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Reactive transport modeling of unsaturated hydrology and geochemistry of neutral and acid rock drainage… Javadi, Mehrnoush 2019

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REACTIVE TRANSPORT MODELING OF UNSATURATED HYDROLOGY AND GEOCHEMISTRY OF NEUTRAL AND ACID ROCK DRAINAGE IN HIGHLY HETEROGENEOUS MINE WASTE ROCK AT THE ANTAMINA MINE, PERU  by Mehrnoush Javadi  M.Sc., Amir Kabir University of Technology, 2008  A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF  DOCTOR OF PHILOSOPHY in THE FACULTY OF GRADUATE AND POST DOCTORAL STUDIES (Geological Engineering)  THE UNIVERSITY OF BRITISH COLUMBIA (Vancouver)  April 2019 © Mehrnoush Javadi, 2019  ii  The following individuals certify that they have read, and recommend to the Faculty of Graduate and Postdoctoral Studies for acceptance, the dissertation entitled:  Reactive transport modeling of unsaturated hydrology and geochemistry of neutral and acid rock drainage in highly heterogeneous mine waste rock at the Antamina Mine, Peru submitted by Mehrnoush Javadi  in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Geological Engineering  Examining Committee: Dr. K. Ulrich Mayer Co-supervisor Dr. Roger D. Beckie Co-supervisor  Dr. Leslie Smith Supervisory Committee Member Dr. Douglas W. Oldenburg University Examiner Dr. Brett Eaton University Examiner Additional Supervisory Committee Members:  Supervisory Committee Member  Supervisory Committee Member    iii  Abstract Drainage quality from variably-saturated mine waste-rock dumps is controlled by multiple processes that are effective at different scales. The objective of this research is to improve the conceptual understanding of coupled hydrological and geochemical processes in mine waste rock using reactive transport modeling.  Multicomponent reactive-transport was modeled using the code MIN3P to investigate sulfide oxidation and acid buffering reactions constrained by two field-scale studies of fine-grained reactive intrusive material at the Antamina mine, Peru: 1) 1 m-high field barrel and 2) 10 m-high experimental pile. At the field-barrel scale, the uniform flow and solute transport model was able to capture long term concentration trends in the discharge. Sulfide mineral oxidation along with pH-buffering reactions, and Cu and Zn secondary mineral precipitation/dissolution were considered the main processes controlling metal concentrations. Results indicate seasonal fluctuations in dissolved concentrations controlled by precipitation/dissolution of secondary minerals in wet and dry cycles and a long-term trend towards more acidic drainage. At the pile scale, the uniform-flow and solute transport model was successful in matching the field-observed basal discharge and cumulative outflow. The results demonstrate the importance of preferential flow not only in rock-like, but also in soil-like waste-rock piles and indicate that calibrating an unsaturated flow model to observed outflow alone is insufficient to evaluate flow patterns and residence times in waste rock. Therefore, mobile-immobile, dual-porosity and dual-permeability approaches were implemented into the MIN3P code and the enhanced code was used to improve the simulation of tracer breakthrough at the pile scale, relative to the uniform flow and solute  iv  transport model. Although substantial improvements could be obtained by using the dual domain approaches, observed tracer peak concentration and tailing were not well captured, suggesting the presence of a third immobile region with a very slow release rate. Based on the geochemical system developed for the field barrel scale and the dual-domain model developed for the pile scale, the applicability of the enhanced code for modeling of multicomponent reactive transport in waste rock at the pile scale was demonstrated, and in the process, the distribution of reactivity in preferential flow and matrix regions was evaluated.        v  Lay Summary Mining provides the metals and materials required for industrial society. Mining may need removal of large amount of waste rock and expose minerals that are below the surface to oxidation processes. Oxidation of sulfide minerals such as pyrite occurs in presence of water and produces acid rock drainage and in some cases neutral rock drainage. In acidic condition heavy metals leach from the waste rock and get mobilized in groundwater and surface water. In this thesis, a numerical model, MIN3P, is used to study the processes that produce acidic and neutral water and release copper, zinc and sulfate in two scales of study: a field barrel, and an experimental waste rock pile. Results show the role of processes precipitation and dissolution of secondary minerals in wet and dry seasons on drainage quality and indicate the effect of fast flow pathways even in fine-grained waste rock pile on distribution of reactivity.       vi  Preface This thesis has been prepared as a collection of five body chapters. One of the chapters was published (Chapter 3) and two chapters are manuscripts in preparation and will be submitted for publication (Chapters 2 and 5). Although these manuscripts have been co-authored with individuals other than myself, I am the first author in each case and have conducted the research and manuscript preparation. The work including all the model development (MIN3P-THCm-DP code) in Chapter 4, implementation and numerical simulations has been entirely done by me with guidance from my supervisors Dr. U. Mayer and Dr. R. D. Beckie and towards content and structure of the manuscripts. Only limited support was provided by co-authors other than my thesis supervisor, as outlined below.  A version of Chapter 3 entitled Evaluating preferential flow in an experimental waste rock pile using unsaturated flow and solute transport modeling was co-authored by H.E. Peterson, S.R. Blackmore, U. Mayer, R.D. Beckie and L. Smith, which was wholly written by me with advice from co-authors. This paper was peer-reviewed and published in 2012 Proceedings of the 9th international Conference of Acid Rock Drainage (Javadi et al., 2012).   A version of Chapter 2 will be submitted as: M. Javadi, U. Mayer and R.D. Beckie:  Multicomponent Reactive Transport Modeling of Acid Mine Drainage Generation and Neutralization in Waste Rock: Field Barrel Scale. I carried out all the simulations and analyzed all the data. I wrote the manuscript guided by my thesis supervisors.   vii  A version of Chapter 5 will be submitted as: M. Javadi, U. Mayer, L. Smith and R.D. Beckie: Evaluation of Uniform and non-Uniform Flow and Solute Transport Models for Simulating Tracer Transport in Mine Waste Rock. I carried the model development, implementation and analyzed the data. I wrote the manuscript guided by my thesis supervisors.  This thesis is part of the Antamina Mine Waste Rock Study which was a collaboration between The University of British Columbia (UBC), Teck Metals Limited’s Applied Research and Technology Group, The University of Alberta and Compania Minera Antamina S.A.   I was the only person responsible for the MIN3P-THCm-DP (preferential flow and solute transport) code development in Chapter 4, implementation, verification and performing numerical simulations using both MIN3P and MIN3P-THCm-DP codes.   I processed and analyzed all data and results presented here unless otherwise noted, including the Pile 2 outflow and tracer test data compilation by H. Peterson (for 2012-2013, I processed the data as a joint effort with H. Peterson), soil characteristic curves B. Speidel, and saturated hydraulic conductivity measurements by S. Blackmore and P. Urrutia.       viii  Table of Contents  Abstract ................................................................................................................................... iii Lay Summary .......................................................................................................................... v Preface ..................................................................................................................................... vi Table of Contents ................................................................................................................. viii List of Tables ........................................................................................................................ xvi List of Figures ....................................................................................................................... xix Acknowledgements ............................................................................................................ xxxi Dedication .......................................................................................................................... xxxii Chapter  1: Introduction ........................................................................................................ 1 1.1 Background and problem definition ......................................................................... 1 1.2 Literature review ....................................................................................................... 3 1.3 Study Site Description: Antamina Mine, Peru .......................................................... 5 1.3.1 Experimental Design of Field Barrel Study .......................................................... 6 1.3.2 Pile 2 Experiment .................................................................................................. 6 1.4 Thesis organization and research objectives ............................................................. 7 Chapter  2: Multicomponent Reactive Transport Modeling of Acid Mine Drainage Generation and Neutralization in Waste Rock: Field Barrel Scale ................................. 12 2.1 Introduction ............................................................................................................. 12 2.2 Materials and Methods ............................................................................................ 