3- Equip: Modeling Tools & Databases#
What are geochemical modeling programs used for?#
Geochemical modeling programs are used for multiple purposes including:
Plotting of activity, calculation of thermodynamic constants, or phase stability diagrams-equilibrium constants (K) of reaction fO2-pH, logaK+/H+, logaSiO2, P-T diagrams
Equilibrium speciation calculations in natural waters
Aqueous speciation, pH, and mineral saturation indices
Complex geochemical processes
mineral solid solutions, surface complexation, nucleation & growth kinetics
Inverse modeling – determine input for known outcome (products)
CO2 partial pressure, amount of HCl/NaOH to reach a certain pH, back-calculate downhole fluid chemistry before boiling
Forward reaction path modeling – predict the outcome for given input (reactants)
Titration model with varying fluid/rock ratios
Dissolution of primary minerals, precipitation of secondary minerals (kinetics or equilibrium) - fluid evolution with increased reaction progress
Coupling with transport models:
1-D, 2-D, 3-D reactive mass and heat transport
Multiphase fluid flow and physical models (fracture networks, faults, permeability)
Geochemical modeling program#
Here is a list of popular modeling programs, including “Law of mass action (LMA)” and “Gibbs Energy Minimization (GEM)” based chemical solvers.
Geochemical equilibrium solver – LMA based
PHREEQC, USGS, D. Parkhurst & Appelo (1999)
Geochemist’s Workbench, Aqueous Solutions LLC,
SOLVEQ, M. Reed, N. Spycher, J. Palandri, U. Oregon; EQ3/6 (Wolery, 1983), MINTEQA2, CHESS (van der Lee et al., 2002), Reaktoro, ETHZ, (Leal), WATEQ4
Geochemical equilibrium solver – GEM based
GEMS code package, Paul Scherrer Institute, D. Kulik, D. Miron
HCh, MSU, Y. Shvarov,
Reactive mass transport codes
TOUGHREACT, LBL, E. Sonnenthal, N. Spycher, T. Xu
Other Tools:
Law of mass action (LMA) and Gibbs Energy Minimization (GEM) based chemical solvers#
These two methods for solving geochemical fluid-rock equilibrium problems have different approaches, which also translates in the overall way a chemical system is setup and a thermodynamic database is compiled. Some of the advantages/disadvantages are speed of calculations, and the complexity of the system (e.g. solid solutions, non-ideal multi-phase/component systems) that can be solved. For the sake of simplicity, I will briefly summarize a comparison between PHREEQC (LMA code) and GEMS (GEM code) in this comparison table:
LMA type code |
GEM type code |
|---|---|
Set of master species (Al3+, H+, OH-, H2O(aq)) |
Mass balance using (IC) independent components (H, O, Al, …) and electric charge (z) |
Other species built from master species (Al3+ + 4OH- = Al(OH)4-) |
Chemical species are (DC) dependent components (aqueous species, minerals, gases…) built from IC |
Database with equilibrium constants (logKr) at T and at water saturation pressure |
Database with standard Gibbs energy (G°) corrected at P-T |
LMA to solve mass balance using Newton-Raphson method (Bethke, 1996) |
GEM to solve mass balance using Interior Points method (Karpov et al. 2001) |
Redox (Eh, pe or redox pair Fe(II)/Fe(III)) and pH (or element charge balance) must be set at input |
pH and redox (pe, Eh) calculated from minimization and chemical potentials |
Only limited (binary) solid solution models |
Solve equilibrium for complex multisite non-ideal solutions |
Fast convergence: kinetics rate laws and reactive transport model |
Slower convergence, but more output data from a single calculation: e.g. phase volumes, fugacity, etc… |
A summary of chemical solvers numerical methods and comparison between LMA, GEM and newer approach such as extended LMA (xLMA) are summarized nicely by Leal et al.[LKSS17]
Limitations of geochemical modeling codes - not a “black-box”#
Most of the geochemical modeling codes have naturally some limitations, many of which are related to the underlying thermodynamic databases and the existing or implementation of equations of state for complex phases and their stability as a function of pressure and temperature. This quote by [OBP09] gives an idea of the importance of not using geochemical modeling as a “black-box”:
All of these codes allow calculations/prediction of the equilibrium and/or evolution of geochemical systems as a function of reaction progress with the press of a few buttons. Such calculations appear to have an amazing accuracy; results of these computer codes are commonly reported to 4 or more significant digits.
Therein lies the disadvantage of these computer codes as they give the appearance that the thermodynamic databases on which they are based are perfect and accurate beyond all imagination. For many species or minerals few data exist, and in many other cases, no experimental data exist at all. In such cases the thermodynamic ‘data’ were ‘created’ using correlations
Common limitations of geochemical modeling codes can be grouped in the following aspects:
Thermodynamic databases
Availability and type of thermodynamic data (databases) – most databases limit to 300 °C at saturated water vapor pressure
Element availability, activity coefficient models suitable for high ionic strength, internal consistency of data
Formats of thermodynamic databases – logKs (LMA type codes) vs. more flexible (GEM type codes) with Cp functions, phase transitions, logK lookup tables, etc.
