO2
CH4
H2
H2O | the dominant
species should be listed last
0 0 0 0 |
endmember flags, 1 -> the endmember composition is not considered part of
the solution, otherwise 0
0.0 1.0 0.1 0 | subdivision scheme for
CO2, see commentary in the header of this file
0.0 1.0 0.1 0 | subdivision scheme for CH4
0.0 1.0 0.1 0
| subdivision scheme for H2
ideal | the ideal tag
indicates excess properties are computed internally
0 | zero
indicates a molecular configurational entropy model
end_of_model
The choice of species for a particular problem
requires some knowledge, but at ordinary petrological conditions C-O-H fluids
are described adequately as CO2-H2O-CH4-H2
mixtures. In fact, for carbon saturated conditions H2 is usually
superfluous (cf. example 2). Many petrologists seem to be
infatuated by insignificant species, most notably O2. One of the
benefits of GFSM, is that such species (e.g., O2, C2H6,
CO) can easily be added to a solution model to verify that they are, in fact,
insignificant in the sense that they have no consequences for phase equilibria.
In the case of O2, its absence from the above model precludes fluid
compositions on the oxygen-rich side of the H2O-CO2 join,
such compositions are highly oxidizing and unlikely to be realized in natural
systems. For any other compositions, the GFSM yields the beloved oxygen
fugacity via the relation f(O2) = exp[{µ(O2)-g0(O2)}/{R*T}], where µ(O2)
is the chemical potential of the oxygen component (obtained by free energy
minimization) and g0(O2) is the Gibbs energy of the pure oxygen
species at the reference pressure (usually 1 bar) and the temperature (T) of
interest.
WARNING
1: if you create a new solution model in an existing
solution model file, be careful to give the new model a unique name. Perple_X does not necessarily read the entire
solution model file and does not test for replicate names.
WARNING
2: if you use an existing GFSM, exclude any unnecessary
endmembers. For example, the GFSM named COH-Fluid has, or had at last count,
nine endmembers, a calculation with all these endmembers will be slow and, in
general, wasteful.
Example
1 – in17b, metabasalt decarbonation
Most bulk rock chemical analyses are reported in
terms of simple oxides that do not reflect the true oxidation state of rock,
i.e., the actual oxygen excess (or deficit) relative to the oxide composition.
It is of course possible to infer the deficit by analysis of mineralogical
data, but even when such an analysis has not been made it may nonetheless be
useful to account for redox processes. The utility of such an accounting is
dependent on whether the oxygen excess is important and whether the solution
models are capable of realistically representing redox processes, these issues
are matter of judgement for the user. To illustrate the effect of allowing
redox in the calculation of a phase diagram section for the carbonated-metabasalt composition, considered in the seismic-velocity
tutorial (Figure 1), is reproduced here (Figure 2) with a calculation in
which redox is allowed and a GFSM is used to represent the fluid. The set-up of
this latter calculation is identical to the former except that: 1) in addition
to the oxide components, O2 is specified as a thermodynamic
component and its amount is set to zero (this permits redox between the phases
of the system subject to the constraint that net oxygen excess is zero); 2) a
GFSM for an H2-CH4-CO2-CO-H2O
molecular fluid (“COH-Fluid”) is created and used in place of the binary H2O-CO2
“F” model, based on the CORK EoS, of the tutorial
calculation; 3) the thermodynamic data file (hp02ver.dat) is modified, as
described above, for the GFSM, and 4) the hybrid_EoS
options for CO2 and H2O must be changed to “2” to
reproduce the CORK results in the H2O-CO2 limit. The input
file for the calculation is in the examples
folder.
This example was chosen not because redox processes
have profound consequences on the metabasalt decarbonation
process, but rather to illustrate the consequences of including redox processes
in a phase equilibrium model based on imperfect information, i.e., in this
case, the assumption that all iron is ferrous and all carbon is quatra-valent (CO2). Because Ferric iron is a
stable constituent in many minerals at extraordinarily reducing conditions
(e.g., Frueh-Green et al., 2004), fluid stability is an almost
inevitable consequence of permitting redox in a system with a redox-neutral
bulk composition. This occurs because the formation of ferric iron requires the
reduction of other oxides. If volatile oxide components are present, then they
are the preferred source of oxygen and their reduction releases hydrogen and
carbon. As the solution of hydrogen is generally not permitted in mineralogical
solution models, the hydrogen must be accommodated by a fluid phase. At low
temperature, where the oxidized volatiles are stable constituents of carbonated
and hydroxylated minerals, the fluid that forms as a
consequence of iron oxidation is dominated by H2 or CH4.
