GEM-Selektor geochemical modeling package: revised algorithm and GEMS3K numerical kernel for coupled simulation codes

Reactive mass transport (RMT) simulation is a powerful numerical tool to advance our understanding of complex geochemical processes and their feedbacks in relevant subsurface systems. Thermodynamic equilibrium defines the baseline for solubility, chemical kinetics, and RMT in general. Efficient RMT simulations can be based on the operator-splitting approach, where the solver of chemical equilibria is called by the mass transport part for each control volume whose composition, temperature, or pressure has changed. Modeling of complex natural systems requires consideration of multiphase–multicomponent geochemical models that include nonideal solutions (aqueous electrolytes, fluids, gases, solid solutions, and melts). Direct Gibbs energy minimization (GEM) methods have numerous advantages for the realistic geochemical modeling of such fluid–rock systems. Substantial improvements and extensions to the revised GEM interior point method algorithm based on Karpov’s convex programming approach are described, as implemented in the GEMS3K C/C+ + code, which is also the numerical kernel of GEM-Selektor v.3 package (http://gems.web.psi.ch). GEMS3K is presented in the context of the essential criteria of chemical plausibility, robustness of results, mass balance accuracy, numerical stability, speed, and portability to high-performance computing systems. The stand-alone GEMS3K code can treat very complex chemical systems with many nonideal solution phases accurately. It is fast, delivering chemically plausible and accurate results with the same or better mass balance precision as that of conventional speciation codes. GEMS3K is already used in several coupled RMT codes (e.g., OpenGeoSys-GEMS) capable of high-performance computing.

[1]  Informatika.  GNU Lesser General Public License , 2010 .

[2]  Laurent De Windt,et al.  Present state and future directions of modeling of geochemistry in hydrogeological systems. , 2001 .

[3]  Mark S. Ghiorso,et al.  Algorithms for the estimation of phase stability in heterogeneous thermodynamic systems , 1994 .

[4]  Peter Engesgaard,et al.  A geochemical transport model for redox-controlled movement of mineral fronts in groundwater flow systems: A case of nitrate removal by oxidation of pyrite , 1992 .

[5]  C. Appelo,et al.  PHT3D: A Reactive Multicomponent Transport Model for Saturated Porous Media , 2010, Ground water.

[6]  D. A. Kulik,et al.  Classic adsorption isotherms incorporated in modern surface complexation models: Implications for sorption of actinides , 2006 .

[7]  Gunnar Eriksson,et al.  A procedure to estimate equilibrium concentrations in multicomponent systems amd related applications , 1989 .

[8]  Olaf Kolditz,et al.  Thermo-Hydro-Mechanical-Chemical Processes in Porous Media , 2012 .

[9]  Haibing Shao,et al.  OpenGeoSys-GEMS: Hybrid parallelization of a reactive transport code with MPI and threads , 2012 .

[10]  Philippe Van Cappellen,et al.  A multicomponent reactive transport model of early diagenesis: Application to redox cycling in coastal marine sediments , 1996 .

[11]  Olaf Kolditz,et al.  A parallel finite element scheme for thermo-hydro-mechanical (THM) coupled problems in porous media , 2009, Comput. Geosci..

[12]  T. Poulet,et al.  PreMDB, a thermodynamically consistent material database as a key to geodynamic modelling , 2009 .

[13]  Glenn E. Hammond,et al.  Subsurface Multiphase Flow and Multicomponent Reactive Transport Modeling using High-Performance Computing , 2007 .

[14]  Olaf Kolditz,et al.  Modeling the competition between solid solution formation and cation exchange on the retardation of aqueous radium in an idealized bentonite column , 2009 .

[15]  Dmitrii A. Kulik,et al.  GEM-SELEKTOR GEOCHEMICAL MODELING PACKAGE: TSolMod LIBRARY AND DATA INTERFACE FOR MULTICOMPONENT PHASE MODELS , 2012 .

[16]  Dmitrii A. Kulik,et al.  The convex programming minimization of five thermodynamic potentials other than Gibbs energy in geochemical modeling , 2002 .

[17]  C. Kelley.  Solving Nonlinear Equations with Newton's Method , 1987 .

[18]  David Lopez,et al.  A state of the art report , 1979 .

[19]  Gunnar Eriksson,et al.  FactSage thermochemical software and databases - recent developments , 2009 .

[20]  James A. D. Connolly,et al.  Computation of phase equilibria by linear programming: A tool for geodynamic modeling and its application to subduction zone decarbonation , 2005 .

[21]  Olaf Kolditz,et al.  Modeling reactive transport in non-ideal aqueous–solid solution system , 2009 .

[22]  Special I Ssue,et al.  OpenGeoSys: an open-source initiative for numerical simulation of thermo-hydro-mechanical/chemical (THM/C) processes in porous media , 2012 .

[23]  Mark S. Ghiorso,et al.  Gibbs energy minimization in gas + liquid + solid systems , 2000, J. Comput. Chem..

[24]  D. Kulik,et al.  Chapter 7 – Standard molar Gibbs energies and activity coefficients of surface complexes on mineral-water interfaces (thermodynamic insights) , 2006 .

[25]  Wilfried Pfingsten,et al.  Efficient modeling of reactive transport phenomena by a multispecies random walk coupled to chemical equilibrium , 1996 .

[26]  Nicolas Spycher,et al.  Calculation of pH and mineral equilibria in hydrothermal waters with application to geothermometry and studies of boiling and dilution , 1984 .

