Perple_X Electrolyte Speciation
at Elevated Pressure and Temperature
Corrections/modifications
relevant to this page:
March 15, 2020, Deep Earth Water (DEW) data
update:
The Huang et al. (2019, Geochem Persp Lett 12:1–6)
data for aqueous Cr-bearing species has been added to DEW19HP622ver_elements.dat.
Courtesy of Vincent van Hinsberg (McGill).
February 18, 2020, DEW_2_VER parsing error for
aqueous Glutamine (C5H10N2O3) and Isobutane (C4H10): a parsing error caused the DEW_2_VER data
conversion program to reject species that included a 2-digit stoichiometric
factor with zero as the second digit. For the 20 elements specified in the
DEW17 and DEW19 data files, this error caused the omission of aqueous Glutamine
and Isobutane. These species have been added to DEW17HP622ver_elements.dat
and DEW19HP622ver_elements.dat.
Correction courtesy of Andrea Maffeis (Torino).
December
11, 2019, DEW model update, CaCl2(aq) stoichiometric
error: The Huang & Sverjensky
(2019, GCA 254:192-230) update to the DEW database has been formatted as DEW19HP622ver_elements.dat. The DEW_2_VER program, which
converts the DEW spreadsheet format to Perple_X format, parses the spreadsheet species
"symbols" for stoichiometry. As of this date, the symbol provided for
CaCl2,aq has been CaCl(0);
consequently the stoichiometry of this species was incorrect in all previous Perple_X versions
of the data. Additionally, no symbol has been provided for Glycinate,aq with the consequence that this species
was, and is, not included in previous versions of the data. Refer to Section 1e
of README_DEW_2_VER for additional information. Update
courtesy of Andrea Maffeis (Torino/ETH).
November 18, 2019, ACETIC-ACID stoichiometry in DEW17HP622ver_elements.dat was not corrected as indicated in
the Nov 6 update. Correction courtesy of Mohit Melwani Deswani (JPL, Cal Tech).
November 6, 2019: the DEW_2_VER program, which
converts the DEW (www.dewcommunity.org/resources.html) spreadsheet formatted
data to Perple_X thermodynamic data file format,
incorrectly parsed species formulae if: 1) the formula was terminated by two successive elements without
stoichiometric coefficients or a charge or group indicator (e.g.,
CH3COOH); 2) a stoichiometric coefficient was > 9 (e.g. C6H14); or 3) a
final stoichiometric coefficient was followed by a + or - sign (e.g., C5H7O4-).
The affected species are:
Species: incorrect ->
correct
ACETIC-ACID,AQ C(2)H2(1.5)O2(1) ->
C(2)H2(2)O2(1)
[H2O(2)CO2(2)O2(-2)]
ETHANOL,AQ C(2)H2(2.5)O2(.5) -> C(2)H2(3)O2(.5) [H2O(3)CO2(2)O2(-3)]
FORMIC-ACID,AQ C(1)H2(.5)O2(1) ->
C(1)H2(1)O2(1)
[H2O(1)CO2(1)O2(-.5)]
GLUTARAT C(5)H2(3.5)O2(.5)
-> C(5)H2(3.5)O2(2) [H2O(3.5)CO2(5)O2(-4.75)]
GLYCOLAT C(2)H2(1.5)O2(.5)
-> C(2)H2(1.5)O2(1.5)
[H2O(1.5)CO2(2)O2(-1.25)]
HEXANE,AQ C(6)H2(.5) ->
C(6)H2(7)
[H2O(7)CO2(6)O2(-9.5)]
LACTATE, C(3)H2(2.5)O2(.5) -> C(3)H2(2.5)O2(1.5) [H2O(2.5)CO2(3)O2(-2.75)]
METHANOL,AQ C(1)H2(1.5)O2(.5) -> C(1)H2(2)O2(.5) [H2O(2)CO2(1)O2(-1.5)]
PROPANOL,AQ C(3)H2(3.5)O2(.5) -> C(3)H2(4)O2(.5) [H2O(4)CO2(3)O2(-4.5)]
These species
have been corrected in DEW17HP622ver_elements.dat, DEW17HP622ver_oxides.dat,
DEW13HP622ver_elements.dat, DEW13HP622ver_oxides.dat, DEW13HP02ver_elements.dat,
and DEW13HP02ver_oxides.dat; the DEW_2_VER program has only been corrected in
the 6.8.8 beta version of Perple_X.
It is probable that this error was responsible for erratic behavior in
calculations with organic carbon solute species. I apologize both for the error
and for falsely attributing the error to the primary DEW data. Correction
courtesy of Mohit Melwani Deswani (JPL, Cal Tech).
October
25, 2019: the lagged speciation error trap:
**warning
ver103** pure and impure solvent phases coexist. To output result set aq_bad_result.
was triggered
incorrectly during calculations when pure solvent was stable. Correction of
this error extends the range of conditions at which the lagged speciation
algorithm is feasible.
Jan 27, 2019: The
DEW13 aqueous solute data-base was not converted to
Perple_X format using the default options
specified in the DEW spreadsheet,
it is used here only for purposes of demonstration, the DEW17 aqueous solute
data-base should be used for quantitative applications.
HKF g-function: as currently configured Perple_X will
abort calculations with an H2O-solvent if the physical conditions are outside
the range of validity for the HKF g-function indicated by Shock et al
(1988); however, for multi-component solvents, Perple_X will
zero the g-function at out-of-range conditions and continue calculations
irrespective of the actual solvent composition.
Nov 21, 2018: The DEW17HP622ver_elements.dat
and DEW17HP622ver_oxides.dat
files generated on Nov 19 did not include the c2 heat capacity coefficient. The
data files and DEW_2_ver have been corrected.
Nov 19, 2018: The May 19, 2017 revision of the DEW
data (www.dewcommunity.org/resources.html) is implemented in Perple_X as DEW17HP622ver_elements.dat
and DEW17HP622ver_oxides.dat.
The program for converting the DEW spreadsheet data format to Perple_X format,
DEW_2_ver, is included with the Perple_X programs and documented at: README_DEW_2_VER.zip.
Sep 22, 2018: See Errata comment in Connolly & Galvez (2018), the
comment also applies to earlier examples reproduced here.
Aug 30, 2018: Updated to provide the files for Connolly & Galvez (2018)
including examples computed with Perple_X 6.8.4.
Oct 19, 2017: results presented here (Figures 1-3)
updated with Perple_X
6.8.0.
Forward and Back-Calculated
Aqueous Electrolyte Speciation
Thermodynamic
Details and Limitations
Molecular Volatiles: Solute or
Solvent?