15 2.2.1 Mine Site Description ......................................................................................... 15 2.2.2 Experimental Design of Field Barrel Study ........................................................ 16  ix  2.2.3 Solid Phase Analysis and Acid Base Accounting ............................................... 17 2.2.4 Description of Numerical Model ........................................................................ 19 2.2.5 Scenario-based Modeling of Waste Rock Weathering in Field Barrel UBC2-3A 20 2.2.5.1 Physical Parameters .................................................................................... 25 2.2.5.2 Reaction Network and Geochemical Parameters ........................................ 28 2.2.5.2.1 Pyrite Oxidation and Sulfide Mineral Weathering Reactions ............... 28 2.2.5.2.2 Acid Neutralization ............................................................................... 32 2.2.5.2.3 Secondary Mineral Formation ............................................................... 36 2.2.5.2.4 Intra-aqueous and gas exsolution-dissolution reactions ........................ 39 2.2.5.3 Initial and Boundary Conditions ................................................................. 39 2.3 Results and Discussion ........................................................................................... 40 2.3.1 Effective Neutralization Potential and Role of Calcite ....................................... 40 2.3.1.1 Calcite Estimated from Bulk NP (0.7 wt%) and Solid Phase Analysis (0.42 wt%) 40 2.3.1.1.1 Seasonal Influences on Secondary Mineralogy .................................... 44 2.3.1.2 Processes Controlling pH and Metal Attenuation: Calcite Estimated by Calibration (0.06 wt%)................................................................................................ 45 2.3.1.2.1 Assessment of Geochemical Evolution, Long-term Trends and Seasonal Influences 45 2.3.1.2.2 Determination of Effective Carbonate NP ............................................ 47 2.3.2 Contribution of Wollastonite and Calcite to Neutralization Potential ................ 48 2.3.2.1 Contribution of Wollastonite ...................................................................... 48  x  2.3.2.2 Contribution of Calcite ............................................................................... 52 2.3.3 Uncertainties and limiting factors ....................................................................... 56 2.4 Summary and Conclusion ....................................................................................... 56 Chapter  3: Evaluating preferential flow in an experimental waste rock pile using unsaturated flow and solute transport modeling ............................................................... 60 3.1 Introduction ............................................................................................................. 60 3.2 Pile 2 Experiment .................................................................................................... 63 3.3 Conceptual Model ................................................................................................... 64 3.4 Field and Model Parameters ................................................................................... 65 3.5 Modeling Approach ................................................................................................ 67 3.6 Results and Discussion ........................................................................................... 67 3.6.1 Hydrologic response and cumulative outflow .................................................... 67 3.6.2 Tracer test and solute transport modeling ........................................................... 73 3.7 Conclusions and Outlook ........................................................................................ 74 Chapter  4: Implementation and verification of mobile-immobile, dual-porosity and dual-permeability models in MIN3P to simulate flow and solute transport in the vadose zone ......................................................................................................................................... 76 4.1 Introduction ............................................................................................................. 76 4.1.1 Background and Concepts .................................................................................. 76 4.2 The mobile-immobile and dual-porosity concept ................................................... 77 4.3 The dual-permeability concept ............................................................................... 82 4.4 Literature review on the existing codes with preferential-flow approach .............. 85 4.5 Objectives of current implementation ..................................................................... 87  xi  4.6 Development of mobile-immobile, dual-porosity and dual-permeability code MIN3P-THCm-DP .............................................................................................................. 87 4.6.1 Existing MIN3P, MIN3PDUAL and MIN3P-THCm code ................................ 87 4.6.2 Conceptual model ............................................................................................... 89 4.6.3 Governing equations ........................................................................................... 90 4.6.4 Boundary conditions ........................................................................................... 92 4.7 MIN3P-THCm-DP code ......................................................................................... 93 4.7.1 Conceptual model ............................................................................................... 93 4.7.2 Governing equations ........................................................................................... 95 4.7.3 Boundary conditions ......................................................................................... 100 4.7.4 Input file ............................................................................................................ 100 4.7.5 Output files........................................................................................................ 100 4.8 Verification of MIN3P-THCm-DP ....................................................................... 101 4.8.1 Verification scenario A) .................................................................................... 106 4.8.1.1 Simulation 1: HYDRUS-1D dual-porosity with diffusive solute transfer between the two pore regions (Mobile-immobile).................................................... 107 4.8.1.2 Simulation 2: HYDRUS-1D dual-permeability mimicking dual-porosity with diffusive solute transfer between the two pore regions (Mobile-immobile) .... 108 4.8.1.3 Results ....................................................................................................... 109 4.8.2 Verification scenario B) .................................................................................... 111 4.8.2.1 Simulation 3: HYDRUS-1D dual-porosity with advective solute transfer between the two pore regions ................................................................................... 112  xii  4.8.2.2 Simulation 4: HYDRUS-1D dual-permeability mimicking dual-porosity with advective solute transfer between the two pore regions ................................... 113 4.8.2.3 Results ....................................................................................................... 114 4.8.3 Verification scenario C) .................................................................................... 119 4.8.3.1 Simulation 5: MIN3P-THCm-DP dual-permeability mimicking dual-porosity with advective mass transfer between the two pore regions ....................... 120 4.8.3.2 Simulation 6: HYDRUS-1D dual-permeability with no mass transfer between the two pore regions ................................................................................... 121 4.8.3.3 Results ....................................................................................................... 121 4.8.4 Verification scenario D) .................................................................................... 125 4.8.4.1 Simulation 7: MIN3P-THCm-DP dual-permeability with diffusive and advective solute transfer between the two pore region ............................................. 126 4.8.4.2 Simulation 8: HYDRUS-1D dual-permeability with diffusive and advective solute transfer between the two pore regions ............................................................ 127 4.8.4.3 Results ....................................................................................................... 127 4.9 Summary ............................................................................................................... 131 Chapter  5: Evaluation of Uniform and non-Uniform Flow and Solute Transport Models for Simulating Tracer Transport in Mine Waste Rock ..................................... 133 5.1 Introduction ........................................................................................................... 133 5.2 Material and Methods ........................................................................................... 137 5.2.1 The Antamina Mine Waste Rock Research Site ............................................... 137 5.2.2 Tracer experiment description .......................................................................... 138 5.2.3 Modeling approach ........................................................................................... 140  xiii  5.2.4 Conceptual models ............................................................................................ 141 5.2.5 Parameter estimation, initial and boundary conditions ..................................... 144 5.2.6 Sensitivity analysis on wf, Ksa, Da and qinf parameters .................................. 149 5.3 Results and Discussion ......................................................................................... 151 5.3.1 Effect of wf and Da parameters ........................................................................ 