MINTEQA2/PRODEFA2, A Geochemical Assessment Model for Environmental Systems: User Manual Supplement for Version 4.0 Prepared for U.S. Environmental Protection Agency National Exposure Research Laboratory Ecosystems Research Division Athens, Georgia by HydroGeoLogic, Inc. Herndon, Virginia and Allison Geoscience Consultants, Inc. Flowery Branch, Georgia June 1998 (revised September 1999) TABLE OF CONTENTS LIST OF FIGURES ......................................................... iv LIST OF TABLES ......................................................... iv SUMMARY ...............................................................v 1. INTRODUCTION AND BACKGROUND .....................................1 1.1 MATHEMATICAL FORMULATION OF MINTEQA2 .....................1 1.2 SUMMARY OF SIGNIFICANT MODIFICATIONS SINCE VERSION 3.0 .....3 1.2.1 Gaussian Model for Dissolved Organic Matter .....................3 1.2.2 Changes to Minimize Violations of Gibb’s Phase Rule ...............4 1.2.3 Other Changes in Model Code .................................4 1.2.4 Database Changes ...........................................4 2. THE GAUSSIAN MODEL FOR DISSOLVED ORGANIC MATTER ................6 2.1 BACKGROUND ..................................................6 2.1.1 Discrete Ligand Models ......................................7 2.1.2 Continuous Distribution Models ................................9 2.1.3 The Gaussian DOM Model ...................................10 2.2 IMPLEMENTATION OF THE GAUSSIAN DOM MODEL IN MINTEQA2 ...16 2.2.1 Calculation of Gradients .....................................17 2.2.2 Modifications in MINTEQA2 Source Code ......................18 2.3 OTHER MODIFICATIONS FOR THE GAUSSIAN DOM MODEL ..........19 2.3.1 Treatment of Charge and Activity Coefficients for Organic Species .....19 3. MODIFICATIONS IN MINTEQA2 TO MINIMIZE VIOLATIONS OF GIBBS PHASE RULE .............................................21 3.1 SOURCE CODE MODIFICATIONS ..................................23 4. OTHER MODIFICATIONS IN MINTEQA2/PRODEFA2 ........................24 4.1 IMPROVEMENT IN EXECUTION SPEED ............................24 4.2 MODIFICATIONS TO MINIMIZE NON-CONVERGENCE ...............25 4.3 MODIFICATIONS FOR MODELING TITRATIONS .....................26 4.4 MODIFICATIONS FOR SPECIALIZED OUTPUT .......................26 ii 4.5 MODIFICATIONS FOR CUSTOMIZED DATABASE FILENAMES .........27 4.6 CORRECTION OF KNOWN ERRORS IN EARLIER VERSIONS ...........27 5. MODIFICATIONS TO THE THERMODYNAMIC DATABASE ...................28 5.1 DATA SOURCES .................................................28 5.1.1 Prioritized List of Sources ...................................29 5.2 DATA REDUCTION ..............................................30 5.2.1 Ionic Strength and Temperature Corrections of Log K ..............30 5.2.2 Expressing the Reaction in Terms of MINTEQA2 Components .......31 5.2.3 Other Data Reduction Methods ...............................32 5.3 QUALITY ASSURANCE EFFORTS ..................................32 5.4 REVIEW AND CORRECTION OF METAL-ORGANIC SPECIES ...........33 5.4.1 Component and Species Names for Organic Species ................34 5.4.2 Database Changes for Metal-Organic Species .....................36 5.5 REVIEW AND UPDATE OF OTHER DATABASE SPECIES ..............36 BIBLIOGRAPHY ..........................................................37 APPENDIX A - THERMODYNAMIC DATA FOR MINTEQA2 V4.0 .................43 APPENDIX B - FORMAT OF THE THERMODYNAMIC DATABASE V4.0 ...........74 iii LIST OF FIGURES Figure 2.1 Illustrating Normal Probability of Occurrence (Concentration) of Ligands Versus Log K within the DOM Mixture ..............................11 Figure 2.2 Bimodal Distribution of Relative Site Concentration Versus Log K ..........12 LIST OF TABLES Table 5.1 Organic Ligands and the Associated MINTEQA2 Component ID No., Name, and Charge ..............................................34 iv SUMMARY This report presents modifications in the geochemical speciation model MINTEQA2 and its associated user interface, PRODEFA2, for version 4.0. The previous release, version 3.11, incorporated changes that were never formally described in model documentation. Important version 3.11 changes that apply to version 4.0 are also described in this document. The basic model theory described in the version 3.0 model documentation is still valid and provides a basic description of the model. The information in this document is intended to supplement that provided in the version 3.0 user manual. Significant changes in the MINTEQA2/PRODEFA2 model since the publication of the version 3.0 user manual include: Incorporation of the Gaussian model for computing trace metal complexation with dissolved organic matter, modifications to minimize the occurrence of violations