With increasing temperature this fluid becomes diluted and oxidized by the
“normal” devolatilization processes. Comparison of the simple-oxide (Fig 1) and redox-enabled (Fig 2) phase
equilibrium models, illustrates that redox-driven fluid generation does
stabilize a low temperature methane-rich fluid (Fig 3).
However, because the amount of ferric iron that forms (mainly in clinopyroxene) is small the amount of this fluid is
insignificant, and once the conditions of normal devolatilization the two phase
equilibrium models are essentially identical. There is no doubt that
redox-driven fluid generation may be an important natural process, but in this
case it is most likely an artifact of the assumed initial bulk composition. The
question then arises whether there is any real value to accounting for redox
processes when the excess oxygen content of the system is unknown. In such
circumstances, the only rigorous approach is to explore phase relations as a
function of excess oxygen content (or oxygen fugacity). The alternative
strategy of assuming an arbitrary excess oxygen content (e.g., zero as done
here), or arbitrary oxygen fugacity buffer, is no different than arbitrarily
assuming the potassium content of a rock for purposes of constructing a phase
diagram section. In the present example, it might be argued that modelling
redox provides a lower limit on the ferric/ferrous ratios of garnet and clinopyroxene. In pursuit of that argument, it would be
logical to increase the excess oxygen content to ~0.6 wt%
(Fig 4) in order to suppress the improbable redox-driven
devolatilization.
Figure 1.
Metabasalt phase relations as computed in the seismic-velocity
tutorial, i.e., assuming simple oxide component stoichiometry and that the
fluid (F) is a binary H2O-CO2 mixture. The fluid phase is
not stable below ~833 K.
Figure
2. Metabasalt
phase relations computed using a GFSM for an H2-CH4-CO2-CO-H2O
molecular fluid with redox subject to the constraint that the bulk oxygen
excess is zero. The fluid is stable at all conditions because ferric iron in clinopyroxene forms by a reaction of the form Silicate-FeO + carbonate + hydroxide = Silicate-Fe2O3
+ fluid-CH4. The input file for the calculation is in the examples
folder
Figure
3. The 
methane
content (left) and volume fraction of the fluid in the in17b example. The plots
show that the methane content is significant only when the total amount of the
fluid is negligible. The amount of dehydration becomes significant roughly at
the conditions for the onset of dehydration in the in17a example. Thus, the
overall effect of redox processes is unimportant.
Figure 4. The net excess solid phase
oxygen-content for the in17b example. This plot shows that an excess
oxygen-content of ~0.06 wt % would suppress the
formation of the low-temperature methane-rich fluid in the in17b example.
Because the solid phase excess is positive at all conditions, fluid
compositions are always on the carbon-rich side of the H2O-CO2
join of the C-O-H composition space.
Example
2 – carbon precipitation induced by methane decomposition
Figure
5. Multi-atomic molecular species decompose to diatomic species
with increasing temperature. For C-O-H fluids this has the consequence that
C-undersaturated H-rich (H/O > 2) fluids become saturated in solid carbon
with increasing temperature, whereas carbon-saturated O-rich (H/O < 2)
fluids become undersaturated with increasing temperature (Connolly 1995).
This calculation illustrates prograde carbon-saturation for a fluid that initially
has the bulk composition of methane. The colored curves are bulk isochores for the system (kg/m3). The input file
for this calculation is in the examples
folder.
Example
3 – H-O-S fluid composition as a function of f(O2) and
f(S2)
Figure 6. Cu-Fe
mineral stabilities and H-O-S fluid composition as function log[f(O2)]
and log[f(S2)] for a system with 1 mol Cu,
4 mol Fe, and 1 mol H2.
The mineral and fluid phase relations for this system are independent, the only
reason for including the H-O-S fluid is to identify plausible f(O2)-f(S2)
in terms of fluid chemistry. The stepped contours of the fluid phase H2O-content
superimposed on the phase diagram section bound the f(O2)-f(S2)
conditions at which H2O is the dominant molecular species in the
fluid. At higher f(O2), SO2 is the dominant fluid species
and lower f(O2), the dominant species is either H2 or H2S.
The boundary between H2- and H2S-dominant fluids
coincides roughly with the pyrrhotite-pyrite phase
boundary. The abrupt changes in fluid composition are poorly resolved because
they are not associated with phase boundaries and therefore samples only on the
scale of the lowest resolution grid during gridded minimization. Because this
poor resolution leads to highly erratic fluid composition contours if the
compositional data is interpolated by WERAMI, the interpolation option was set
to off resulting in the stepped contours. The cosmetic flaw could be eliminated
by using a single-level, high resolution grid. The input file for this
calculation is in the examples
folder.