155 5.3.1.1 Mobile-Immobile Approach ..................................................................... 155 5.3.1.2 Dual-porosity Approach............................................................................ 165 5.3.1.3 Dual-permeability 1 Approach ................................................................. 174 5.3.1.4 Dual-permeability 2 Approach ................................................................. 183 5.3.1.5 Dual-permeability 3 Approach ................................................................. 189 5.4 Summary and Conclusions ................................................................................... 195 Chapter  6: Application of non-uniform flow and transport models for the simulation of reactive transport in mine waste rock ............................................................................... 199 6.1 Introduction ........................................................................................................... 199 6.2 Materials and Methods .......................................................................................... 200 6.2.1 Conceptual model ............................................................................................. 200 6.2.2 Model parametrization and discretization ......................................................... 201 6.2.3 Reaction network .............................................................................................. 202 6.2.3.1 Pyrite oxidation and sulfide mineral weathering reactions, acid neutralization and secondary mineral formation....................................................... 202 6.2.4 Boundary and initial conditions ........................................................................ 207 6.2.5 Water and Solute Mass Transfer Terms ............................................................ 208 6.3 Results and discussion .......................................................................................... 209  xiv  6.3.1 UBC2-1A waste rock ........................................................................................ 209 6.3.2 UBC2-1B waste rock ........................................................................................ 217 6.4 Summary and conclusions .................................................................................... 222 Chapter  7: Conclusions and Recommendations ............................................................. 225 7.1 Multicomponent Reactive Transport in Waste Rock: Field Barrel Scale ............. 225 7.2 Variably Saturated Hydrology-Experimental Waste Rock Pile Scale .................. 228 7.3 Development of a Generalized Dual Domain Formulation for Flow and Solute Transport ........................................................................................................................... 228 7.4 Variably-saturated Flow and Conservative Solute Transport in Macroporous Waste Rock at the Experimental Waste Rock Pile Scale ............................................................ 229 7.5 Demonstration of Multicomponent Reactive Transport in Macroporous Waste Rock at the Experimental Pile Scale ................................................................................. 232 7.6 Recommendations ................................................................................................. 234 Bibliography ........................................................................................................................ 235 Appendices ........................................................................................................................... 247 Appendix A ....................................................................................................................... 247 A.1 Numerical methods in MIN3P and MIN3P-THCm codes ................................ 247 A.2 Input file in MIN3P-THCm-DP code ............................................................... 249 Appendix B ....................................................................................................................... 255 B.1 Effect of Ksa ..................................................................................................... 255 B.2 Mobile-Immobile .............................................................................................. 256 B.3 Dual-porosity .................................................................................................... 259 B.4 Dual-permeability 1 .......................................................................................... 262  xv  B.5 Dual-permeability 2 .......................................................................................... 265 B.6 Dual-permeability 3 .......................................................................................... 268 Appendix C ....................................................................................................................... 271 C.1 Concentration of selected species versus time for field barrels: ....................... 271   xvi  List of Tables Table 2.1. The waste rock type classification system used at the mine (Aranda et al., 2009) 15 Table 2.2. Summary of unmodified Sobek ABA test, solid phase elemental analysis results and water:rock ratio of field barrels for intrusive waste rock type (Modified from Peterson, 2014) ....................................................................................................................................... 17 Table 2.3. Results of quantitative XRD analyses for field cell UBC2-3A (Modified from Peterson, 2014, ND = non detected) ....................................................................................... 19 Table 2.4. Summary of scenario-based models for field barrel UBC2-3A. ........................... 21 Table 2.5. Mineral dissolution-precipitation, aqueous oxidation and gas dissolution-exsolution reactions ................................................................................................................ 22 Table 2.6. Physical input parameters for flow and reactive transport simulations in field barrel UBC2-3A (see Javadi et al., 2012 for more details) ..................................................... 28 Table 2.7. Reaction rate expressions used for primary mineral weathering (combined reaction paths) ....................................................................................................................................... 31 Table 2.8. Initial volume fraction, effective rate, and calibrated surface area for primary and secondary minerals (ND= not detected) ................................................................................. 35 Table 2.9. Chemical composition of recharge water and initial waste rock pore water in the model....................................................................................................................................... 39 Table 3.1. Table 3.2. Physical input parameters for unsaturated flow and tracer test ............ 66 Table 4.1. Summary of dual-porosity, dual-permeability verification scenarios. All verifications are performed against HYDRUS-1D code. ..................................................... 103 Table 4.2. Physical input parameters for the HYDRUS-1D and MIN3P simulations .......... 105  xvii  Table 4.3. Input parameters for mass transfer between the two pore regions for the HYDRUS-1D and MIN3P-THCm-DP simulations .............................................................. 106 Table 5.1. Parametrization and sensitivity analysis of uniform and preferential flow models, PF: Preferential Flow pore region, NA: Not Applicable. ..................................................... 147 Table 5.2. Hydraulic parameters used in uniform and non-uniform (preferential) flow simulations ............................................................................................................................ 148 Table 5.3. Inflow boundary condition for unsaturated flow and solute transport applied on the surface of mobile/PF and immobile/matrix pore regions. PF: Preferential Flow region, qinf: Transient Recharge infiltration as inflow boundary condition ............................................. 150 Table 6.1. Hydraulic parameters used in the non-uniform reactive transport simulations ... 201 Table 6.2. Summary of unmodified Sobek ABA test, solid phase elemental analysis results and water:rock ratio of material UBC2-1A and UBC2-1B for intrusive waste rock type (Modified from Peterson, 2014) ........................................................................................... 202 Table 6.3. Results of quantitative XRD analyses for UBC2-1A and UBC2-1B waste materials (Modified from Peterson, 2014, ND = Not Detected) .......................................................... 203 Table 6.4. Initial volume fractions, effective rate coefficients, and calibrated surface areas for primary and secondary minerals in UBC2-1A material. The mineral content in wt (%) is from XRD analysis. Mineral content expressed as volume fractions represent model-calibrated values (PF: preferential flow region, M: matrix, ND= not detected).................................... 205 Table 6.5. Mineral dissolution-precipitation, aqueous oxidation and gas dissolution-exsolution reactions .............................................................................................................. 206 Table 6.6. Chemical composition of recharge water and initial waste rock pore water in the model..................................................................................................................................... 208  xviii  Table 6.7. Dual-permeability mass transfer parameters for the sand and clay-loam soil profiles used for the simulations of Antamina Mine waste rock .......................................... 