Thermodynamic
Data Files for Electrolytic Fluids
Simple back-Calculated Electrolyte
Speciation (Figure 1)
Limitations
Relevant
Options
Lagged Forward-Calculated
Electrolyte Speciation (Figure 2)
Limitations
Relevant
Options
Files
for calculations in Connolly & Galvez (2018)
Brute-Force Forward-Calculated Electrolyte
Speciation (Figure 3)
Limitations
Relevant
Options
Electrolyte
speciation can be calculated in Perple_X 6.7.9 in three different
ways: in lagged (Figure 2) and brute-force
forward-calculations (Figure 3) electrolytic fluid
speciation is evaluated during optimization, whereas in back-calculation (Figure 1) the chemical potentials obtained from a forward
calculation or from optimization without considering the effects of
electrolytes are used to compute electrolyte speciation. For most purposes lagged
forward-calculation (aka lagged speciation, Connolly & Galvez 2018) is the
best method. Simple back-calculated speciation based on a pure-solvent
forward model (Galvez et al. 2015)
often provides an excellent approximation for solution chemistry in rock-dominated
hydrothermal systems and is useful for verification of lagged and brute-force
forward-calculations. Brute-force forward-calculation is the normal mode
of treating solutions in Perple_X
and is robust with regard to any kind of phase separation, but has limited
precision and the configuration of electrolytic solution models requires user
expertise.
Both
the extended HKF (Helgeson-Kirkham-Flowers)
formulation (Perple_X
EoS
16; Shock et al. 1992, Sverjensky et al. 2014)
and the Anderson density model (Perple_X EoS 15; Anderson et al. 1991, Holland & Powell 1998)
for solute species are implemented in Perple_X; however, at present, only the HKF is
linked to speciation calculations. The implementation of HKF/SUPCRT data was
benchmarked against Harrison & Sverjensky's (DEW,
2013) spreadsheet calculator, minor discrepancies arise because of the choice
of the equation of state for water. Specifically, the spreadsheet uses, though
other options are offered, Zhang & Duan (2005) to
compute the density of water. This density is then used in the Sverjensky et al. (2014) expression for the dielectric
constant and the Gibbs energy of water is taken from Delaney & Helgeson (1978). In Perple_X all properties of water are
obtained by whatever equation of state is specified (the initial implementation
of the HKF in Perple_X
6.7.3 did use Zhang & Duan's (2005) EoS for density, this EoS will be
restored once the routine has been modified to compute water fugacity). Of the
available water EoS in Perple_X:
the CORK and HSMRK EoS should not be used at ambient
conditions because they do not reproduce liquid water properties; the Haar EoS provides the most
accurate representation of low pressure (< 1 GPa)
water properties; and the PSEoS and MRK EoS give reasonable liquid densities at 298.15 K and 1 bar.
I have not checked the boiling curves predicted by the latter two EoS.
The
extension of the HKF to non-aqueous solvents follows if the Born coefficient
(ω) of a solute is only a function of pressure (P) and temperature (T).
The HKF then gives the change in the reference Gibbs energy of the solute due
to a change in the dielectric constant (ε) of the solvent as
ΔG0_solute = ω0·(1/ε0_solvent -
1/ε0_H2O), [1]
where
0 denotes the reference P-T condition. The solvent contribution to the solute
Gibbs energy at elevated pressure and temperature is:
ΔG_solute = ΔG0_solute + (ω
- ω0)·(1/ε_solvent
- 1/ε0_solvent) - (T - T0)·ΔS0_solute [verify
this equation]
which
simplifies to
ΔG_solute = ω·(1/ε_solvent - 1) - ω0·(1/ε0_H2O -
1) - (T - T0)·ΔS0_solute,
and
ΔS0_solute = ω0·([∂ln(ε0_H2O)/∂T]/ε0_H2O - [∂ln(ε0_solvent)/∂T]/ε0_solvent) [2]
is
the change in the entropy of an HKF solute due to a change in solvent chemistry. This entropic effect is relatively minor and is
not currently evaluated in Perple_X to avoid
the computational overhead associated with evaluating [∂ln(ε0_solvent)/∂T]/ε0_solvent
for every solvent composition considered. Instead the latter term is
approximated by the value for [∂ln(ε0_H2O)/∂T]/ε0_H2O
commonly cited in SUPCRT applications (-5.79865·10-5/K). This
practice should be changed for applications where the solvent is not
water-rich. The S0 values in SUPCRT data do not include the solvent term
-ω0·([∂ln(ε0_H2O)/∂T]/ε0_H2O), hence a small
discrepancy between the S0 values indicated in HKF thermodynamic data files and
the solute entropy obtained by Perple_X's FRENDLY thermodynamic
calculator.
The
HKF includes several additional parameters (e.g., the characteristic
temperature, θ, and pressure, ψ) that may mask dependencies on
solvent chemistry. Even if standard state solute properties are influenced by
solvent chemistry only through the dielectric constant, the conditions used to
discriminate the different regions of applicability for the empirical
expressions for the HKF correlation function used to compute Born coefficients
(Shock et al., 1992) are H2O specific. As the correlation function is non-zero
only for water densities < 1 g/cm3, this particular limitation is likely to
be unimportant for calculations at high pressure. For dilute non-aqueous
solvents, the influence of solvent chemistry on the bulk dielectric constant
and solute thermodynamic properties (as predicted by the HKF) is minor, thus
these effects may well be insignificant in comparison to other sources of
uncertainty.
Solvent
dielectric constants for pure non-aqueous volatile species are computed from
empirical expressions (Harvey & Lemmon 2005; Harvey & Mountain 2017),
but using the partial molar volume of the species in the impure solvent rather
than the volume of the pure species (Galvez
et al. 2015). The dielectric constant of pure water is using the expression
given by Sverjenksy et al. (2014), which is indicated
to be valid to 6 GPa and 1473 K. This expression
yields a dielectric constant of 81.97 at 298.15 K and 1 bar for a density of
~0.997 g/cm3, this value differs from the value of 78.47 usually used in SUPCRT
and leads to a change in the standard state Gibbs energy of solutes equal to
ω0·(1/81.39 - 1/78.47) (Eq [1]). The dielectric
constant of the impure solvent is computed using the Looyenga
mixing rule (Mountain & Harvey 2015) with volume fractions computed from
the partial molar volumes of the solvent species.