[27]  M. Reed,et al.  Calculation of multicomponent chemical equilibria and reaction processes in systems involving minerals, gases and an aqueous phase , 1982 .

[28]  Philipp Birken,et al.  Numerical Linear Algebra , 2011, Encyclopedia of Parallel Computing.

[29]  Takashi Nakagawa,et al.  Incorporating self‐consistently calculated mineral physics into thermochemical mantle convection simulations in a 3‐D spherical shell and its influence on seismic anomalies in Earth's mantle , 2009 .

[30]  David A. C. Manning,et al.  Bethke, C.M. Geochemical and Biogeochemical Reaction Modeling Second Edition, 2007Cambridge University Press, Cambridge, UK. 564pp., Price £45, ISBN 978 0 521 87554 7 , 2008 .

[31]  Sebastian Geiger,et al.  A parallel FE-FV scheme to solve fluid flow in complex geologic media , 2008, Comput. Geosci..

[32]  G. Eriksson,et al.  ChemSage—A computer program for the calculation of complex chemical equilibria , 1990 .

[33]  Agence pour l'Energie Nucléaire.  Chemical Thermodynamics of Solid Solutions of Interest in Radioactive Waste Management , 2007 .

[34]  Patrick Goblet,et al.  Module-oriented modeling of reactive transport with HYTEC , 2003 .

[35]  E Brian Smith.  Non-ideal solutions , 2004 .

[36]  E. Rastetter.  Modeling coupled biogeochemical cycles , 2011 .

[37]  C. Bethke.  Geochemical and Biogeochemical Reaction Modeling , 2007 .

[38]  A. Koschinsky,et al.  Oxidative scavenging of cerium on hydrous Fe oxide: Evidence from the distribution of rare earth elements and yttrium between Fe oxides and Mn oxides in hydrogenetic ferromanganese crusts , 2009 .

[39]  Olaf Kolditz,et al.  A geochemical transport model for thermo‐hydro‐chemical (THC) coupled processes with saline water , 2011 .

[40]  C. Steefel,et al.  Reactive transport modeling: An essential tool and a new research approach for the Earth sciences , 2005 .

[41]  Robert M. Key,et al.  A global model for the early diagenesis of organic carbon and organic phosphorus in marine sediments , 1995 .

[42]  Thomas H. Brown,et al.  The computation of chemical equilibrium in complex systems containing non-ideal solutions , 1987 .

[43]  D. L. Parkhurst,et al.  User's guide to PHREEQC (Version 2)-a computer program for speciation, batch-reaction, one-dimensional transport, and inverse geochemical calculations , 1999 .

[44]  Taras V. Gerya,et al.  Numerical modelling of spontaneous slab breakoff dynamics during continental collision , 2010 .

[45]  Olaf Kolditz,et al.  Numerical simulation of non-isothermal compositional gas flow: Application to carbon dioxide injection into gas reservoirs , 2011 .

[46]  Yuri Shvarov.  A numerical criterion for existence of the equilibrium state in an open chemical system. Un critère numérique de l'existence d'un état d'équilibre pour un système chimique ouvert , 1989 .

[47]  Yen-Chih Peng,et al.  A Research of Software Combination under Free Software License- Focusing on GNU General Public License Version 3 , 2010 .

[48]  Olaf Kolditz,et al.  GeoSysBRNS - A flexible multidimensional reactive transport model for simulating biogeochemical subsurface processes , 2010, Comput. Geosci..

[49]  Yu. V. Shvarov,et al.  HCh: New potentialities for the thermodynamic simulation of geochemical systems offered by windows , 2008 .

[50]  Jordi Bruno,et al.  Chemical thermodynamics of solid solutions of interest in radioactive waste management : a state-of-the-art report , 2007 .

[51]  Gunnar Eriksson,et al.  FactSage thermochemical software and databases , 2002 .

[52]  Dmitrii A. Kulik,et al.  MODELLING CHEMICAL EQUILIBRIUM PARTITIONING WITH THE GEMS-PSI CODE , 2004 .

[53]  Konstantin Petrakakis,et al.  The computation of equilibrium assemblage diagrams with Theriak/Domino software , 2010 .

[54]  Hans Leo Lukas,et al.  Computational Thermodynamics: The Calphad Method , 2007 .

[55]  James A. D. Connolly,et al.  An automated strategy for calculation of phase diagram sections and retrieval of rock properties as a function of physical conditions , 2002 .

[56]  Konstantin V. Chudnenko,et al.  Modeling chemical mass transfer in geochemical processes; thermodynamic relations, conditions of equilibria and numerical algorithms , 1997 .

[57]  Olaf Kolditz,et al.  Hybrid analytical and finite element numerical modeling of mass and heat transport in fractured rocks with matrix diffusion , 2009 .

[58]  Thomas Monecke,et al.  Unusual rare earth element fractionation in a tin-bearing magmatic-hydrothermal system , 2011 .

[59]  Thomas Wagner,et al.  Thermodynamic modeling of non-ideal mineral–fluid equilibria in the system Si–Al–Fe–Mg–Ca–Na–K–H–O–Cl at elevated temperatures and pressures: Implications for hydrothermal mass transfer in granitic rocks , 2008 .

[60]  Olaf Kolditz,et al.  Application of the geomechanical facies approach and comparison of exploration and evaluation methods used at Soultz-sous-Forêts (France) and Spa Urach (Germany) geothermal sites , 2010 .

[61]  M. Reed,et al.  Calculation of Simultaneous Chemical Equilibria in Aqueous-Mineral-Gas Systems and its Application to Modeling Hydrothermal Processes , 1998 .