209 Table A8. Example of data block 3: spatial discretization for MIN3P-THCm-DP input file............................................................................................................................................... 250 Table A9. Example of data block 9: physical parameters-porous medium for MIN3P-THCm-DP input file .......................................................................................................................... 251 Table A10. Example of data block 11B: physical parameters-porous dual-permeability for MIN3P-THCm-DP input file ................................................................................................ 253   xix  List of Figures Figure 2.1. a) Field barrels and their collection buckets at the mine site and b) top view of field barrel UBC2-3A ............................................................................................................. 16 Figure 2.2. Conceptual model of acid rock drainage generation and pH buffering in the field barrel ....................................................................................................................................... 23 Figure 2.3. Conceptual model of different stages of field barrel life in wet and dry seasons 25 Figure 2.4. Particle size distribution curve for the field barrel UBC2-3A material. ............... 27 Figure 2.5. Calcium and sulfate variations over time compared to pH in UBC2-3A field barrel ....................................................................................................................................... 37 Figure 2.6. Equilibrium phases predicted from geochemical modeling of UBC2-3A field barrel ....................................................................................................................................... 38 Figure 2.7. Calcite amount calculated from NP (0.7 wt%), solid phase elemental analysis (0.42 wt%) and calibrated (0.06 wt%). Plots compare the pH, SO4, Cu, Zn and Ca from data and model. The colored squares are the drainage data from field barrel. ............................... 42 Figure 2.8. Comparison of calcite, gypsum and wollastonite abundance, in the middle of the field barrel (control volume = 50) as a function of time for the three simulations ................. 43 Figure 2.9. Left: Precipitation of secondary mineral presumably gypsum in the holes punctured on the walls of field barrel UBC2-3A; Right: precipitation of secondary iron oxyhydroxides and hydroxysulfates close to the bottom of field barrel UBC2-3A (images by E. Skierszkan in May 2016) .................................................................................................... 44 Figure 2.10. Left: pH from data and model for“Calcite calibrated” simulation (0.06 wt%). The colored squares are the drainage data from field barrel. Right: Abundance of calcite and selected secondary minerals (gibbsite, gypsum, ferrihydrite, malachite, brochantite, antlerite,  xx  k-jarosite and SiO2 phase), expressed as volume fraction, at the outflow boundary of field barrel as a function of time for “Calcite calibrated” simulation. ............................................ 46 Figure 2.11. Left: pH trend over time for data and model for simulation with wollastonite mineral “Calcite calibrated” (green line) and without wollastonite mineral “without wollastonite” (blue line); Right: Ca concentration trend over time for data and model for simulation with wollastonite “Calcite calibrated” (green line) and without wollastonite (blue line). ........................................................................................................................................ 49 Figure 2.12. Abundance of calcite and selected secondary minerals (gibbsite, gypsum, malachite, antlerite, k-jarosite and SiO2 phase), expressed as volume fraction, at the outflow boundary of field barrel as a function of time in the “without wollastonite” simulation. ...... 51 Figure 2.13. Left: pH trend over time for data and model for simulation with wollastonite and calcite minerals “Calcite calibrated” scenario (green line) and with wollastonite and without calcite minerals “without calcite” scenario (blue line). Right: Ca concentration versus time for data and model for simulations with wollastonite and calcite minerals “Calcite calibrated” (green line) and with wollastonite and without calcite minerals “without calcite” (blue line).................................................................................................................................................. 53 Figure 2.14. Left: Abundance of selected secondary minerals (gibbsite, gypsum, malachite, antlerite, k-jarosite and SiO2 phase), expressed as volume fraction, at the outflow boundary of field barrel as a function of time in “without calcite” conceptual model; Right: Cu concentration versus time for data and model for simulation with wollastonite and calcite minerals “Calcite calibrated” (green line) and with wollastonite and without calcite minerals “without calcite” (blue line) .................................................................................................... 55  xxi  Figure 3.1. a) Conceptual depiction of pile geometry and simulation approach, Ai corresponds to exposed area of each level; b) Cross section containing five soil profiles 2-10m, each profile represents one level of the pile. ................................................................. 65 Figure 3.2. Observed and simulated response to precipitation events for base case simulation (K = 1.34 x 10-5 m/s) a) Cumulative discharge b) Outflow hydrograph and precipitation..... 71 Figure 3.3. Observed and simulated response to precipitation events calibrated saturated hydraulic conductivities a) Cumulative discharge b) Outflow hydrograph and precipitation. 72 Figure 3.4. Field-observed and simulated tracer breakthrough at the base of pile 2, depicted with observed and simulated hydrograph ............................................................................... 73 Figure 4.1. Conceptual physical nonequilibrium models for water flow and solute transport: a) uniform flow, b) mobile-immobile, 3) dual-porosity, and d) dual-permeability model. The dark blue and red arrows indicate the water flow and solute transport, respectively. The horizontal arrows demonstrate the water and solute transfer between the two pore regions. 85 Figure 4.2. Jacobian matrix structure in MIN3P and MIN3PDUAL (Cheng, 2006) .............. 89 Figure 4.3. The conceptual model of the physicochemical system (Mayer et al., 2002) ....... 90 Figure 4.4. Conceptual model of MIN3P-THCm-DP model .................................................. 94 Figure 4.5. HYDRUS-1D: The pink plot: concentration of tracer in mobile domain using dual-porosity (mobile-immobile, pressure head mass transfer) with zero advective mass transfer and only diffusive mass transfer between the two pore regions. The blue plot: concentration of tracer in preferential-flow domain using dual-permeability (no flow in matrix to mimic dual-porosity) with zero advective mass transfer and only diffusive mass transfer between the two pore regions. Both results are plotted for 0.01 day output time. .. 110  xxii  Figure 4.6. HYDRUS-1D: The pink plot: solute mass transfer rate of tracer between mobile and immobile domains using dual-porosity (mobile-immobile, pressure head mass transfer) with zero advective mass transfer and only diffusive mass transfer on interface. The blue plot: solute mass transfer rate of tracer between preferential-flow region and matrix domains using dual-permeability (no flow in matrix to mimic dual-porosity) with zero advective mass transfer and only diffusive mass transfer between the two pore regions. Both results are plotted for 0.01 day output time. ........................................................................................... 111 Figure 4.7.  HYDRUS-1D: The pink plot: concentration of tracer in mobile domain using dual-porosity (mobile-immobile, head mass transfer) with zero diffusive mass transfer and only advective mass transfer between the two pore regions. The blue plot: concentration of tracer in preferential-flow region using dual-permeability (no flow in matrix to mimic dual-porosity) with zero diffusive mass transfer and only advective mass transfer between the two pore regions. .......................................................................................................................... 115 Figure 4.8. HYDRUS-1D: The pink plot: solute mass transfer rate of tracer between mobile and immobile domains using dual-porosity (mobile-immobile, pressure head mass transfer) with zero diffusive mass transfer and only advective mass transfer between the two pore regions. The blue plot: solute mass transfer rate of tracer between the preferential-flow region and matrix using dual-permeability (no flow in matrix to mimic dual-porosity) with zero diffusive mass transfer and only advective mass transfer between the two pore regions. .... 116 Figure 4.9. HYDRUS-1D: The blue plot: pressure head in mobile domain using dual-porosity (mobile-immobile, pressure head mass transfer) with zero diffusive mass transfer and only advective mass transfer between the two pore regions. The pink plot: pressure head of tracer in preferential-flow region (also called fracture) and matrix domains using dual-permeability  xxiii  (no flow in matrix to mimic dual-porosity) with zero diffusive mass transfer and only advective mass transfer between the two pore regions. ........................................................ 117 Figure 4.10. HYDRUS-1D: The blue plot: water content in mobile and immobile domains using dual-porosity (mobile-immobile, pressure head mass transfer) with zero diffusive mass transfer and only advective mass transfer between the two pore regions. The pink plot: water content in preferential-flow region (also called fracture) and matrix using dual-permeability (no flow in matrix to mimic dual-porosity) with zero diffusive mass transfer and only advective mass transfer between the two pore regions. ........................................................ 