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References

This page lists the software, databases, models and papers that discopt.speciation implements or relies on. For each, it says where the package uses it. DOIs were checked against Crossref. Entries without a DOI give a stable library or publisher link.

Citing results computed with this package

Cite: - the package and discopt; - the database you used (see Databases); - the activity model, if the result depends on it (see Activity models).

For example, a calculation with sit.dat should cite PHREEQC (Parkhurst and Appelo 2013), ThermoChimie (Giffaut et al. 2014) and the SIT references.

Software

Databases

file cite
phreeqc.dat Parkhurst and Appelo (2013)
pitzer.dat Plummer et al. (1988); Appelo (2015)
wateq4f_PWN.dat Ball and Nordstrom (1991)
llnl.dat Delany and Lundeen (1991)
sit.dat Giffaut et al. (2014); ThermoChimie v12a
minteq.v4.dat (tests only) Allison et al. (1991)
  • Plummer, L.N., Parkhurst, D.L., Fleming, G.W., and Dunkle, S.A. (1988). A computer program incorporating Pitzer's equations for calculation of geochemical reactions in brines. USGS Water-Resources Investigations Report 88-4153. https://doi.org/10.3133/wri884153
  • Appelo, C.A.J. (2015). Principles, caveats and improvements in databases for calculating hydrogeochemical reactions in saline waters from 0 to 200 °C and 1 to 1000 atm. Applied Geochemistry 55, 62–71. https://doi.org/10.1016/j.apgeochem.2014.11.007
  • Ball, J.W., and Nordstrom, D.K. (1991). User's manual for WATEQ4F, with revised thermodynamic data base and test cases for calculating speciation of major, trace, and redox elements in natural waters. USGS Open-File Report 91-183. https://doi.org/10.3133/ofr91183
  • Delany, J.M., and Lundeen, S.R. (1991). The LLNL thermochemical data base: revised data and file format for the EQ3/6 package. Lawrence Livermore National Laboratory, UCID-21658. https://www.osti.gov/biblio/138193
  • Giffaut, E., Grivé, M., Blanc, P., Vieillard, P., Colàs, E., Gailhanou, H., et al. (2014). Andra thermodynamic database for performance assessment: ThermoChimie. Applied Geochemistry 49, 225–236. https://doi.org/10.1016/j.apgeochem.2014.05.007; data (v12a) and terms of use: https://www.thermochimie-tdb.com
  • Allison, J.D., Brown, D.S., and Novo-Gradac, K.J. (1991). MINTEQA2/PRODEFA2, a geochemical assessment model for environmental systems: version 3.0 user's manual. EPA/600/3-91/021. https://www.osti.gov/biblio/5673069 — origin of the minteq.v4 constants used in the validation cases.

Activity models

activity.py:

  • Debye–Hückel (DebyeHuckel, ExtendedDebyeHuckel, and the long-range term of every model): Debye, P., and Hückel, E. (1923). Zur Theorie der Elektrolyte. I. Gefrierpunktserniedrigung und verwandte Erscheinungen. Physikalische Zeitschrift 24, 185–206.
  • Davies (Davies, and the fallback for ions without size parameters in TruesdellJones and LLNL):
  • Davies, C.W. (1938). The extent of dissociation of salts in water. Part VIII. Journal of the Chemical Society, 2093. https://doi.org/10.1039/JR9380002093
  • Davies, C.W. (1962). Ion Association. Butterworths, London.
  • Truesdell–Jones (TruesdellJones, also used for exchange species): Truesdell, A.H., and Jones, B.F. (1974). WATEQ, a computer program for calculating chemical equilibria of natural waters. Journal of Research of the U.S. Geological Survey 2(2), 233–248. https://pubs.usgs.gov/publication/70232379
  • B-dot (BDot, LLNL): Helgeson, H.C. (1969). Thermodynamics of hydrothermal systems at elevated temperatures and pressures. American Journal of Science 267, 729–804. https://doi.org/10.2475/ajs.267.7.729
  • CO₂(aq) activity coefficient (-co2_llnl_gamma in LLNL): Drummond, S.E. (1981). Boiling and mixing of hydrothermal fluids: chemical effects on mineral precipitation. PhD thesis, Pennsylvania State University.
  • Salting-out of neutral species (the bI term): Setschenow, J. (1889). Über die Konstitution der Salzlösungen auf Grund ihres Verhaltens zu Kohlensäure. Zeitschrift für Physikalische Chemie 4, 117–125. https://doi.org/10.1515/zpch-1889-0409
  • Specific ion interaction theory (SIT):
  • Brønsted, J.N. (1922). Studies on solubility. IV. The principle of the specific interaction of ions. Journal of the American Chemical Society 44, 877–898. https://doi.org/10.1021/ja01426a001
  • Scatchard, G. (1936). Concentrated solutions of strong electrolytes. Chemical Reviews 19, 309–327. https://doi.org/10.1021/cr60064a008
  • Guggenheim, E.A., and Turgeon, J.C. (1955). Specific interaction of ions. Transactions of the Faraday Society 51, 747. https://doi.org/10.1039/TF9555100747
  • Ciavatta, L. (1980). The specific interaction theory in evaluating ionic equilibria. Annali di Chimica (Rome) 70, 551–567.
  • Grenthe, I., Fuger, J., Konings, R.J.M., Lemire, R.J., Muller, A.B., Nguyen-Trung, C., and Wanner, H. (1992). Chemical Thermodynamics of Uranium. NEA-OECD, North-Holland. https://www.oecd-nea.org/jcms/pl_13704 — the NEA TDB form, with the 1.5√I denominator used by ThermoChimie.
  • Pitzer (Pitzer, _etheta.py):
  • Pitzer, K.S. (1973). Thermodynamics of electrolytes. I. Theoretical basis and general equations. Journal of Physical Chemistry 77, 268–277. https://doi.org/10.1021/j100621a026
  • Pitzer, K.S., and Mayorga, G. (1973). Thermodynamics of electrolytes. II. Activity and osmotic coefficients for strong electrolytes with one or both ions univalent. Journal of Physical Chemistry 77, 2300–2308. https://doi.org/10.1021/j100638a009
  • Pitzer, K.S., and Kim, J.J. (1974). Thermodynamics of electrolytes. IV. Activity and osmotic coefficients for mixed electrolytes. Journal of the American Chemical Society 96, 5701–5707. https://doi.org/10.1021/ja00825a004
  • Pitzer, K.S. (1975). Thermodynamics of electrolytes. V. Effects of higher-order electrostatic terms. Journal of Solution Chemistry 4, 249–265. https://doi.org/10.1007/BF00646562 — the unsymmetrical mixing terms (E-θ).
  • Harvie, C.E., Møller, N., and Weare, J.H. (1984). The prediction of mineral solubilities in natural waters: the Na-K-Mg-Ca-H-Cl-SO4-OH-HCO3-CO3-CO2-H2O system to high ionic strengths at 25 °C. Geochimica et Cosmochimica Acta 48, 723–751. https://doi.org/10.1016/0016-7037(84)90098-X
  • MacInnes, D.A. (1919). The activities of the ions of strong electrolytes. Journal of the American Chemical Society 41, 1086–1092. https://doi.org/10.1021/ja02228a006 — the convention for individual-ion activity coefficients.

Water properties

water.py:

  • Wagner, W., and Pruß, A. (2002). The IAPWS formulation 1995 for the thermodynamic properties of ordinary water substance for general and scientific use. Journal of Physical and Chemical Reference Data 31, 387–535. https://doi.org/10.1063/1.1461829 — density on the saturation curve.
  • Bradley, D.J., and Pitzer, K.S. (1979). Thermodynamics of electrolytes. 12. Dielectric properties of water and Debye–Hückel parameters to 350 °C and 1 kbar. Journal of Physical Chemistry 83, 1599–1603. https://doi.org/10.1021/j100475a009 — dielectric constant and Debye–Hückel parameters.

Phases, exchange and surfaces

phases.py, species.py:

  • Appelo, C.A.J., Parkhurst, D.L., and Post, V.E.A. (2014). Equations for calculating hydrogeochemical reactions of minerals and gases such as CO₂ at high pressures and temperatures. Geochimica et Cosmochimica Acta 125, 49–67. https://doi.org/10.1016/j.gca.2013.10.003 (molar volumes and the pressure dependence of log K)
  • Peng, D.-Y., and Robinson, D.B. (1976). A new two-constant equation of state. Industrial & Engineering Chemistry Fundamentals 15, 59–64. https://doi.org/10.1021/i160057a011
  • Søreide, I., and Whitson, C.H. (1992). Peng-Robinson predictions for hydrocarbons, CO₂, N₂, and H₂S with pure water and NaCl brine. Fluid Phase Equilibria 77, 217–240. https://doi.org/10.1016/0378-3812(92)85105-H (PHREEQC's default H₂O(g) binary parameters)
  • Gaines, G.L., and Thomas, H.C. (1953). Adsorption studies on clay minerals. II. A formulation of the thermodynamics of exchange adsorption. Journal of Chemical Physics 21, 714–718. https://doi.org/10.1063/1.1698996 — exchange activities as equivalent fractions.
  • Dzombak, D.A., and Morel, F.M.M. (1990). Surface Complexation Modeling: Hydrous Ferric Oxide. Wiley, New York. ISBN 978-0-471-63731-8. — the diffuse double layer model (SurfaceType(edl="ddl")).
  • Ideal solid solutions, ideal gas phases, and \(\log K(T,P)\) from van 't Hoff, ΔCp, ΔV or analytic expressions follow the PHREEQC conventions (Parkhurst and Appelo 2013).
  • Non-ideal gases use the Peng–Robinson equation of state with PHREEQC's constants, mixing rule and default binary parameters (Søreide and Whitson 1992).

Solution methods

solve.py:

  • Fischer, A. (1992). A special Newton-type optimization method. Optimization 24, 269–284. https://doi.org/10.1080/02331939208843795 — the Fischer–Burmeister complementarity function.
  • Kanzow, C. (1996). Some noninterior continuation methods for linear complementarity problems. SIAM Journal on Matrix Analysis and Applications 17, 851–868. https://doi.org/10.1137/S0895479894273134 — the smoothed function and the ε-homotopy.
  • Smith, W.R., and Missen, R.W. (1982). Chemical Reaction Equilibrium Analysis: Theory and Algorithms. Wiley, New York. — Gibbs energy minimization (method="gibbs") and the stoichiometric formulation.
  • Leal, A.M.M., Kulik, D.A., Smith, W.R., and Saar, M.O. (2017). An overview of computational methods for chemical equilibrium and kinetic calculations for geochemical and reactive transport modeling. Pure and Applied Chemistry 89, 597–643. https://doi.org/10.1515/pac-2016-1107 — a review of mass-action and Gibbs minimization methods.

Global stability

Stability:

  • Baker, L.E., Pierce, A.C., and Luks, K.D. (1982). Gibbs energy analysis of phase equilibria. Society of Petroleum Engineers Journal 22(5), 731–742. https://doi.org/10.2118/9806-PA — the tangent plane criterion for global stability.
  • Michelsen, M.L. (1982). The isothermal flash problem. Part I. Stability. Fluid Phase Equilibria 9(1), 1–19. https://doi.org/10.1016/0378-3812(82)85001-2 — the tangent plane distance stability test.
  • Glynn, P.D. (1991). MBSSAS: a code for the computation of Margules parameters and equilibrium relations in binary solid-solution aqueous-solution systems. Computers & Geosciences 17(7), 907–966. https://doi.org/10.1016/0098-3004(91)90090-Z — binary miscibility gaps, as computed by PHREEQC.
  • Moore, R.E., Kearfott, R.B., and Cloud, M.J. (2009). Introduction to Interval Analysis. SIAM, Philadelphia. https://doi.org/10.1137/1.9780898717716 — the interval arithmetic in the certificate.

Parameter fitting

fit.py:

  • Venzon, D.J., and Moolgavkar, S.H. (1988). A method for computing profile-likelihood-based confidence intervals. Applied Statistics 37, 87–94. https://doi.org/10.2307/2347496
  • Raue, A., Kreutz, C., Maiwald, T., Bachmann, J., Schilling, M., Klingmüller, U., and Timmer, J. (2009). Structural and practical identifiability analysis of partially observed dynamical models by exploiting the profile likelihood. Bioinformatics 25, 1923–1929. https://doi.org/10.1093/bioinformatics/btp358

Diagrams

plot.py:

  • Pourbaix, M. (1966). Atlas of Electrochemical Equilibria in Aqueous Solutions. Pergamon Press, Oxford. Reprinted by NACE, Houston (1974).
  • Ellingham, H.J.T. (1944). Reducibility of oxides and sulphides in metallurgical processes. Journal of the Society of Chemical Industry 63(5), 125–133. https://doi.org/10.1002/jctb.5000630501

Validation cases and examples