of Gibbs phase rule, modifications to allow direct simulation of a titration in one model run, modifications to allow selected output to be written for easy importing to a spreadsheet, modifications to improve model execution speed and convergence, and modifications to improve the thermodynamic database used by the model, including the addition of beryllium (II), cobalt (II and III), molybdenum (VI), and tin (II and IV) compounds. Also, errors in thermodynamic constants associated with certain metal- organic reactions in earlier versions have been corrected in version 4.0, thermodynamic constants for inorganic species have been reviewed and updated, and all reference citations for equilibrium constants have been included in the revised database. In addition, the model has been made Y2K compliant. These and other revisions are described in this document. v CHAPTER 1 INTRODUCTION AND BACKGROUND MINTEQA2 is a equilibrium speciation model that can be used to calculate the equilibrium composition of dilute aqueous solutions in the laboratory or in natural aqueous systems. The model is useful for calculating the equilibrium mass distribution among dissolved species, adsorbed species, and multiple solid phases under a variety of conditions including a gas phase with constant partial pressure. A comprehensive database is included that is adequate for solving a broad range of problems without need for additional user-supplied equilibrium constants. The model employs a pre- defined set of components that includes free ions such as Na+ and neutral and charged complexes 0 + (e.g., H4SiO4 , Cr(OH)2 ). The database of reactions is written in terms of these components as reactants. An ancillary program, PRODEFA2, serves as an interactive pre-processor to help produce the required MINTEQA2 input files. Several modifications important to the user have been made since the last publication of a MINTEQA2/PRODEFA2 user manual (Allison et al.,1991; version 3.0). This document is intended to supplement the basic information provided in the version 3.0 user manual. After a brief introduction and description of MINTEQA2, it describes significant changes since version 3.0. 1.1 MATHEMATICAL FORMULATION OF MINTEQA2 A system of n independent components that can combine to form m species is represented by a set of mass action expressions of the form n &a ' ij Ki 6Si> k Xj (1) j'1 where Ki is the formation constant for species i, {Si} is the activity of species i, Xj is the activity of component j, and aij is the stoichiometric coefficient of component j in species i. Rearranging to express the concentration Ci in terms of the activities of components gives 1 n K a ' i ij Ci k Xj (2) ' (i j 1 where (i represents the activity coefficient of species i. In addition to the mass action expressions, the set of n independent components is governed by n mass balance equations of the form n ' & Yj j aij Ci Tj (3) i'1 where Tj is the known total concentration of component j (an input parameter). Thus, Yj is the difference between the calculated total concentration and the known total concentration of component j. The mathematical solution of the equilibrium problem is the set of component activities that give species concentrations from equation (2) which produce a component mass imbalance of zero in equation (3) for each and every component. The equilibrium problem is solved iteratively— the Xj values are deemed correct and the problem is solved when the Yj values are reduced to an acceptably small value for every component. If this is not the case, new estimates are made for component activities Xj, and the calculations are repeated in a new iteration beginning at Equation (2). MINTEQA2 uses the Newton-Raphson approximation method to estimate the new Xj at each iteration. This method utilizes a Jacobian matrix whose elements represent the partial derivatives of each component mass balance difference Yj with respect to every other component activity Xk where both j and k range from 1 to the number of components (n). Each gradient element of the Jacobian is given by MY n MC ' j ' i uj,k j aij (4) ' MXk i 1 MXk In summary, the mathematical solution to the equilibrium problem is that set of component activities X (using bold symbols to indicate matrix notation for brevity) which results in the set of concentrations C such that each individual of the set of mass balance differences Y is equal to zero. In practice, it is only necessary to find X such that each individual of Y is made less than some tolerance value. The general procedure is to first guess X, then calculate C and Y. If any individual of Y exceeds (in absolute terms) its prescribed tolerance value, a new estimate is made for X, then C and Y are recalculated, and the test is repeated. This