118 Figure 4.11. HYDRUS-1D: The blue plot: water mass transfer rate of tracer between mobile and immobile domains using dual-porosity (mobile-immobile, pressure head mass transfer) with zero diffusive mass transfer and only advective mass transfer between the two pore regions. The pink plot: water mass transfer rate of tracer between the preferential-flow region (also called fracture) and matrix using dual-permeability (no flow in matrix to mimic dual-porosity) with zero diffusive mass transfer and only advective mass transfer between the two pore regions. .......................................................................................................................... 119 Figure 4.12. HYDRUS-1D: The blue plots: pressure head in matrix and preferential-flow (also named fracture) domains using dual-porosity (pressure head mass transfer) with advective and diffusive solute transfer between the two pore regions. MIN3P-THCm-DP: The pink plots: pressure head in preferential-flow region (also named fracture) and matrix using dual-porosity (dual-permeability with no flow in matrix to mimic dual-porosity) with advective and diffusive solute transfer between the two pore regions. ................................ 122 Figure 4.13. HYDRUS-1D: The blue plots: water content in matrix and preferential-flow region (also named fracture) using dual-porosity (pressure head mass transfer) with advective  xxiv  and diffusive solute transfer between the two pore regions. MIN3P-THCm-DP: The pink plots: water content in the preferential-flow region (also named fracture) and matrix using dual-porosity (dual-permeability with no flow in matrix to mimic dual-porosity) with advective and diffusive solute transfer between the two pore regions. ................................ 123 Figure 4.14. HYDRUS-1D: The blue plot: water transfer rate between the two pore regions of matrix and preferential-flow region (also named fracture) using dual-porosity (pressure head mass transfer) with advective and diffusive solute transfer between the two pore regions. MIN3P-THCm-DP: The pink plots: water transfer rate between the two pore regions of preferential-flow region (also named fracture) and matrix using dual-porosity (dual-permeability with no flow in matrix to mimic dual-porosity) with advective and diffusive solute transfer between the two pore regions. ....................................................................... 124 Figure 4.15. HYDRUS-1D: The blue plot: concentration of tracer in matrix and preferential-flow region (also named fracture) using dual-porosity (pressure head mass transfer) with advective and diffusive solute transfer between the two pore regions. MIN3P-THCm-DP: The pink plots: concentration of tracer in preferential-flow region (also named fracture) and matrix using dual-porosity (dual-permeability with no flow in matrix to mimic dual-porosity) with advective and diffusive solute transfer between the two pore regions. ........................ 125 Figure 4.16. HYDRUS-1D: The dash line plots: pressure head in matrix and preferential-flow region (also named fracture) using dual-permeability with advective and diffusive solute transfer between the two pore regions. MIN3P-THCm-DP: The line plots: pressure head in preferential-flow region (also named fracture) and matrix using dual-permeability with advective and diffusive solute transfer between the two pore regions. ................................ 128  xxv  Figure 4.17. HYDRUS-1D: The dash line plots: water content in matrix and preferential-flow region (also named fracture) using dual-permeability with advective and diffusive solute transfer between the two pore regions. MIN3P-THCm-DP: The line plots: water content in the preferential-flow region (also named fracture) and matrix using dual-permeability with advective and diffusive solute transfer between the two pore regions. ................................ 129 Figure 4.18. HYDRUS-1D: The dash line plots: water transfer rate between the matrix and preferential-flow regions (also named fracture) using dual-permeability with advective and diffusive solute transfer between the two pore regions. MIN3P-THCm-DP: The line plots: water transfer rate between the matrix and preferential-flow region (also named fracture) using dual-permeability with advective and diffusive solute transfer between the two pore regions. .................................................................................................................................. 130 Figure 4.19. HYDRUS-1D: The dash line plots: concentration of tracer in matrix and preferential-flow region (also named fracture) using dual-permeability with advective and diffusive solute transfer between the two pore regions. MIN3P-THCm-DP: The line plots: concentration of tracer in preferential-flow region (also named fracture) and matrix using dual-permeability with advective and diffusive solute transfer between the two pore regions. F: is the abbreviation for fracture or preferential-flow region; and, M: is the abbreviation for matrix. ................................................................................................................................... 131 Figure 5.1. The schematic diagram of the preferential and matrix flow phases in porous medium ................................................................................................................................. 136 Figure 5.2. a) Schematic illustration of instrumentation lines, L1 to L6, Lysimeter D and Sub-lysimeters A, B, and C; b) Side view of experimental waste rock Pile 2 shows the three tipping phases (TP1, TP2 and TP3), Lysimeter D and Sub-lysimeters A, B and C and  xxvi  instrumentation lines, L1, L2 an L4; c) Application of bromide tracer using sprinkler system on the crown of the pile (all figures from Peterson, 2014). .................................................. 140 Figure 5.3. Conceptual models for water flow and solute transport in uniform and non-uniform flow models. Applied recharge condition are shown using the vertical light blue arrow atop each column. Water flow in the column is shown using the vertical dark blue arrow and tracer transport is represented by the vertical red arrow. The water transfer between the two pore regions is demonstrated by the horizontal dark blue arrow. The solute mass transfer between the two pore regions is represented by the horizontal red arrow. Dual-perm.: is the abbreviation for dual-permeability model, and P.F. is abbreviation for the preferential flow pore region. ............................................................................................... 142 Figure 5.4. a) Particle size distribution for Pile 2 sub-tipping phase 1 (D1A), the missing fine fraction is estimated  using two methods: (1) the red circles show results for method used by Blackmore et al., (2014), (2) the blue and white diamonds show results obtained with  ........ the method of extrapolation of the PSD tail; b) Texture of the waste rock of Pile 2 sub-tipping phase 1 (D1A) represented over USDA soil texture triangle classes for the fine-grain particles (<4.75 mm size fraction). The blue circle shows the texture of the bulk material (sandy-loam). The texture of preferential flow (sand) and matrix (clay-loam) regions used in the conceptual models in this study are shown with pink and green colored areas on the triangle, respectively. ............................................................................................................ 146 Figure 5.5. Uniform-flow model: outflow, bromide concentration and bromide mass flux of Pile 2 sub-lysimeter B drainage for the experimental period since August 2007 (blue line: field observations, red and green line: simulated data)......................................................... 154  xxvii  Figure 5.6. Sensitivity analysis scenarios to investigate the effect of Da parameter on outflow, bromide concentration and bromide mass flux in Pile 2 Lysimeter B drainage. ... 155 Figure 5.7. Mobile-immobile model: outflow of Pile 2 sub-lysimeter B drainage for the experimental period since August 2007. Black curve: field data collected from Pile 2 sub-lysimeter B. Colored curves: simulation results. Sensitivity analysis is performed on Da  and wf parameters. ....................................................................................................................... 158 Figure 5.8. Mobile-immobile model: concentration of bromide tracer in Pile 2 sub-lysimeter B drainage for the experimental period since August 2007. Data are shown from 800 to 1800 days for clarity. Black curve: field data collected from Pile 2 sub-lysimeter B. Sensitivity analysis is performed on Da  and wf parameters. ................................................................. 160 Figure 5.9. Mobile-immobile model: mass flux of bromide tracer in Pile 2 sub-lysimeter B drainage for the experimental period since August 2007. Data are shown from 800 to 1800 days for clarity. Sensitivity analysis is performed on Da  and wf parameters. ..................... 164 Figure 5.10. Dual-porosity model: outflow of Pile 2 sub-lysimeter B drainage for the experimental period since August 2007. Data are shown from 800 to 1800 days for clarity. Sensitivity analysis is performed on Da  and wf parameters. ............................................... 167 Figure 5.11. Dual-porosity model: concentration of bromide tracer in Pile 2 sub-lysimeter B drainage for the experimental period since August 2007. Data are shown from 800 to 1800 days for clarity. Sensitivity analysis is performed on Da  and wf parameters. ..................... 169 Figure 5.12. Dual-porosity model: mass flux of bromide tracer in Pile 2 sub-lysimeter B drainage for the experimental period since August 2007. Data are shown from 800 to 1800 days for clarity. Sensitivity analysis is performed on Da  and wf parameters. ..................... 172  xxviii  Figure 5.13. Dual-permeability 1 model: outflow of Pile 2 sub-lysimeter B drainage for the experimental period since August 2007. Data are shown from 800 to 1800 days for clarity. Sensitivity analysis is performed on Da  and wf parameters. ............................................... 