Mathematical Formulation Requirements and Specifications for the Process Models

LBNL-4085E Mathematical Formulation Requirements and Specifications for the Process Models November 9, 2010 ASCEM-HPC-10-01-1 United States Department of Energy C. Steefel, LBNL D. Moulton, LANL G. Pau, LBNL K. Lipnikov, LANL J. Meza, LBNL P. Lichtner, LANL T. Wolery, LLNL D. Bacon, PNNL N. Spycher, LBNL J. Bell, LBNL G. Moridis, LBNL S. Yabusaki, PNNL E. Sonnenthal, LBNL G. Zyvoloski, LANL B. Andre, LBNL L. Zheng, LBNL J. Davis, LBNL LBNL affiliates were partially supported by U.S. DOE and LBNL under Contract No. DE-AC02-05CH11231.

[1]  Carla M. Koretsky,et al.  Surface complexation modeling of Co(II) adsorption on mixtures of hydrous ferric oxide, quartz and kaolinite , 2009 .

[2]  M. Biot.  THEORY OF ELASTICITY AND CONSOLIDATION FOR A POROUS ANISOTROPIC SOLID , 1955 .

[3]  Kenneth S. Pitzer,et al.  Thermodynamics of electrolytes. V. effects of higher-order electrostatic terms , 1975 .

[4]  V. S. Vaidhyanathan,et al.  Transport phenomena , 2005, Experientia.

[5]  Matthias Kohler,et al.  Methods for estimating adsorbed uranium(VI) and distribution coefficients of contaminated sediments. , 2004, Environmental science & technology.

[6]  Kenneth S. Pitzer,et al.  Thermodynamics of electrolytes. I. Theoretical basis and general equations , 1973 .

[7]  Marc Aertsens,et al.  The BRAG and GM2003 Models for Glass Dissolution , 2006 .

[8]  Markus Olin,et al.  Uranium adsorption on weathered schist – intercomparison of modelling approaches , 2004 .

[9]  Kaj Thomsen.  Modeling electrolyte solutions with the extended universal quasichemical (UNIQUAC) model , 2005 .

[10]  L. Onsager.  Reciprocal Relations in Irreversible Processes. II. , 1931 .

[11]  C. Steefel,et al.  Approaches to modeling of reactive transport in porous media , 1996 .

[12]  Bruce A. Robinson,et al.  New form of dispersion tensor for axisymmetric porous media with implementation in particle tracking , 2002 .

[13]  A Revil,et al.  Introducing interacting diffuse layers in TLM calculations: a reappraisal of the influence of the pore size on the swelling pressure and the osmotic efficiency of compacted bentonites. , 2007, Journal of colloid and interface science.

[14]  Ruben Kretzschmar,et al.  Influence of Natural Organic Matter on Colloid Transport Through Saprolite , 1995 .

[15]  P. W. Reimus,et al.  Sorption Characteristics of Radionuclides on Clays in Yucca Mountain Alluvium , 2006 .

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

[17]  M. Biot.  General Theory of Three‐Dimensional Consolidation , 1941 .

[18]  Scott C Brooks,et al.  U(VI) adsorption to heterogeneous subsurface media: application of a surface complexation model. , 2002, Environmental science & technology.

[19]  James A. Davis,et al.  Modeling the influence of variable pH on the transport of zinc in a contaminated aquifer using semiempirical surface complexation models , 2000 .

[20]  Peter C. Lichtner,et al.  Continuum model for simultaneous chemical reactions and mass transport in hydrothermal systems , 1985 .

[21]  Jillian F. Banfield,et al.  The search for a molecular-level understanding of the processes that underpin the Earth's biogeochemical cycles , 2005 .

[22]  K. Kobe.  The properties of gases and liquids , 1959 .

[23]  Q. Jin,et al.  Predicting the rate of microbial respiration in geochemical environments , 2005 .

[24]  Michael L. Michelsen,et al.  State function based flash specifications , 1999 .

[25]  J. McCarthy,et al.  Subsurface transport of contaminants , 1989 .