A
minor contradiction between the HKF and Debye-Hueckel
theory, is that the latter identifies charged species and solvent, whereas the
former differentiates the solvent (water), neutral species, and charged
species. In the context of Debye-Hueckel theory,
neutral solute species are properly considered solvent species. In Perple_X: solvent species are considered to be any neutral
species that is assigned a thermodynamic reference state in which the species
is pure and neutral solute species are any neutral
species described by a solute reference state. Activity coefficients for
electrolytes are computed by the Davies extension of the Debye-Hueckel equation, other formulations can easily be
incorporated. Neutral solutes are assumed to be ideal, though, if available,
interaction terms can be accommodated. Solvent species activities are computed
from the molecular EoS selected by the user. Wolery 1990 notes that this approach violates the Gibbs-Duhem relation and uses the Gibbs-Duhem
relation to derive an expression for the activity of water in a Debye-Hueckel fluid. This approach cannot be extended to a
multicomponent solvent. The inconsistencies may become significant at high
solute concentrations.
The
thermodynamic properties of molecular volatiles are described more accurately
by solvent species molecular EoS than they are by
solute species thermodynamic extrapolations. However, the resolution on the
molar fractions of solvent species is ~ final_resolution/speciation_factor
(~ 1e-5 by default), whereas the resolution on solute species is essentially
unlimited for both lagged and back-calculated speciation. Consequently,
molecular volatiles should only be included as solvent species if their
concentrations are likely to be significantly above final_resolution/speciation_factor. If the concentration of a solvent
species is at this limit, then the concentrations of all species at or below
the limit may become limited by the resolution of the solvent species.
To
permit calculations with silicate solution models, a file containing Harrison
& Sverjensky's (DEW, 2013) revised SUPCRT/HKF
data (DEW13ver.dat) has been merged with the hp02ver.dat (Holland & Powell
1998, rev. 2002), hp622ver.dat (Holland & Powell 2011, rev. 2013), and the
ba96ver.dat (Berman & Aranovich 1996) thermodynamic
data bases. The merged files are DEW13HP02ver_elements.dat,
DEW13HP02ver_oxides.dat,
DEW13HP622ver_elements.dat,
and DEW13HP622ver_oxides.dat,
and DEW13BA96ver_oxides.dat,
where the suffixes _elements and _oxides indicate whether the data is
formulated in terms of element or oxide components. The Berman & Aranovich (1996) data is nominally consistent with the DEW
data, but provides a relatively limited description of condensed phases. The
Holland & Powell data bases include electrolyte data, but it appears the
data is not maintained. To avoid conflicts with the revised SUPCRT data, the
Holland & Powell electrolyte data has been moved to the file hpaqver.dat.
The Holland & Powell aqueous data is for an equation of state that assumes
solute thermodynamic properties at elevated pressure can be predicted from
ambient pressure data as a function of temperature and solvent density (Manning
1998, Anderson et al. 2002). The characterization of the solvent by only two
state variables implies the solvent is either pure (i.e., H2O) or that its
properties are independent of chemistry, which is demonstrably false in the
case of carbonic solvents (Harvey & Lemmon 2005). The density extrapolation
method is supported in Perple_X
(EoS 15).
For additional equation of state and data file documentation refer to Perple_X_Thermodynamic_Data_Files.
Figure 1.
Back-calculated solute speciation at 1000 K and 3 GPa
obtained by running MEEMUM with the aq3_el.dat
problem definition file.
Stable phases at:
T(K) = 1000.00
P(bar) = 30000.0
Phase Compositions (molar proportions):
wt % vol % mol % mol H2 Mg Si C O2
COH-Fluid 32.09 53.79 87.88 2.90 0.96560 0.00000 0.00000 0.03456 0.51719
en 23.43 14.85 6.04 0.199 0.00000 2.00000 2.00000 0.00000 3.00000
ta 44.46 31.35 6.07 0.200 1.00000 3.00000 4.00000 0.00000 6.00000
mag 0.02 0.01 0.01 0.308E-03 0.00000 1.00000 0.00000 1.00000 1.50000
Phase speciation (molar proportions):
COH-Fluid CO2: 0.03447, CH4: 0.00008, H2: 0.00002, CO: 0.00000, H2O: 0.96543
...output abridged...
Chemical Potentials (J/mol):
H2 Mg Si C O2
-51276.9 -395063. -423268. 1173.80 -428493.
Back-calculated solute speciation in the solvent:
pH = 3.569+/-0.000; Delta_pH = 0.202; ionic_strength = 0.7146E-02; gamma/q^2 = 0.8559
dielectric constant = 16.81; solvent molar mass, g/mol = 18.9107; solute molality = 0.4542
Solute endmember properties:
charge molality mol_fraction g,J/mol* g0,J/mol**
SiO2,aq 0 0.360240 0.675435E-02 -851760 -843271
Si2O4,aq 0 0.809606E-01 0.151798E-02 -1703520 -1682620
Mg(HCO3) 1 0.366108E-02 0.686437E-04 -1104964 -1057027
HCO3- -1 0.349006E-02 0.654373E-04 -624506 -576171
HSiO3- -1 0.243878E-02 0.457261E-04 -1048947 -997632
MgOH+ 1 0.169718E-02 0.318215E-04 -677645 -623316
OH- -1 0.797071E-03 0.149448E-04 -197187 -136574
Mg+2 2 0.419445E-03 0.786443E-05 -480458 -410627
H+ 1 0.314842E-03 0.590316E-05 -68336 0
Mg(HSiO3 1 0.214319E-03 0.401840E-05 -1529405 -1457872
CO3-2 -2 0.200102E-06 0.375184E-08 -556169 -422751
MgCO3,aq 0 0.512487E-10 0.960892E-12 -1036628 -839623
HO2- -1 0.292313E-19 0.548076E-21 -411433 -36165
Normalized solvent endmember properties:
molality mol_fraction vol_fraction v,cm3/mol* g,J/mol* g0,J/mol***
CO2 1.8228 0.03447 0.06465 32.729 -427318 -401095
CH4 0.0042 0.00008 0.00015 33.019 -101380 -35518
H2 0.0010 0.00002 0.00002 18.858 -51276 26445
CO 0.0002 0.00000 0.00001 30.729 -213072 -124463
H2O 51.0519 0.96543 0.93517 16.904 -265523 -265235
*partial molar, **molal ref. state, ***molar ref. state.
Back-calculated fluid bulk composition:
mol % wt %
H2 62.7985 9.97159
Mg 0.736845E-02 0.141090E-01
Si 0.645369 1.42796
C 2.25587 2.13464
O2 34.2929 86.4517
Given the chemical potentials of the
thermodynamic components of a system, Perple_X formulates a closed system of
equations for the molal concentrations of all solute species by using the
charge balance constraint. Perple_X can solve the speciation in terms of any arbitrarily
chosen ion. The algorithm currently solves for speciation in terms of H+,
should numerical error become significant the code can easily be modified for a
more rational basis ion (e.g., OH-). A peculiarity
of the contradiction between the HKF and Debye-Hueckel
theory, is that the concentrations of electrolytic solute species are
independent of the concentrations of neutral solute species. This independence
reflects that the neutral solutes have no interactions with the electrolyte
species and that the partial molar Gibbs energies of the solvent species are
assumed to be identical to those in the solute-free solvent.