175 Figure 5.14. Dual-permeability 1 model: concentration of bromide tracer in Pile 2 sub-lysimeter B drainage for the experimental period since August 2007. Data are shown from 800 to 1800 days for clarity. Sensitivity analysis is performed on Da  and wf parameters. . 177 Figure 5.15. Dual-permeability 1 model: mass flux of bromide tracer in Pile 2 sub-lysimeter B drainage for the experimental period since August 2007. Data are shown from 800 to 1800 days for clarity. Sensitivity analysis is performed on Da  and wf parameters. ..................... 179 Figure 5.16. Dual-permeability 2 model: outflow of Pile 2 sub-lysimeter B drainage for the experimental period since August 2007. Data are shown from 800 to 1800 days for clarity. Sensitivity analysis is performed on Da  and wf parameters. ............................................... 184 Figure 5.17. Dual-permeability 2 model: concentration of bromide tracer in Pile 2 sub-lysimeter B drainage for the experimental period since August 2007. Data are shown from 800 to 1800 days for clarity. Sensitivity analysis is performed on Da  and wf parameters. . 186 Figure 5.18. Dual-permeability 2 model: mass flux of bromide tracer in Pile 2 sub-lysimeter B drainage for the experimental period since August 2007. Data are shown from 800 to 1800 days for clarity. Sensitivity analysis is performed on Da and wf parameters. ...................... 188 Figure 5.19. Dual-permeability 3 model: outflow of Pile 2 sub-lysimeter B drainage for the experimental period since August 2007. Data are shown from 800 to 1800 days for clarity. Sensitivity analysis is performed on Da  and wf parameters. ............................................... 190  xxix  Figure 5.20. Dual-permeability 3 model: concentration of bromide tracer in Pile 2 sub-lysimeter B drainage for the experimental period since August 2007. Data are shown from 800 to 1800 days for clarity. Sensitivity analysis is performed on Da  and wf parameters. . 192 Figure 5.21. Dual-permeability 3 model: mass flux of bromide tracer in Pile 2 sub-lysimeter B drainage for the experimental period since August 2007. Data are shown from 800 to 1800 days for clarity. Sensitivity analysis is performed on Da  and wf parameters. ..................... 194 Figure 6.1. pH and concentration of key components sulfate, calcium, copper and zinc, and recharge applied on preferential flow and matrix pore regions over the simulation period in the column containing waste rock material UBC2-1A ......................................................... 214 Figure 6.2. Water saturation and hydraulic head calcite volume fraction over depth of the column for preferential flow region and matrix. Note the vertical axis is depth (m) for both plots. PF = Preferential flow and M = Matrix ....................................................................... 214 Figure 6.3. From top left to bottom right: pH, sulfate concentration, calcite and gypsum volume fraction, and gypsum saturation indices over the depth of the column for preferential flow region and matrix at five output times. Note the vertical axis is depth (m) for sulfate concentration plot and elevation (Z (m)) for calcite volume fraction and pH. PF = Preferential flow and M = Matrix ............................................................................................................. 216 Figure 6.4. Water transfer and advective and diffusive mass transfer for sulfate between the preferential flow pore region and the matrix over depth. ..................................................... 217 Figure 6.5. pH and concentrations of key components sulfate, calcium, copper and zinc, and recharge applied to preferential flow and matrix pore regions over the simulation period for waste rock material UBC2-1B .............................................................................................. 220  xxx  Figure 6.6. pH, sulfate concentrations, calcite and gypsum volume fractions, and gypsum saturation indices over the depth in the preferential flow and matrix regions at five output times. Note the vertical axis is depth (m) for the sulfate concentration plot and elevation (Z (m)) for calcite volume fractions and pH. PF = Preferential flow and M = Matrix ............. 221 Figure 6.7. Water transfer, advective and diffusive mass transfer fluxes for sulfate between preferential flow and matrix regions over depth. .................................................................. 222   xxxi  Acknowledgements I owe particular thanks to my supervisor Dr. Uli Mayer for his unconditional support, constructive guidance and patience in all the hard times, and my supervisor Dr Roger Beckie and my committee member Dr Leslie Smith for their encouragement, support and mentorship over these years.  I offer my gratitude to staff, faculty and fellow students at UBC who inspired me to continue my work in this field.  I would like to thank my parents, and my family who have supported me throughout my years of education.  Funding for this research was provided by The Compania Minera Antamina S.A., Natural Science and Engineering Research Council of Canada, and Teck Metals Limited’s Applied Research and Technology Group.       xxxii  Dedication  To my parents, Minoo and Javad, Arash and Masoud      1  Chapter  1: Introduction 1.1 Background and problem definition Mining activities result in production of large quantities of tailings and waste rock that can pose a risk to the receiving environment. Mine waste rock is commonly stored in large piles exposed to environmental conditions, i.e. precipitation and atmospheric oxygen. This exposure may result in oxidation of sulfide minerals and the release of acid rock drainage (ARD) containing contaminants such as sulfate and dissolved metals. In the presence of pH-neutralizing minerals, pH is buffered to circum-neutral conditions resulting in the occurrence of neutral rock drainage (NRD), often leading to the mobilization of metals and metalloids such as zinc, arsenic, molybdenum and lead (Lindsay et al., 2015; Nicholson and Rinker, 2000; Price, 2003).   Strategies for reducing the environmental impact of mine waste rock dumps is related to the management of the quality and quantity of drainage, both in the short-term and during the long-term. One of the main goals of studying mine waste rock focuses on developing an understanding of the processes that affect mine waste rock drainage quality and solute loadings. The main processes that have been studied are hydrological properties and particle size distribution, geochemical characteristics and mineralogical composition, microbiology and meteorology (e.g.: Moncur et al., 2005; Peterson, 2014; Sracek et al., 2004). Under field conditions, many of the underlying hydrological and geochemical processes controlling sulfide oxidation and solute loading rates in mine waste rock are considered to be coupled (Amos et al., 2015). Reactive transport models have gained credibility for the study of coupled processes in complex environments such as mine waste rock.   2  Dumping techniques and the large range of particle size in mine waste result in the gradation of waste rock. The particle size distribution range often spans from clay to boulders (Blackmore et al., 2014; Smith and Beckie, 2003). In case of the end-dumping method, which is the method often used in mine waste dump construction, much of the fine-grained material is commonly retained near the crown of the pile, while the coarse-grained material and boulders are pushed towards the bottom of the piles. The resultant physical heterogeneity creates paths for non-equilibrium flow and solute transport within mine waste rock piles. Generally, these are described as preferential flow paths or macropores. Thus, preferential flow is considered to be recurring dominant process in the majority of mine waste rock piles. The paths with slower flow are characterized as “matrix” (Gerke and van Genuchten, 1993a) and often there are parts of porous medium with stagnant pore water, which is considered immobile (Simunek and van Genuchten, 2008).   Presence of preferential flow paths that channel flow and create a fast flow path, can significantly increase the volume of the drainage released from the waste rock material during specific periods of time (Eriksson and Destouni, 1997). They can also result in recharge by-passing parts of the waste rock, without transporting solutes resulting from irreversible weathering reactions in low permeability regions of the waste rock (Smith and Beckie, 2003). The presence of the waste rock matrix decreases the water to rock ratio and increases the flow path length and residence time of pore water in the waste rock. This may result in equilibrium-controlled mineral dissolution, acidic pH and high concentrations of heavy metals in the drainage (Evans and Banwart, 2006; Maher, 2010). The pore water that drains down through the pile  3  supplies a large portion of basal drainage, often with substantial contributions from the relatively concentrated water transported through the matrix (Smith and Beckie, 2003).  Non-equilibrium flow and solute transport in macropores and matrix regions is captured in dual-domain models. A crucial component in a dual-domain models is the mass transfer term governing the exchange of water between the two co-existing sub-domains. Several empirical and semi-empirical expressions are used to represent mass transfer in current models. Generally speaking, water transfer between the two flow domains is a transient, nonlinear process (Vogel et al., 2010). The majority of chemical reactions typically occur in the fine-grained matrix region, due to higher reactive surface areas. In the event of heavy rainfall, the fast flow paths get activated.   