[26]  M. Schaap,et al.  ROSETTA: a computer program for estimating soil hydraulic parameters with hierarchical pedotransfer functions , 2001 .

[27]  Miroslav Černík,et al.  Affinity distribution description of competitive ion binding to heterogeneous materials , 1996 .

[28]  Kenneth S. Pitzer,et al.  Thermodynamics of concentrated electrolyte mixtures and the prediction of mineral solubilities to high temperatures for mixtures in the system Na-K-Mg-Cl-SO4-OH-H2O , 1987 .

[29]  Ruben Juanes,et al.  Impact of relative permeability hysteresis on the numerical simulation of WAG injection , 2006 .

[30]  D. R. Nielsen,et al.  A consistent set of parametric models for the two‐phase flow of immiscible fluids in the subsurface , 1989 .

[31]  B. Robinson,et al.  Summary of the Models and Methods for the FEHM Application-A Finite-Element Heat- and Mass-Transfer Code , 1997 .

[32]  C. Clauser,et al.  Permeability Prediction For Reservoir Sandstones And Basement Rocks Based On Fractal Pore Space Geometry , 1998 .

[33]  David K. Peeler,et al.  Performance of a buried radioactive high level waste (HLW) glass after 24 years , 2008 .

[34]  James A. Davis,et al.  Approaches to surface complexation modeling of Uranium(VI) adsorption on aquifer sediments , 2004 .

[35]  P. Aagaard,et al.  Thermodynamic and kinetic constraints on reaction rates among minerals and aqueous solutions; I, Theoretical considerations , 1982 .

[36]  Kaj Thomsen,et al.  Aqueous Electrolytes Model Parameters and Process Simulation , 1997 .

[37]  E. A. Sudicky,et al.  Colloid‐facilitated contaminant transport in discretely fractured porous media: 1. Numerical formulation and sensitivity analysis , 1995 .

[38]  Denis M. Strachan,et al.  Compositional effects on long-term dissolution of borosilicate glass , 2000 .

[39]  K. Pruess,et al.  Thermohydrological conditions and silica redistribution near high‐level nuclear wastes emplaced in saturated geological formations , 1988 .

[40]  Steven B. Yabusaki,et al.  Building conceptual models of field‐scale uranium reactive transport in a dynamic vadose zone‐aquifer‐river system , 2008 .

[41]  J. C. Cunnane,et al.  High-level waste borosilicate glass: A compendium of corrosion characteristics. Volume 3 , 1994 .

[42]  S. Goldberg.  Geochemistry, Groundwater and Pollution , 2006 .

[43]  D. L. Parkhurst,et al.  Application of the Pitzer equations to the PHREEQE geochemical model , 1990 .

[44]  G. I. Barenblatt,et al.  Basic concepts in the theory of seepage of homogeneous liquids in fissured rocks [strata] , 1960 .

[45]  N. Møller,et al.  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 , 1984 .

[46]  J. Herzig,et al.  Flow of Suspensions through Porous Media—Application to Deep Filtration , 1970 .

[47]  Michael Locht Michelsen,et al.  Thermodynamic Modelling: Fundamentals and Computational Aspects , 2004 .

[48]  Florian Kuhnen,et al.  Multicomponent transport of major cations predicted from binary adsorption experiments , 2000 .

[49]  S. H. Storey,et al.  The computation of chemical equilibria , 1970 .

[50]  John H. Weare,et al.  The prediction of borate mineral equilibria in natural waters: Application to Searles Lake, California , 1986 .

[51]  Tetsu K. Tokunaga,et al.  Film Straining of Colloids in Unsaturated Porous Media: Conceptual Model and Experimental Testing , 1997 .

[52]  N. T. Burdine.  Relative Permeability Calculations From Pore Size Distribution Data , 1953 .

[53]  G. Hooyman,et al.  ON THERMODYNAMIC COUPLING OF CHEMICAL REACTIONS. , 1961, Proceedings of the National Academy of Sciences of the United States of America.

[54]  J. A. Davis,et al.  Modeling the movement of a pH perturbation and its impact on adsorbed zinc and phosphate in a wastewater‐contaminated aquifer , 2007 .