Except for some minor technical
details, the implementation of simple back-calculated speciation in Perple_X follows
Galvez et al. (2015). The term
"simple back-calculated" speciation is used here to distinguish the
back-calculated speciation obtained as in Galvez
et al. (2015) from the back-calculated speciation output during lagged speciation calculations
(Connolly & Galvez 2018).
The calculations are surprisingly
robust (Figure 1), except that they are critically
dependent on the availability of chemical potentials from a forward
calculation. C-O-H-S-N solvents have a strong tendency to order for certain
bulk compositions (pure H2O and the H2O-CO2 join) at low temperature. These
degenerate compositions may prevent Perple_X from determining elemental
chemical potentials, when this occurs the problem should be formulated in terms
of oxide components. Three examples
illustrate how the choice of components controls the feasibility of
back-calculated speciation: aq1_ox.dat is the input file for H2O solvent;
aq2_ox.dat is the input file for a binary H2O-CO2 solvent; and aq3_el.dat is
the input file for a ternary C-O-H solvent.
NOTE: for calculations with oxide
components it is necessary to include O2 as a component so that Perple_X will
include nominally reduced aqueous species, e.g., H+ = 1/2 H2O - 1/4 O2 - 1
electron. The amount of O2 may be specified as zero (i.e., to preclude
fluid-rock redox processes), in which case its chemical potential is undefined (and irrelevant). An electron/proton component is not
necessary in Perple_X
because charge balance is implicit.
Perple_X automatically
does back-calculated speciation if: 1) solute species data is present in
thermodynamic data file; 2) a recognized solvent is stable; and 3) the Perple_X option
keyword aqueous_output
is set to true (it is true by default). Recognized solvents are either pure H2O, a generic
hybrid mixed-volatile solution model (solution model type 39), or an
aqueous electrolyte solution model (solution model type 20, e.g., Aq_Solvent).
At present, saturated phases, and saturated or mobile components cannot, or at
least should not, be specified in back-calculated speciation problems.
Back-calculated speciation can be
obtained directly with the program MEEMUM or by running VERTEX and then using
WERAMI (Mode 1) to recover the speciation. In the latter case, speciation and
some solvent properties can be recovered as a function of one or two variables
with WERAMI (Mode 2-4, Property choice 4). The resulting spread-sheet format
tab file can be analyzed with Perple_X_plot (MatLab), PSTABLE, or PYWERAMI. By default
the concentrations of the 20 most abundant aqueous species in the chemical
system of interest are output. The number of species output can be changed by
setting the aqueous_species keyword to the desired number.
Concentration units can be specified via the aq_solvent_composition
and aq_solute_composition keywords.
In tests I found that the HKF
formulation may substantially overestimate the concentrations of molecular
volatiles if they are entered as neutral solute
species (e.g., ETHANE,Aq; CO2,Aq; CO,Aq; H2,Aq etc.) rather than as solvent species. This
problem is egregious for some high molecular weight organic compounds for
GLUTARAT (glutarate, C5H7O4-)
GLYCOLAT (glycolate, C2H3O3-)
and LACTATE (C3H5O3-) which cause
convergence to an implausible result if included in calculations for carbonic
systems. To facilitate identification of potentially anomalous species both
MEEMUM and VERTEX print the aqueous species considered in a calculation to the
user console at the beginning of a calculation (trailing commas or otherwise icomplete names result because the Perple_X data conversion program
DEW_2_VER truncates the SUPCRT names to 8 characters). Molecular volatiles such
as CO2, CH4, and H2S may be included as either solute or solvent species, but
should not be present as both. Including molecular volatiles as solute species
increases numerical stability and reduces computational cost, but prevents Perple_X from
predicting solvent-phase immiscibility (e.g., the coexistence of a water-rich
phase with CH4- or CO2-rich phases in carbonic systems).
The error
on the back-calculated pH is half the mismatch between log(K_w) and ΔG_w/R/T. If this
error is non-zero it is diagnostic of computational problems.
- Back-calculation implicitly assumes
the solute-bearing phase is in equilibrium with the pure solvent (an
assumption that is only rigorous in the infinitely dilute limit). This has
the consequence that in the limit of small, but finite, solute
concentrations back-calculation always underestimates
solute-content.
- Back-calculation implicitly assumes
the mass of the solute-bearing phase is infinitesimal and therefore cannot
affect the solid/melt phase proportions. However, the real mass of the
solvent may be such that, if the solvent phase were to have the
back-calculated solute load, one or more chemical components would be
completely depleted from the solid/melt phase assemblage. E.g., if Gibbs
energy minimization predicts stability of 1 mol
of H2O (solvent), and back-calculation predicts that this fluid should
contain 0.1 mol of Na2O, but the solid
assemblage contains only 0.01 mol of Na2O, then
the results are inconsistent and may be in substantial error.
- The phase proportions obtained by
obtained optimization do not account for the solute-content of the solvent
phase. Consequently, the method cannot be used for reactive transport
calculations without introducing ad-hoc corrections.
- If no forward model for solute
speciation is included in the calculation, then an implicit assumption of
back-calculation is that solute species have no significant influence on
the partial molar free energies of the solvent species. While much is made
of activity-composition phase relations and the limitations of the Debye-Huckel equation, the error introduced by this
assumption is probably smaller than the error in the data if the total
mole fraction of the solutes exceeds 10% (~5 molal solute concentration).
Relevant Perple_X options
Figure 2.
Lagged forward-calculated solute speciation at 573 K and 1 GPa
obtained by running MEEMUM with the gloss0.dat
problem definition file. The output of the Gibbs energy and chemical potentials
after each iteration indicates well resolved solution. This example was done
with aq_lagged_iterations
= 2; thus, for each major iteration, the lagged speciation and chemical
potentials of the system are recomputed 2 times. Use of aq_lagged_iterations
generally does not result in a significant improvement to the solution, but may
be helpful in low resolution calculations. In contrast to the simple
back-calculated model results in Figure 1, the
composition of the solvent phase (COH-Fluid) accounts for solute species. In
addition to the complete speciation in the "Phase speciation" section
of the output, the lagged ionic strength (ionic_st), total molality (tot_mola), solvent
mass (solv_mas),
the error in the base 10 log of the water dissociation constant (err_lgKw), the pH, the difference between the pH and neutral pH (Delta_pH), the total
solute molality (solute_m),
and the solvent dielectric constant (epsilon)
are output at the end of the list of species. The latter parameter is
indicative of the quality of the solution. The comparison of the
back-calculated and lagged (optimized)
speciation at the end of the output also demonstrates convergence. Note: the back-calculated result reported for
lagged calculations is calculated from the chemical potentials obtained from
the impure solvent phase and therefore is not subject to the limitations mentioned for simple
back-calculation.
