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
The
7.1.8 Release of Perple_X
largely obviates the
modifications described here. Section 1, below, may be pertinent if old
thermodynamic data files. Section 2, remains good practice. In 7.1.8+,
thermodynamic data files with a “special_component”
section can be used for saturated fluid-phase constraints, internal fluid
speciation EoS, and GFSM without modification.
Setting the GFSM option or eliminating the “special_component”
section in the header of the thermodynamic data file, as described in Section
3, are no longer necessary. If the GFSM option is set to T, then prompts for
and use of saturated fluid-phase constraints and fluid solution models that
rely on internal fluid speciation routines are suppressed.
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 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 stable, the transformations Fe = 1 FeO - ˝ O2 and C = 1 CO2 - 1 O2 allow the input of bulk compositions that are reduced relative to a bulk composition specified entirely in terms of oxide components.
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.