1.2 Literature review There are several studies on hydrological processes in mine waste rock using different approaches including field and lab analysis, numerical modeling and tracer tests (e.g., Bay, 2009; Blackmore et al., 2012, 2014; Dawood and Aubertin, 2014; Eriksson et al., 1997; Fretz et al., 2011; Neuner et al., 2009, 2013; Nichol et al., 2005; Peterson, 2014; Smith and Beckie, 2003; Smith et al., 1995). Geochemical processes in mine waste rock piles have also been studied extensively (e.g., Aranda, 2010; Bailey et al., 2012, 2013; Bay et al., 2009; Blackmore, 2015; Demers et al., 2011; Fala et al., 2005, 2006, 2013; Hirsche et al., 2017; Lefebvre et al., 2001a, 2001b; Molson et al., 2005; Peterson, 2014; Peterson et al., 2012; Smith et al., 2013; Sracek et al., 2004).    4  Extensive experimental and numerical modeling studies on the characterization of preferential flow and solute transport processes in structured and macroporous media at different scales can be found in the literature. Tracer tests have been used as the main experimental method to infer preferential flow in soils (Germann et. al 1984, Kohne et al 2009, Beven and Germann, 2013). Numerical advancements include development of physically- based models for preferential flow and application of non-equilibrium solute transport to structured soils (Gerke, 2006; Jarvis, 2007; Simunek and van Genuchten, 2008; Simunek et al., 2003).   Reactive transport models have been developing rapidly over the past two decades for contaminant transport investigations at the lab and field scale (Steefel and Van Cappellen, 1998). These models have been used to investigate processes controlling the generation and attenuation of acid - and neutral-rock drainage in mine tailings and waste rock at laboratory and field scales (Amos et al., 2004; Brookfield et al., 2006; Demers et al., 2013; Jaynes et al., 1984; Jurjovec et al., 2002; Mayer et al., 2000, 2002a, 2006). Recently, Wilson et al. (2018) used reactive transport modeling to develop a conceptual model for waste rock weathering on the scale of a humidity cell.   In contrast, only a limited number of studies have targeted developing an understanding of preferential flow and solute transport in mine waste rock in the recent years. Several reactive transport modeling modeling studies have been performed that consider processes occurring in waste rock piles as a coupled system (Fala et al., 2013; Gerke et al., 1998, 2001; Molson et al., 2005; Pedretti et al.; da Silva et al., 2007; Sracek et al., 2004; Stockwell et al., 2006). However, reactive transport modeling studies considering waste rock piles as heterogeneous systems are  5  very rare. Molson et al. (2012) studied the reactive transport in a mine waste rock which overlies a fractured bed rock using a discrete fracture network (DFN) approach.   1.3 Study Site Description: Antamina Mine, Peru Several of the modeling studies presented in this thesis were contrained by data from the Antamina Mine, Peru. Antamina is a polymetallic skarn mine located in the high Andes of Peru at an elevation ranging from 4200 to 4700 m.a.s.l. The mine produces mainly copper, zinc and molybdenum. The climate at the mine site is marked by distinct wet (October to April) and dry seasons (May to September). Average annual precipitation ranges from 1200 to 1500 mm depending on location at the site with average annual temperatures ranging between 5.4 and 8.5 oC (Harrison et al., 2012).   The waste rock research program at the mine site was designed to study and characterize at various scales the physical and chemical processes that affect drainage from waste rock. This program involved over 50 field barrels that were built in conjunction with five 36 m (l) X 36 m (l) X 10 m (h) extensively-instrumented experimental waste rock piles, named Piles 1 to 5 (Aranda, 2010; Peterson, 2014). The field barrels each contained approximately 300 kg of various types of waste rock with an average particle diameter less than 10 cm. The material types to be tested were defined by the mine’s waste rock classification system. Waste rock contained in each field barrel part of the waste rock research program is associated with one tipping phase in the experimental waste rock piles.    6  1.3.1 Experimental Design of Field Barrel Study All field barrels were constructed using one-meter tall, 60-cm in diameter plastic barrels. The tops of the field barrels are open to the atmosphere with an outflow spout located at the base to allow drainage to exit freely into 20-L collection buckets. Samples were collected on a bi-weekly or monthly basis, unless when there was no discharge from the field barrels, which commonly occurred during the dry season (Peterson, 2014). Field parameters were measured including specific conductance, pH, and temperature, and samples were collected and analyzed at an external laboratory for major ions and total metals including Ag, Al, As, Ba, B, Be, Bi, Ca, Cd, Cl, Co, Cr, Cu, F, Fe, Hg, K, L, Mg, Mn, Mo, Na, Ni, N, Pb, P, Sb, Se, Si, Sn, SO4, Sr, Ti, V and Zn. The field barrel considered in this thesis (UBC2-3A) was constructed in 2008-2009 and contains class A intrusive igneous quartz monzonite waste rock with elevated sulfide and Zn concentrations. This material is characterized by relatively high sulfide and low carbonate content and is considered potentially acid generating.   1.3.2 Pile 2 Experiment Pile 2 is one of five 36 m (L) x 36 m (W) x 10 m tall instrumented test piles constructed at the Antamina Mine in Peru and designed to study the physical and chemical processes controlling drainage and mass loadings from mine waste rock (see Hirsche et al., 2012 for a project overview). Approximately 20,000-25,000 tonnes of waste rock was placed in each pile by end dumping in three tipping phases (Bay et al., 2009; Hirsche et al., 2012). Pile 2 is composed of a relatively fine-grained intrusive waste rock material in which matrix flow is hypothesized to dominate. All drainage from the pile is captured by basal lysimeters and conveyed to tipping bucket flow meters which continuously monitor flow rates.   7   To gain insight into transport processes, a conservative bromide tracer was applied to the crown (flat surface at the top) of each test pile (Blackmore et al. 2012). In the case of Pile 2, bromide was applied on January 24, 2010, and tracer samples were collected from pile outflow at time intervals that varied from 15 minutes immediately following tracer application to weekly.  1.4 Thesis organization and research objectives The thesis consists of five main chapters (Chapters 2-6) which present the research on hydrogeology and geochemistry of the variably saturated waste rock material at the field barrel and experimental pile scales. The study focuses first on small scale simulations on the field barrel scale (Chapter 2), expanding to larger scale simulations of uniform flow and solute transport on the pile scale (Chapter 3). These simulations demonstrate that a uniform flow model is insufficient to describe weathering and solute transport through the waste rock. In Chapter 4, a non-uniform flow and solute transport mode is developed based on the existing reactive transport code MIN3P. Various formulations including the mobile-immobile, dual porosity and dual permeability concepts are considered. Chapter 5 evaluates these model formulations for the description of non-uniform flow and conservative solute transport at the pile-scale constrained by field data from a tracer test. Lastly, Chapter 6 demonstrates – in a conceptual manner - the applicability of the non-uniform flow and transport formulation for simulating reactive transport in heterogeneous waste rock at the pile scale. The overarching objectives of the entire thesis are to: (1) advance the understanding of the processes that control the release and attenuation of contaminants in acid rock drainage and neutral rock drainage produced from waste rock piles and (2) investigate the role of preferential flow regimes on contaminant mass release from fine  8  grained waste rock material. In the following, more detailed summaries of each of these main research chapters are provided, outlining the objectives of each chapter.  Chapter 2: Multicomponent Reactive Transport Modeling of Acid Mine Drainage Generation and Neutralization in Waste Rock: Field Barrel Scale The overarching objective of Chapter 2 is to use reactive transport modeling to analyze and interpret the data collected from a six-year field barrel experiment that contains potentially acid-generating intrusive waste rock (UBC2-3A). This field barrel is part of an extensive waste rock characterization study in Antamina Mine, Peru.  Objectives: Specifically, this chapter aimed to: 1) reproduce the long-term evolution of drainage water composition from the field barrel including seasonal variations, 2) estimate effective rates of acid generation and pH buffering for individual mineral phases, 3) evaluate the controlling acid production and neutralization processes, 4) assess the contributions of carbonate and silicate minerals (namely calcite and wollastonite) towards the neutralization potential of the waste rock, and 5) assess the static test results for predicting waste rock weathering and metal release for the field barrel under investigation.  Chapter 3: Evaluating Preferential Flow in an Experimental Waste Rock Pile Using Unsaturated Flow and Solute Transport Modeling In Chapter 3 a model was used based on the well-established matrix-flow formulation described by Richards equation to simulate flow and transport observations collected in the field experiment. The extent of preferential flow was assessed by comparing the flow and tracer dynamics produced by the matrix-flow model with observations from the field.  Discrepancies  9  between simulations and observations was used as a motivation to continue the research on the role of preferential flow in mine waste rock and develop preferential flow capabilities to refine the conceptual understanding of the pile hydrology and geochemistry in fine-grained waste rock. Objectives: The objective of this chapter is to investigate the behavior of water flow and solute transport within an experimental waste rock pile composed of relatively fine-grained materials, to identify whether fast flow pathways are of importance in this pile, and to evaluate whether a non-uniform model is sufficient to simulate flow and solute transport through waste rock at the pile scale.  