Iteration G(J/mol) H2 C Si Al Fe Mg Ca Na K O2 S2
0 -362014.3184 -32455 2507 -424252 -485527 -69861 -405900 -491465 -232928 -266660 -425912 -87475
1 -362019.4133 -32569 2507 -424392 -485518 -69383 -406448 -491675 -232977 -266906 -425772 -87953
1 -362019.8024 -32554 2507 -424361 -485510 -69508 -406281 -491630 -233041 -266859 -425802 -87828
2 -362019.8032 -32553 2507 -424361 -485510 -69501 -406289 -491628 -233039 -266855 -425803 -87836
2 -362019.8189 -32608 2507 -424470 -485537 -69564 -406318 -491792 -233027 -267177 -425694 -87772
3 -362019.8222 -32600 2507 -424453 -485533 -69557 -406310 -491767 -233030 -267129 -425710 -87779
3 -362019.8293 -32599 2507 -424451 -485532 -69540 -406327 -491763 -233026 -267116 -425713 -87796
4 -362019.8293 -32600 2507 -424452 -485533 -69546 -406321 -491766 -233027 -267123 -425711 -87790
4 -362019.8301 -32597 2507 -424447 -485532 -69545 -406318 -491758 -233029 -267107 -425716 -87791
5 -362019.8299 -32597 2507 -424447 -485532 -69545 -406318 -491758 -233029 -267107 -425716 -87791
5 -362019.8356 -32597 2507 -424448 -485532 -69546 -406318 -491759 -233029 -267110 -425716 -87790
6 -362019.8356 -32597 2507 -424448 -485532 -69546 -406317 -491759 -233029 -267110 -425716 -87790
6 -362019.8601 -32597 2507 -424446 -485531 -69545 -406317 -491757 -233030 -267106 -425717 -87791
...output abridged...
Stable phases at:
T(K) = 573.000
P(bar) = 10000.0
Phase Compositions (molar proportions):
wt % vol % mol % mol H2 C Si Al Fe Mg Ca Na K O2 S2
COH-Fluid 5.05 12.04 26.38 0.275 0.99290 0.00270 0.00202 0.00000 0.00000 0.00000 0.00001 0.00443 0.00022 0.50217 0.00009
Mica(CF) 34.75 32.19 8.45 0.882E-01 1.00000 0.00000 3.47763 2.04473 0.11373 0.36390 0.00000 0.52237 0.47763 6.00000 0.00000
Stlp 3.68 3.63 0.35 0.366E-02 6.25000 0.00000 8.00000 2.00000 2.54252 2.45748 0.00000 0.00000 0.50000 15.25000 0.00000
Omph(GHP) 13.09 10.41 5.79 0.604E-01 0.00000 0.00000 2.00000 0.42677 0.22667 0.34655 0.49081 0.50919 0.00000 3.00000 0.00000
law 3.26 2.83 0.99 0.103E-01 2.00000 0.00000 2.00000 2.00000 0.00000 0.00000 1.00000 0.00000 0.00000 5.00000 0.00000
q 29.98 30.15 47.66 0.497 0.00000 0.00000 1.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 1.00000 0.00000
arag 6.64 6.12 6.33 0.660E-01 0.00000 1.00000 0.00000 0.00000 0.00000 0.00000 1.00000 0.00000 0.00000 1.50000 0.00000
pyr 3.53 2.60 3.83 0.400E-01 0.00000 0.00000 0.00000 0.00000 1.00000 0.00000 0.00000 0.00000 0.00000 0.00000 1.00000
gph 0.03 0.03 0.21 0.221E-02 0.00000 1.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000
Phase speciation (molar proportions):
COH-Fluid CO2: 0.45298E-04, CH4: 0.45298E-04, H2S: 0.0000, H2O: 0.99058, FeC4H6O4: 0.26531E-14
FeC2H3O2: 0.34127E-11, NaCO3-: 0.13357E-02, CO3-2: 0.38938E-02, Al+3: 0.81673E-19, AlO2-: 0.11490E-03
Ca(HCO3): 0.17634E-03, Ca(OH)+: 0.15771E-04, Ca+2: 0.58796E-04, CaCO3,aq: 0.12484E-03, CaSO4,aq: 0.11425E-07
Fe+2: 0.30274E-08, Fe+3: 0.15452E-21, H+: 0.51578E-06, HAlO2,aq: 0.87282E-06, HCO3-: 0.13340
HO2-: 0.20913E-29, HS-: 0.89052E-02, HSiO3-: 0.85012E-01, HSO3-: 0.39968E-09, HSO4-: 0.18151E-08
HSO5-: 0.35642E-37, K+: 0.12351E-01, KOH,aq: 0.51236E-04, KSO4-: 0.80588E-08, Mg(HCO3): 0.14026E-06
Mg(HSiO3: 0.44222E-07, Mg+2: 0.13930E-06, MgCO3,aq: 0.11397E-08, MgOH+: 0.15213E-06, MgSO4,aq: 0.98381E-11
Na+: 0.23349, NaHCO3,a: 0.72751E-02, NaHSiO3,: 0.52021E-02, NaOH,aq: 0.87291E-03, OH-: 0.95995E-02
S2-2: 0.19353E-07, S2O3-2: 0.21926E-10, S2O4-2: 0.13241E-22, S2O5-2: 0.14639E-24, S2O6-2: 0.88111E-28
S2O8-2: 0.69529E-53, S3-2: 0.12550E-10, S3O6-2: 0.18380E-32, S4-2: 0.62297E-14, S4O6-2: 0.45653E-28
S5-2: 0.23632E-17, S5O6-2: 0.30092E-40, Si2O4,aq: 0.20937E-02, SiO2,aq: 0.18946E-01, SO3-2: 0.21376E-10
SO4-2: 0.17753E-05, ionic_st: 0.25011, tot_mola: 56.029, solv_mas: 0.18016E-01, err_lgKw: -0.40811E-02
pH: 6.4719, Delta_pH: 2.1369, solute_m: 0.52292, epsilon: 36.545*
Mica(CF) cel: 0.36390, fcel: 0.11373, mu: 0.00000, pa: 0.52237
Stlp mstp: 0.49150, fstp: 0.50850
Omph(GHP) di: -0.25412, jd: -0.09859, acm: 0.02052, hed: 0.00705, om: 0.92694, cfm: 0.27440, jac: 0.12379
*molar solvent, molal solute concentrations.
...output abridged...