[55]  J. A. Davis,et al.  Influence of variable chemical conditions on EDTA-enhanced transport of metal ions in mildly acidic groundwater. , 2008, Environmental pollution.

[56]  James A. Davis,et al.  Comparison of in situ uranium KD values with a laboratory determined surface complexation model , 2004 .

[57]  M. Biot,et al.  THE ELASTIC COEFFICIENTS OF THE THEORY OF CONSOLIDATION , 1957 .

[58]  J. L. Dussossoy,et al.  Current state of knowledge of nuclear waste glass corrosion mechanisms: the case of R7T7 glass , 1992 .

[59]  T. H. Pigford,et al.  Mass Transfer in a Geologic Environment , 1984 .

[60]  Rodney C. Ewing,et al.  Chemical corrosion of highly radioactive borosilicate nuclear waste glass under simulated repository conditions , 1990 .

[61]  Per Schjønning,et al.  Predicting the Gas Diffusion Coefficient in Undisturbed Soil from Soil Water Characteristics , 2000 .

[62]  Daniel Grolimund,et al.  Experimental determination of colloid deposition rates and collision efficiencies in natural porous media , 1997 .

[63]  Roland Hellmann,et al.  Dissolution kinetics as a function of the Gibbs free energy of reaction: An experimental study based on albite feldspar , 2006 .

[64]  Karsten Pruess,et al.  Software qualification of selected TOUGH2 modules , 1996 .

[65]  Scott C. Brooks,et al.  Comparison of Approaches to Calibrate a Surface Complexation Model for U(VI) Sorption to Weathered Saprolite , 2009 .

[66]  C. Steefel,et al.  A new kinetic approach to modeling water-rock interaction: The role of nucleation, precursors, and Ostwald ripening , 1990 .

[67]  Bernd Grambow,et al.  First-order dissolution rate law and the role of surface layers in glass performance assessment , 2001 .

[68]  Christophe Tournassat,et al.  Modeling the composition of the pore water in a clay-rock geological formation (Callovo-Oxfordian, France) , 2007 .

[69]  Garrison Sposito,et al.  The thermodynamics of soil solutions , 1981 .

[70]  Carlon S. Land,et al.  Calculation of Imbibition Relative Permeability for Two- and Three-Phase Flow From Rock Properties , 1968 .

[71]  BOTANiCAL Gazette,et al.  Handbook of Soil Science , 1933, Botanical Gazette.

[72]  A. Lasaga.  Chemical kinetics of water‐rock interactions , 1984 .

[73]  B. Grambow,et al.  A General Rate Equation for Nuclear Waste Glass Corrosion , 1984 .

[74]  H. L. Stone.  Estimation of Three-Phase Relative Permeability And Residual Oil Data , 1973 .

[75]  Scott C. James,et al.  Transport of polydisperse colloid suspensions in a single fracture , 1999 .

[76]  M. Moo-young,et al.  Environmental Biotechnology: Principles and Applications , 2010 .

[77]  Anderson L. Ward,et al.  Performance Evaluation of a Field‐Scale Surface Barrier , 1997 .

[78]  H. Helgeson,et al.  Thermodynamics of hydrothermal systems at elevated temperatures and pressures , 1969 .

[79]  H. E. Nuttall,et al.  Radiocolloid Transport in Saturated and Unsaturated Fractures , 1991 .

[80]  Herman Bouwer,et al.  Simple Derivation of the Retardation Equation and Application to Preferential Flow and Macrodispersion , 1991 .

[81]  C. Steefel,et al.  Kaolinite dissolution and precipitation kinetics at 22 °C and pH 4 , 2007 .

[82]  S. Hubbard,et al.  Effects of physical and geochemical heterogeneities on mineral transformation and biomass accumulation during biostimulation experiments at Rifle, Colorado. , 2010, Journal of contaminant hydrology.

[83]  Carl I. Steefel,et al.  Scale dependence of mineral dissolution rates within single pores and fractures , 2008 .

[84]  Rainer Horn,et al.  Handbook of soil science. , 1996 .