Corrections for pressure (P) and temperature (T), and solutions mixing properties
Equations of State (EoS) – used for calculating phase properties such as fugacities and volumes of gases or gas mixtures, properties of aqueous species at high P-T (HKF model, density model)
Mixing properties and complexity of solutions – includes mineral solid solutions (binary, ternary, or more) and non-ideal gases mixing properties (e.g. CO2-H2O)
“User friendliness” and feature availability
GUI, plotting of certain activity-activity diagrams, adding/editing of thermodynamic database, coupling to reactive transport
Thermodynamic databases#
Different approaches are being used to compile, evaluate, and curate thermodynamic databases in various formats. One of the key components is maintaining internal consistency, critical evaluation (reliability and uncertainty) of the data and methods to retrieve them, and testing of the data to real-world problems. It is also important to understand the validity limits of each databases and how they are retrieved. Hence a fundamental knowledge in thermodynamics is crucial for the seasoned geochemical modeler.
Here is a non-exhaustive list of some common thermodynamic databases used in geochemical modeling:
Minerals, gases, aqueous species:
MINES thermodynamic database [GHP+23] NMBGMR/NMT (ore deposits, critical minerals, geothermal, CO2 sequestration, hydrothermal fluid-rock)
SUPCRT92, slop98.dat, and updated SUPCRTBL, Zimmer et al. [ZZL+16], Indiana U.
Provided in PHREEQC (see review by Lu et al. [LZAZ22]), many of these are also part of GWB software: phreeqc.dat, llnl.dat, wateq4f.dat, carbfix.data, minteq.data, supcrtbl.dat, pitzer.dat, etc.
Application specific: PSI-NAGRA and THEREDA (radioactive wastes), Cemdata (cement industry), THERMODDEM (wastes, geothermal, acid mine, cement)
Mineral specific databases
Holland and Powell [HP98, HP11], based on metamorphic phase equilibria, least-squares regression technique to optimize the thermodynamic parameters, minimizing inconsistencies between calculated and observed phase equilibria
Gottschalk [Got97], calorimetry, phase equilibria, solubility data, empirical estimations
Berman and Brown [BB85], fitting and revised equation for heat capacity
Robie and Hemingway (1995), USGS compilation and critical evaluation, based on calorimetric measurements
Citations#
Robert G Berman and Thomas H Brown. Heat capacity of minerals in the system Na2O-K2O-CaO-MgO-FeO-Fe2O3-Al2O3-SiO2-TiO2-H2O-CO2: representation, estimation, and high temperature extrapolation. Contributions to Mineralogy and Petrology, 89:168–183, 1985.
Matthias Gottschalk. Internally consistent thermodynamic data for rock-forming minerals in the system SiO2-TiO2-Al2O3-CaO-MgO-FeO-K2O-Na2O-H2O-CO2. European Journal of Mineralogy, 9(1):175–223, 1997.
A.P. Gysi, N.C. Hurtig, R. Pan, G.D. Miron, and D.A. Kulik. Mines thermodynamic database. New Mexico Bureau of Geology and Mineral Resources, 2023. doi:https://doi.org/10.58799/mines-tdb.
TJB Holland and R Powell. An internally consistent thermodynamic data set for phases of petrological interest. Journal of metamorphic Geology, 16(3):309–343, 1998.
TJB Holland and R Powell. An improved and extended internally consistent thermodynamic dataset for phases of petrological interest, involving a new equation of state for solids. Journal of metamorphic Geology, 29(3):333–383, 2011.
Allan MM Leal, Dmitrii A Kulik, William R Smith, and Martin O Saar. An overview of computational methods for chemical equilibrium and kinetic calculations for geochemical and reactive transport modeling. Pure and Applied Chemistry, 89:597–643, 2017. doi:https://doi.org/10.1515/pac-2016-1107.
Peng Lu, Guanru Zhang, John Apps, and Chen Zhu. Comparison of thermodynamic data files for phreeqc. Earth-Science Reviews, 225:103888, 2022. doi:https://doi.org/10.1016/j.earscirev.2021.103888.
Eric H Oelkers, Pascale Benezeth, and Gleb S Pokrovski. Thermodynamic databases for water-rock interaction. Reviews in Mineralogy and Geochemistry, 70(1):1–46, 2009.
Kurt Zimmer, Yilun Zhang, Peng Lu, Yanyan Chen, Guanru Zhang, Mehmet Dalkilic, and Chen Zhu. Supcrtbl: a revised and extended thermodynamic dataset and software package of supcrt92. Computers & geosciences, 90:97–111, 2016. doi:https://doi.org/10.1016/j.cageo.2016.02.013.