Back-calculated solute speciation in the solvent:
pH = 6.472+/-0.000; Delta_pH = 2.135; ionic_strength = 0.2501; gamma/q^2 = 0.6541
dielectric constant = 36.55; solvent molar mass, g/mol = 18.0161; solute molality = 0.5228
Solute endmember properties:
optimized
charge molality mol_fraction mol_fraction g,J/mol* g0,J/mol**
Na+ 1 0.233433 0.416632E-02 0.416736E-02 -287727 -278774
HCO3- -1 0.133353 0.238009E-02 0.238085E-02 -597669 -586049
HSiO3- -1 0.850083E-01 0.151723E-02 0.151729E-02 -1024624 -1010859
SiO2,aq 0 0.189461E-01 0.338151E-03 0.338150E-03 -850164 -831269
K+ 1 0.123596E-01 0.220594E-03 0.220447E-03 -321804 -298851
OH- -1 0.959905E-02 0.171324E-03 0.171331E-03 -174460 -150303
HS- -1 0.890483E-02 0.158933E-03 0.158940E-03 -5497 19016
NaHCO3,a 0 0.727120E-02 0.129776E-03 0.129845E-03 -885397 -861939
NaHSiO3, 0 0.520078E-02 0.928234E-04 0.928466E-04 -1312352 -1287297
CO3-2 -2 0.389249E-02 0.694731E-04 0.694968E-04 -526674 -492150
Si2O4,aq 0 0.209366E-02 0.373677E-04 0.373676E-04 -1700328 -1670939
NaCO3- -1 0.133503E-02 0.238276E-04 0.238396E-04 -814401 -780846
NaOH,aq 0 0.872686E-03 0.155757E-04 0.155796E-04 -462187 -428629
Ca(HCO3) 1 0.176324E-03 0.314703E-05 0.314724E-05 -1198821 -1155622
CaCO3,aq 0 0.124837E-03 0.222810E-05 0.222809E-05 -1127825 -1085003
AlO2- -1 0.114892E-03 0.205058E-05 0.205075E-05 -856551 -811311
Ca+2 2 0.588051E-04 0.104955E-05 0.104938E-05 -601151 -546654
KOH,aq 0 0.512700E-04 0.915066E-06 0.914457E-06 -496264 -449202
Ca(OH)+ 1 0.157739E-04 0.281533E-06 0.281473E-06 -775612 -720912
HSO3- -1 0.399499E-09 0.713025E-11 0.713352E-11 -644073 -538951
Solvent endmember properties:
molality mol_fraction opt_mol_frac vol_fraction# v,cm3/mol* g,J/mol* g0,J/mol***
CO2 0.0025 0.00005 0.00005 0.00009 35.526 -423209 -388964
CH4 0.0025 0.00005 0.00005 0.00010 35.898 -62687 -35054
H2S 0.0000 0.00000 0.00000 0.00000 35.237 -76493 -27157
H2O 55.5008 0.99058 0.99058 0.99981 17.233 -245456 -245411
#normalized, *partial molar, **molal ref. state, ***molar ref. state.
Back-calculated vs optimized fluid bulk composition:
optimized optimized
mol % mol % wt % wt %
H2 65.9941 65.9939 10.9518 10.9518
C 0.179400 0.179457 0.177419 0.177475
Si 0.134456 0.134462 0.310923 0.310935
Al 0.137329E-03 0.137340E-03 0.305085E-03 0.305109E-03
Fe 0.359553E-08 0.359543E-08 0.165326E-07 0.165321E-07
Mg 0.565796E-06 0.565921E-06 0.113226E-05 0.113250E-05
Ca 0.445747E-03 0.445744E-03 0.147091E-02 0.147090E-02
Na 0.294331 0.294408 0.557147 0.557291
K 0.147228E-01 0.147130E-01 0.473964E-01 0.473648E-01
O2 33.3772 33.3772 87.9396 87.9394
S2
0.528289E-02 0.528312E-02 0.139477E-01 0.139482E-01
The lagged forward-calculated
speciation algorithm (aka, lagged speciation, Connolly & Galvez 2018) exploits
the iterative nature of adaptive optimization calculations in Perple_X. After
each iteration, the chemical potentials are used to formulate expressions for
the solute concentrations in terms of the solvent concentrations and partial
molar Gibbs energies. These expressions together with an equation of state for
the solvent species and the charge balance and closure constraints comprise a
closed system of equations which is solved iteratively for the concentrations
of both solute and solvent species. The solution becomes exact in the limit
that the chemical potentials of the system do not change significantly during
successive iterations. The degree to which this limit has been realized can be
assessed by setting the output_iteration_G keyword to True and/or by
simultaneously evaluating the back-calculated speciation by setting the aqueous_output
keyword to True. The difference between the back- and lagged-speciation is
attributable to the use of lagged chemical potentials to compute the latter,
i.e., the back-calculated composition is a more precise solution, but the
composition from the lagged solution is used to compute phase proportions and
is therefore to be preferred for reactive transport modelling. Note: the "back-calculated"
result reported for lagged-speciation calculations corresponds to the
speciation obtained from Eq 12 of Connolly and Galvez (2018) at h = n, i.e.,
once iteration has ceased after n iterations; this differs from the "simple back-calculated" result reported
if the aq_lagged_speciation is set to false. The
latter corresponds to the speciation obtained from Eq 12 at h = 0.
Perple_X automatically
does lagged speciation if: 1) solute species data is present in the thermodynamic
data file; 2) a recognized solvent solution model is present; and 3) the Perple_X option
keyword lagged_aq_speciation is set to true (it is true by
default). Currently the only recognized solvent solution model is the generic
hybrid mixed-volatile solution model (solution model type 39). In contrast
to other solution models, generic hybrid solution models may have only one
endmember (e.g., the WADDAH
solution model) so that lagged speciation calculations can be done for a pure
water solvent. At present, saturated phases, and saturated or mobile components
cannot, or at least should not, be specified in lagged speciation problems.
Lagged speciation calculations will
not converge if the equilibrium solute concentrations are extraordinarily high.
Thus, at least with the DEW version of the SUPCRT data, the organic species
mentioned re back-calculation must be excluded. If lagged speciation
calculations do not converge, back-calculation with lagged speciation turned
off (i.e., lagged_aq_speciation set to False), will identify
the problematic species.
In addition to species
concentrations, in lagged speciation calculations Perple_X includes eight mock-species in
the computational results (Figure 2): ionic_st (molal ionic
strength), tot_mola (total molality), solv_mas (solvent
molar mass, kg/mol), err_lgKw (the
error in the base 10 log of the water dissociation constant), pH, Delta_pH (the difference between the pH and neutral pH), solute_m (total
solute molality), and epsilon (solvent
dielectric constant). The err_lgKw
parameter is diagnostic of the precision of the calculation. Results involving
a lagged speciation electrolyte solution models are analyzed using WERAMI or
MEEMUM in the same manner as a non-electrolytic solution model.