[85]  David L. Parkhurst,et al.  A computer program incorporating Pitzer's equations for calculation of geochemical reactions in brines , 1988 .

[86]  B. Bunker,et al.  CHAPTER 10. LEACHING OF MINERAL AND GLASS SURFACES DURING DISSOLUTION , 1990 .

[87]  Pedro B. Macedo,et al.  Mechanisms of defense waste glass dissolution , 1986 .

[88]  Robert A. Berner,et al.  Stoichiometric models for nutrient regeneration m anoxic sediments1 , 1977 .

[89]  Jonathan P. Icenhower,et al.  Towards a consistent rate law: glass corrosion kinetics near saturation , 2004, Geological Society, London, Special Publications.

[90]  James R. Hunt,et al.  Transport of colloidal contaminants in groundwater : radionuclide migration at the Nevada Test Site , 1988 .

[91]  T. Hoehler.  Biological energy requirements as quantitative boundary conditions for life in the subsurface , 2004 .

[92]  W. Luder.  Introduction to thermodynamics of irreversible processes , 1955 .

[93]  J. Quirk,et al.  Permeability of porous solids , 1961 .

[94]  Edward L Cussler,et al.  Diffusion: Mass Transfer in Fluid Systems , 1984 .

[95]  Kamy Sepehrnoori,et al.  Development of a Thermodynamically Consistent, Fully Implicit, Equation-of-State, Compositional Steamflood Simulator , 1991 .

[96]  Francis R. Livens,et al.  The kinetics and mechanisms of simulated British Magnox waste glass dissolution as a function of pH, silicic acid activity and time in low temperature aqueous systems , 2000 .

[97]  David E. Clark,et al.  Nuclear waste solids , 1986 .

[98]  D. K. Smith,et al.  Migration of plutonium in ground water at the Nevada Test Site , 1999, Nature.

[99]  Jean-Eric Lartigue,et al.  Application of the GRAAL model to leaching experiments with SON68 nuclear glass in initially pure water , 2009 .

[100]  F. Morel,et al.  Surface Complexation Modeling: Hydrous Ferric Oxide , 1990 .

[101]  Kenneth M. Krupka,et al.  Waste Form Release Data Package for the 2005 Integrated Disposal Facility Performance Assessment , 2004 .

[102]  D. Langmuir.  Aqueous Environmental Geochemistry , 1997 .

[103]  Eric E. Roden,et al.  Microbiological Controls on Geochemical Kinetics 1: Fundamentals and Case Study on Microbial Fe(III) Oxide Reduction , 2008 .

[104]  Norman Epstein,et al.  Fine particle deposition in smooth parallel-plate channels , 1979 .

[105]  James A. Davis,et al.  Uranium(VI) Release from Contaminated Vadose Zone Sediments: Estimation of Potential Contributions from Dissolution and Desorption , 2007 .

[106]  Kenneth S. Pitzer,et al.  Thermodynamics of multicomponent, miscible, ionic systems: theory and equations , 1986 .

[107]  Ian C. Bourg,et al.  Modeling the diffusion of Na+ in compacted water-saturated Na-bentonite as a function of pore water ionic strength , 2008 .

[108]  Lisa D. Olsen,et al.  Natural attenuation of chlorinated volatile organic compounds in a freshwater tidal wetland: Field evidence of anaerobic biodegradation , 1999 .

[109]  Anil Kumar,et al.  Prediction of densities of concentrated brines by Pitzer theory , 1986 .

[110]  E. Paleologos,et al.  Stochastic Methods for Flow in Porous Media, Coping With Uncertainties , 2003 .

[111]  D. I. Kaplan,et al.  Colloid suspension stability and transport through unsaturated porous media , 1997 .

[112]  P. Brimblecombe,et al.  Solubility of volatile electrolytes in multicomponent solutions with atmospheric applications , 1990 .

[113]  A. Leijnse,et al.  Assessment of the effect of kinetics on colloid facilitated radionuclide transport in porous media. , 1997 .

[114]  A. Lasaga.  Rate laws of chemical reactions , 1981 .

[115]  Kathryn L. Nagy,et al.  Simultaneous precipitation kinetics of kaolinite and gibbsite at 80°C and pH 3 , 1993 .