- Lagged speciation calculations will
identify electrolytic phase separation between phases with different
solvent compositions. For example, it will identify CH4- and CO2-rich solvent
phases coexisting with a water-rich solvent phase, but it will not
identify an electrolyte-rich H2O brine coexisting with an electrolyte-poor
H2O solvent (explicit solution models such as F(salt) should be used in
such cases). This limitation is not truly algorithmic, but reflects the
limited range of solute concentrations that can be modeled with the HKF
formulation, at least as currently implemented in Perple_X.
- Lagged speciation calculations become
invalid if the composition of the impure solvent phase moves outside of
the composition space bounded by phase compositions identified in the
previous iteration. This is inescapable if a solute component (e.g., K2O, CaO, or Na2O) is dissolved entirely in the solvent
phase; it may also occur at high solute concentrations (~5-10 m). When
this occurs Perple_X
reports that the optimization failed although technically the optimization
is possible, though numerically unstable. The results of such optimizations
can be obtained by specifying the aq_bad_results
option. Characteristically, such optimizations identify both the pure and
impure solvent as stable coexisting phases.
- As currently implemented, in lagged
speciation calculations there is no accounting for solvent-solute
interaction parameters other than Debye-Huckel
activity coefficients. This has the consequence that the solvent activity
coefficients are not a function of solute content. This behavior is likely
to be a reasonable approximation if the total mole fraction of the solutes
is less than 10% (~5 molal solute concentration). This limitation is not
algorithmic.
Relevant Perple_X options
- species_output
- controls whether phase speciation is output.
- aq_bad_results
- allows output of results once a solute component is completely depleted
from the solid/melt assemblage (not recommended, see limitations).
- aq_vapor_epsilon
- allows specification of a threshold for the dielectric constant of the
solvent, below this threshold the solvent is assumed to be vapor and incapable
of dissolving solutes.
- aq_output
- controls whether the forward result is compared to the back-calculated
speciation.
- aq_oxide_components
- disables certain traps for speciation calculations with oxide components
(not recommended).
- aq_solvent_composition - controls solvent
concentration units on output.
- aq_solute_composition
- controls solute concentration units on output.
- aq_lagged_iterations
- controls number of lagged speciation iterations made for each adaptive
minimization iteration.
- aq_lagged_speciation
- controls whether lagged speciation is computed.
- output_iteration_G
- controls whether the free energy and chemical potentials of the system
are output during iteration.
The 6.8.1 version of Perple_X used for
the calculations shown in Connolly
& Galvez (2018) had an error that caused the solvent dielectric
constant to be computed by the MRK EoS regardless of
the molecular EoS specified by the user. The error
was not corrected because its consequences are minor, but the error has the
consequence that the current (6.8.4) version does not exactly reproduce all the
published figures (Figure 2 and A.1 are exceptions because these figures were
calculated for the revised version of the paper). The COHS-solvent model used
in the paper, while perhaps useful for purposes of illustration, is not the
optimal practical configuration. In most of the examples below this model has
been replaced by a CO2-H2O-solvent model. The distinction between these models
is clarified below and has no significant impact on
computational results. The files listed below include some output for testing
purposes and/or comparison. The collected files are in example_connolly_epsl_2018.zip.
Notes on the calculations and Matlab plotting*:
- The H2O-solvent model was invoked by the
WADDAH solution model (gloss1d6).
- The COHS-solvent model was invoked by the
COH-Fluid+ solution model (gloss1d), including H2O,
CH4, CO2, and H2S as solvent species, and excluding all DEW C-O-H-S
molecular solute species.
- The CO2-H2O-solvent model was invoked by the
COH-Fluid+ solution model (gloss1d1, gloss1di, gloss1d5),
including H2O and CO2 as solvent species, and including all DEW C-O-H-S molecular
solute species except CO2(aq). This model is
preferred over the COHS solvent model for reasons outlined above. Comparison of
the gloss1d and gloss1d1 results demonstrates that the complexity of the
COHS-solvent model is not justified.
- WADDAH, COH-Fluid+ and COH-Fluid are generic
hybrid fluid EoS. COH-Fluid+ and COH-Fluid
are interchangeable, the distinction between these models is that
COH-Fluid+ specifies non-linear subdivision that provides higher
resolution at low (insignificant) concentrations. COH-Fluid specifies
linear (uniform) resolution and may be preferable for situations in which
the concentrations of molecular C- and/or S-species become comparable to
that of H2O.
- High solute concentrations may be a
source of numerical instability near
the fluid-dominated limit. This instability is dampened in the
calculations presented here by setting the global_reach_increment option to 6. The
instability is manifest by irregular compositional variations, spurious
solvi (notably for garnet and magnesite as in gloss1d_modes.jpg),
and failed optimizations (missing data).
- The gloss1d calculations were
configured in BUILD as a "1-d Phase fractionation calculation"
with "path coordinates entered from a file".
Most of the plots reproduced here were made with the nodal coordinates in this file as the independent variable. The coordinate
file was generated by incrementing pressure by a constant value (100 bar)
such that P = 1 + (node# - 1) * 100.
- Cumulative modal abundance
plots generated with the perple_x_simple_plot (or perple_x_plot)
Matlab script are aesthetically pleasing, but the
raw plot may be difficult to interpret for several reasons: 1) Overlapping
lines have the consequence that the colors indicated in the legend cannot
be used to identify the various phase fields; use WERAMI mode 1
calculations or make a non-cumulative mode plot to identify the phase
fields. 2) Both real and spurious solvi may result in spiky phase
boundaries. The only phase with a real solvus is Omph(GHP)
and in most examples this solvus is drawn with only one spike. The reason
for the spike is that WERAMI does not have compositional criteria for
identifying the phases that coexist across a solvus. Rather it tabulates
the phases in the order in which they are identified during optimization, thus
although the tab file contains two columns for Omph(GHP),
the Ca-rich phase may appear in either column and any change this ordering
will cause a spike. For this reason a minimum of one spike (gloss1d6_modes.jpg
at node ~350) will be drawn if a profile passes through a 2-phase solvus,
e.g., in the present models, initially the single Na-rich phase in the
first Omph(GHP) column and, after passing
through the solvus, the single Ca-rich phase is located in the first Omph(GHP) column. These spikes reflect the way WERAMI
works and are not indicative of computational instability. In contrast,
spurious solvi are indicative of computational instability and, generally,
lead to a more irregular pattern of spikes (e.g., gloss1d6_modes.jpg
at nodes ~640-670). Spurious solvi can be recognized from irregular
behavior and/or coexistence of several phases of the same solution with
nearly identical composition. In the gloss1d6 case, this occurs for both
garnet "Grt(JH)" and magnesite
"M(HP)"; the consequences are largely cosmetic. Optimization
options can be modified
to eliminate spurious solvi; the effort rarely justifies the result.