[116]  F. G. Bader,et al.  Analysis of double‐substrate limited growth , 1978, Biotechnology and bioengineering.

[117]  S. P. Neuman.  Universal scaling of hydraulic conductivities and dispersivities in geologic media , 1990 .

[118]  James A. Davis,et al.  Simulation of reactive transport of uranium(VI) in groundwater with variable chemical conditions , 2006 .

[119]  A. Lasaga.  Kinetic theory in the earth sciences , 1998 .

[120]  P. Vaughan,et al.  Analysis of Permeability Reduction During Flow of Heated, Aqueous Fluid Through Westerly Granite , 1987 .

[121]  Kathryn L. Nagy,et al.  Dissolution and precipitation kinetics of sheet silicates , 1995 .

[122]  W. H. Somerton,et al.  High Temperature Behavior of Rocks Associated with Geothermal Type Reservoirs , 1974 .

[123]  Constantinos V. Chrysikopoulos,et al.  Modeling of colloid and colloid-facilitated contaminant transport in a two-dimensional fracture with spatially variable aperture , 1995 .

[124]  Donald L. Sparks,et al.  Thermodynamics of the soil solution. , 1986 .

[125]  T. J. Wolery,et al.  EQ3NR, a computer program for geochemical aqueous speciation-solubility calculations: Theoretical manual, user`s guide, and related documentation (Version 7.0); Part 3 , 1992 .

[126]  Qinjun Kang,et al.  Lattice Boltzmann pore-scale model for multicomponent reactive transport in porous media , 2006 .

[127]  M. Yavuz Corapcioglu,et al.  Governing Equations for Particle Transport in Porous Media , 1987 .

[128]  Van Genuchten,et al.  A closed-form equation for predicting the hydraulic conductivity of unsaturated soils , 1980 .

[129]  Andrew W. Dale,et al.  Anaerobic oxidation of methane (AOM) in marine sediments from the Skagerrak (Denmark): II. Reaction-transport modeling , 2008 .

[130]  R. Reid,et al.  The Properties of Gases and Liquids , 1977 .

[131]  Matthias Kohler,et al.  Experimental Investigation and Modeling of Uranium (VI) Transport Under Variable Chemical Conditions , 1996 .

[132]  R. M. Bowen,et al.  On the stoichiometry of chemically reacting materials , 1968 .

[133]  Carl I. Steefel,et al.  The role of reaction affinity and secondary minerals in regulating chemical weathering rates at the Santa Cruz Soil Chronosequence, California , 2009 .

[134]  Kim F Hayes,et al.  Surface complexation modeling of U(VI) adsorption by aquifer sediments from a former mill tailings site at Rifle, Colorado. , 2009, Environmental science & technology.

[135]  R. Aguilar,et al.  Waste Form and Indrift Colloids-Associated Radionuclide Concentrations: Abstraction and Summary , 2003 .

[136]  Andrea Saltelli,et al.  Americium Filtration in Glauconitic Sand Columns , 1984 .

[137]  Howard W. Reeves,et al.  Multicomponent mass transport with homogeneous and heterogeneous chemical reactions: Effect of the chemistry on the choice of numerical algorithm: 1. Theory , 1988 .

[138]  J. E. Warren,et al.  The Behavior of Naturally Fractured Reservoirs , 1963 .

[139]  Jeffery J. Roberts,et al.  Electrical properties of partially saturated Topopah Spring Tuff: Water distribution as a function of saturation , 1997 .

[140]  V. V. KUZNETSOV,et al.  Determination of pH , 2001 .

[141]  H. C. Slider.  Practical petroleum reservoir engineering methods : an energy conservation science , 1976 .

[142]  Maurice A. Biot,et al.  Nonlinear and semilinear rheology of porous solids , 1973 .

[143]  G. Marsily.  Quantitative Hydrogeology: Groundwater Hydrology for Engineers , 1986 .

[144]  S. Goldberg,et al.  Chemistry of the Solid-Water Interface Processes at the Mineral-Water and Particle-Water Interface in Natural Systems , 1993 .