- Species abundances plot made with the perple_x_simple_plot
(or perple_x_plot) Matlab script were modified by using the property
editor to make the y-axis logarithmic and set the y-range from 1e-2 to
1e1. Selecting individual curves while the property editor is open is a
simple means of identifying which species is represented by a curve.
Spikes/irregularity in these plots is indicative of numerical
instability.
*Similar plots can be generated with
PYWERAMI or the Perple_X program
PSTABLE.
Files common to multiple
calculations:
Figures 2 and A.1. K/Si-solubility,
Closed system, H2O-Solvent Model, Lagged
Speciation (Figures 2, A.1):
Lagged Speciation (Figures 4a, 5, 6ab), GLOSS Closed-System, CO2-H2O-Solvent
Model:
Lagged
Speciation
(Figures 5c, 6c), GLOSS Open-System, CO2-H2O-Solvent Model:
Lagged
Speciation
(Figure 7), GLOSS Open-System + infiltration, CO2-H2O-Solvent Model:
Simple
Back-Calculated
Speciation (Figures 4b, 5a), GLOSS
Closed-System, CO2-H2O-Solvent Model:
Lagged
Speciation
(Figures 4a, 5b, 6b), GLOSS Closed-System, H2O-Solvent
Model:
Lagged
Speciation
(Figures 4a, 5, 6ab), GLOSS Closed-System, COHS-Solvent
Model:
Figure 3. Forward and back-calculated solute speciation at 1200 K and 0.5 GPa obtained by running MEEMUM with the aq1_ox_forward.dat problem definition file.
Stable phases at:
T(K) = 1200.00
P(bar) = 5000.00
Phase Compositions (molar proportions):
wt % vol % mol % mol H2O MgO O2
Aq_solvent 57.28 75.00 75.00 3.00 1.00000 0.00000 0.00000
per 42.72 0.00 25.00 1.00 0.00000 1.00000 0.00000
Phase speciation (molar proportions):
Aq_solvent H2O: 1.0000, H+: 0.10522E-06, Mg+2: 0.44455E-09, MgOH+: 0.27080E-06,
OH-: 0.37691E-06
...output abridged...
Chemical Potentials (J/mol):
H2O MgO O2
-340564. -621905. NaN
Back-calculated solute speciation in the solvent:
pH = 5.300+/-0.000; neutral_pH = 4.969; ionic_strength = 0.2089E-04; gamma/q^2 = 0.9806
dielectric constant = 7.060; solvent molar mass, g/mol = 18.0150;
total solute molality = 0.4173E-04
Solute endmember properties:
optimized
charge molality mol_fraction mol_fraction g,J/mol* g0,J/mol**
OH- -1 0.234248E-04 0.421998E-06 0.376910E-06 -218814 -112244
MgOH+ 1 0.131595E-04 0.237069E-06 0.270805E-06 -743653 -631330
H+ 1 0.511649E-05 0.921735E-07 0.105216E-06 -121749 0
Mg+2 2 0.196915E-07 0.354742E-09 0.444549E-09 -524838 -347030
HO2- -1 0.706131E-08 0.127209E-09 -218814 -31359
Solvent endmember properties:
molality mol_fraction vol_fraction v,cm3/mol* g,J/mol* g0,J/mol***
H2O 55.5093 1.00000 1.00000 28.502 -340563 -340563
*partial molar, **molal ref. state, ***molar ref. state.
Back-calculated vs optimized (forward) fluid bulk composition:
optimized optimized
mol % mol % wt % wt %
H2O 100.0000 100.0000 100.0000 99.9999
MgO 0.237423E-04 0.271250E-04 0.531174E-04 0.606852E-04
O2 0.231070E-05 0.194976E-14 0.410436E-05 0.346324E-14
In brute-force
forward-calculated electrolyte speciation models it is currently assumed
that the activity coefficients of the solvent species are the same in the
solute-bearing fluid as in a fluid consisting only of the solvent species. The
concentrations of neutral and electrolyte solutes influence the partial molar
free energies of the solvent species, unlike the back-calculated case, by
affecting the concentrations of the solvent species.
Brute-force forward-calculation of
electrolyte speciation involves specification of a solution model for the
electrolytic fluid. Electrolytic solution models are identified as solution
model type 20. Three examples, Aq_solvent,
Aq_solven0, and Aq_Solven1 are present in solution_model.dat (input files
for the forward solution models that correspond to the three back-calculated
examples are included with those
examples, the input files were run with MEEMUM at 1200 K and 5000 bar). The
conditions for the use of these models are the same as for generic
hybrid mixed-volatile solution models. In contrast to other solution model
types in Perple_X,
the initial resolution of the model is not controlled by initial resolution
keyword; rather, the initial resolution is taken as specified in the solution
model subdivision scheme. If it is desired to resolve concentrations that span
many orders of magnitude the a non-linear
subdivision scheme is recommended and the stretch factor should be adjusted
to obtain the desired density of compositions. The lowest concentration (as a
mole fraction) that Perple_X
can resolve is final_resolution * speciation_factor.
It is futile to include species present in concentrations below this limit.
Results involving brute-force
forward-calculated electrolyte solution models are analyzed using WERAMI or MEEMUM
in the same manner as a non-electrolytic solution model.
The accuracy of forward speciation
(i.e., "optimized") calculations can be
assessed by comparison with the back-calculated speciation and bulk composition (Figure 3).
Brute-force calculation is
computationally intensive and is impractical for >> 10 species. Selecting
the species to be included in the model requires expertise (which may be
gleaned by doing a preliminary calculation with back-calculated speciation).
Additionally, it may be necessary to adjust the default resolution and
subdivision parameters to obtain precise solutions. In the future, an adaptive
algorithm will be introduced to identify the dominant species as a function of physico-chemical conditions.
Relevant Perple_X options
- species_output
- controls whether phase speciation is output. NOTE:
the species concentrations output in brute-force calculation is
in molar molar units regardless of the aq_solvent_composition and aq_solute_composition
keywords.
- aq_output
- controls whether the forward result is compared to the back-calculated
speciation.
- aq_oxide_components
- allows back- and lagged-forward calculated speciation with oxide
components (not recommended, necessary in this example only to obtain the
back-calculated result for comparison).
- stretch_factor - controls the assymetry
of non-linear subdivision models, the subdivision is quasi-logarithmic in
the limit that the stretch factor goes to zero.
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