[145]  David R. Turner,et al.  Determination of pH , 2007 .

[146]  William L. Bourcier,et al.  Critical Review of Glass Performance Modeling , 1994 .

[147]  R. H. Brooks,et al.  Hydraulic properties of porous media , 1963 .

[148]  Stephen P. Garabedian,et al.  Use of colloid filtration theory in modeling movement of bacteria through a contaminated sandy aquifer , 1991 .

[149]  T. J. Wolery.  On the thermodynamic framework of solutions (with special reference to aqueous electrolyte solutions) , 1990 .

[150]  Jerry P. Greenberg,et al.  The prediction of mineral solubilities in natural waters: A chemical equilibrium model for the Na-K-Ca-Cl-SO4-H2O system to high concentration from 0 to 250°C , 1989 .

[151]  Hari S. Viswanathan,et al.  Generalized dual porosity : A numerical method for representing spatially variable sub-grid scale processes , 2008 .

[152]  Etienne Vernaz,et al.  Present understanding of R7T7 glass alteration kinetics and their impact on long-term behavior modeling , 2001 .

[153]  Carl I. Steefel,et al.  Fluid-rock interaction: A reactive transport approach , 2009 .

[154]  David K. Peeler,et al.  Measurement of kinetic rate law parameters on a NaCaAl borosilicate glass for low-activity waste , 1997 .

[155]  T. Arnold,et al.  Sorption behavior of U(VI) on phyllite: experiments and modeling. , 2001, Journal of contaminant hydrology.

[156]  John H. Weare,et al.  The prediction of mineral solubilities in natural waters: the NaKMgCaClSO4H2O system from zero to high concentration at 25° C , 1980 .

[157]  Howard W. Reeves,et al.  Multicomponent mass transport with homogeneous and heterogeneous chemical reactions: The effect of the chemistry on the choice of numerical algorithm, part 1. Theory , 1988 .

[158]  J. Conca,et al.  Unsaturated Zone and Saturated Zone Transport Properties (U0100) , 2000 .

[159]  R. Aris.  Prolegomena to the rational analysis of systems of chemical reactions , 1965 .

[160]  Andrew W. Dale,et al.  Bioenergetic Controls on Anaerobic Oxidation of Methane (AOM) in Coastal Marine Sediments: A Theoretical Analysis , 2006 .

[161]  J. Nunemacher,et al.  Optimal management of giant cell arteritis and polymyalgia rheumatica , 2012, Therapeutics and clinical risk management.

[162]  C. Monnin.  An ion interaction model for the volumetric properties of natural waters: Density of the solution and partial molal volumes of electrolytes to high concentrations at 25°C , 1989 .

[163]  A. Navarre‐Sitchler,et al.  Evolution of porosity and diffusivity associated with chemical weathering of a basalt clast , 2009 .

[164]  T. N. Narasimhan,et al.  A PRACTICAL METHOD FOR MODELING FLUID AND HEAT FLOW IN FRACTURED POROUS MEDIA , 1985 .

[165]  Albert P. Vanselow,et al.  EQUILIBRIA OF THE BASE‐EXCHANGE REACTIONS OF BENTONITES, PERMUTITES, SOIL COLLOIDS, AND ZEOLITES , 1932 .

[166]  K. Denbigh,et al.  The principles of chemical equilibrium : with applications in chemistry and chemical engineering , 1981 .

[167]  Jean-Eric Lartigue,et al.  SON68 nuclear glass dissolution kinetics: Current state of knowledge and basis of the new GRAAL model , 2008 .

[168]  J. A. Davis,et al.  Surface complexation modeling in aqueous geochemistry , 1990 .

[169]  William L. Bourcier,et al.  Overview of chemical modeling of nuclear waste glass dissolution , 1990 .

[170]  Carol M. Jantzen,et al.  Durable Glass for Thousands of Years , 2010 .

[171]  C. Steefel,et al.  A coupled model for transport of multiple chemical species and kinetic precipitation/dissolution rea , 1994 .

[172]  David R. Tallant,et al.  The structure of leached sodium borosilicate glass , 1988 .