Chapter 4: Implementation and verification of mobile-immobile, dual-porosity and dual-permeability models in MIN3P to simulate flow and solute transport in unsaturated waste rock In Chapter 4, the development of a multi-component non-uniform flow and reactive transport model named MIN3P-THCm-DP, based on the existing MIN3P and MIN3P-THCm codes, is presented. This new model includes mobile-immobile, dual-porosity and dual-permeability in one-dimensional porous media systems. This model has the capability of simulating variably-saturated flow conditions in either steady-state/transients in addition to multi-component reactive transport in both preferential-flow region and matrix in dual-systems. The accuracy of the code is successfully verified against the established code HYDRUS-1D.  Objectives: The objective of this chapter is the implementation of the three above-mentioned approaches for non-uniform flow and reactive solute transport into the MIN3P code and verification of the resulting code against established benchmarks.   10  Chapter 5: Evaluation of Uniform and non-Uniform Flow and Solute Transport Models for Simulating Tracer Transport in Mine Waste Rock In chapter 5, the results of a detailed comparative study of the different numerical modeling approaches for simulating water flow and conservative solute transport through waste rock are presented, constrained by data from an experimental waste rock pile at the Antamina Mine, Peru. The modeling approaches include uniform, mobile-immobile, dual-porosity and dual-permeability flow and solute transport.  Objectives: 1) evaluate the suitability of uniform- and non-uniform flow and transport modeling approaches to reproduce measured discharge rates, concentrations and mass loadings from waste rock constrained by data from a conservative tracer test, 2) identify and constrain the most sensitive parameters controlling flow rates, concentrations and mass loadings for each method, 3) identify and constrain sensitive parameters that are common to several or all methods, and 4) determine limitations of the approaches in reproducing field observations and evaluate reasons for the observed discrepancies.   Chapter 6: Application of the non-uniform model formulation for simulation of reactive transport in mine waste rock Chapter 6 aims to demonstrate the application of MIN3P-THCm-DP code to investigate acid rock drainage production and buffering in an experimental waste rock pile that is affected by preferential flow. The conceptual model includes the infiltration of recharge through both preferential flow region and matrix with different distribution of acid generating and pH-neutralizing/ buffering minerals in preferential flow and matrix regions. The simulations are  11  conceptual in nature but are loosely constrained by data from experimental Pile 2 at the Antamina site and findings contained in Chapters 2 and 5 of this thesis.  Objectives: 1) demonstrate the capabilities of the non-uniform flow and solute transport formulation for simulating reactive transport in heterogeneous waste rock, accounting for both preferential flow and matrix pore regions and 2) to provide a preliminary investigation of the effect of reactivity distribution in preferential flow and matrix regions in the dual-domain porous medium.   Finally, Chapter 7 presents the general conclusions from this research and the recommendations for future work in reactive transport modeling of mine waste rock.      12  Chapter  2: Multicomponent Reactive Transport Modeling of Acid Mine Drainage Generation and Neutralization in Waste Rock: Field Barrel Scale  2.1 Introduction Mining activities result in production of large quantities of tailings and waste rock that can pose a risk to the receiving environment. Mine waste rock is commonly stored in large piles exposed to environmental conditions, i.e. precipitation and atmospheric oxygen. This exposure may result in oxidation reactions of sulfide minerals and the release of acid rock drainage (ARD) containing contaminants such as sulfate and dissolved metals. In the presence of pH-neutralizing minerals, pH is buffered to circum-neutral conditions resulting in the occurrence of neutral rock drainage (NRD), often leading to the mobilization of metals and metalloids such as zinc, arsenic, molybdenum and lead (Lindsay et al., 2015; Nicholson and Rinker, 2000; Price, 2003). The degree of metal release is influenced by two main factors: (1) source rock characteristics including, but not limited to, the mineralogy, relative abundance, distribution and reactivity of acid producing and acid neutralizing minerals, type and texture of waste rock, and particle size distribution, and (2) environmental factors such as rain and snow fall, climate and air temperature (Jamieson et al., 2015; Paktunc, 1999; Plumlee, 1999).   Techniques commonly used for prediction of the onset of acid rock drainage generation are categorized into static and kinetic tests. The static tests are laboratory-scale, rapid and low-cost measurements; however, these tests do not provide any information on reaction rates, or the minerals that are the main reactants for generating or attenuating acidity (GARDGuide, 2014;  13  Jambor et al., 2002; Morin and Hutt, 2001; Price, 2009). Therefore, to more accurately predict the effective neutralization potential (NP), it is advisable to investigate how much NP a particular mineral contributes in a static test and whether that NP is going to be readily available to attenuate acidity in the field. Kinetic tests include lab-based humidity cells, field-based leach pads (Price, 2009), field barrels (Lapakko, 2015; Price, 2009), or test piles (Bailey et al., 2012; Peterson et al., 2012). These kinetic tests take longer to complete than static testing and are more expensive.   Field-based experiments are mainly used for understanding the geochemical evolution of waste rock under environmental conditions (Aranda et al., 2009; Lapakko, 2015; Price, 2009; Shaw and Samuels, 2012). Field barrels more closely mimic site conditions; they provide a lower water to rock ratio and longer residence times compared to humidity cells and aid in quantifying the parameters that affect the solute release such as effective mineral weathering rates under field conditions (Lapakko, 2015; Shaw and Samuels, 2012).  Physical and chemical heterogeneity in mine waste rock contribute to the complexity of the system. To predict and manage drainage-water quality, physical and chemical processes occurring within a waste rock pile have to be identified and the coupling between these processes has to be characterized. In preparation for mine closure or remediation of abandoned mine sites, it is essential to develop improved methods for predicting the long-term geochemical behavior of waste rock upon exposure to weathering.    14  Reactive transport models have been developing rapidly over the past two decades for contaminant transport investigations at the lab and field scale (Steefel and Van Cappellen, 1998). These models have been used to investigate processes controlling the generation and attenuation of acid - and neutral-rock drainage in mine tailings and waste rock at laboratory and field scales (Amos et al., 2004; Brookfield et al., 2006; Demers et al., 2013; Jaynes et al., 1984; Jurjovec et al., 2002; Mayer et al., 2000, 2002a, 2006). Recently, Wilson et al. (2018) used reactive transport modeling to develop a conceptual model for waste rock weathering on the scale of a humidity cell. However, to date reactive transport modeling has not been used to interpret data from long-term field-barrel tests.   The overarching objective of this study is to use reactive transport modeling to analyze and interpret the data collected from a six-year field barrel experiment that is part of an extensive waste rock characterization study in Peru. This field barrel, UBC2-3A, contains potentially acid-generating intrusive waste rock. Specifically, this study aimed to:  1) reproduce the long-term evolution of drainage water composition from the field barrel including seasonal variations, 2) estimate effective rates of acid generation and pH buffering for individual mineral phases, 3) evaluate the controlling acid production and neutralization processes, 4) assess the contributions of carbonate and silicate minerals (namely calcite and wollastonite) towards the neutralization potential of the waste rock, and 5) assess the static test results for predicting waste rock weathering and metal release for the field barrel under investigation.   15  2.2 Materials and Methods 2.2.1 Mine Site Description The experiments were conducted at a polymetallic skarn mine located in the high Andes of Peru at an elevation ranging from 4200 to 4700 m.a.s.l. The mine produces mainly copper, zinc, and molybdenum. The climate at the mine site is marked by distinct wet (October to April) and dry seasons (May to September). Average annual precipitation ranges from 1200 to 1500 mm depending on location at the site with average annual temperatures ranging between 5.4 and 8.5 oC (Harrison et al., 2012).   Table 2.1. The waste rock type classification system used at the mine (Aranda et al., 2009) Class Reactivity Lithology Zinc (%) Arsenic (%) Sulfides (%) Oxides (%) A Reactive Hornfels Limestone Marble Skarn Intrusive > 0.15 > 0.04 > 3 > 10 B Slightly Reactive Hornfels Limestone Marble 0.07-0.15 < 0.04 2-3 < 10 C Non-Reactive Hornfels Limestone Marble < 0.07 < 0.04 < 2 Minimal  The waste rock research program at the mine site was designed to study and characterize at various scales the physical and chemical processes that affect drainage from waste rock. This program involved over 50 field barrels that were built in conjunction with five 36 m (l) X 36 m (l) X 10 m (h) extensively-instrumented experimental waste rock piles, named Piles 1 to 5 (Aranda, 2010; Peterson, 2014). The field barrels each contained approximately 300 kg of one of the various waste rock with an average particle diameter less than 10 cm. The material types to  16  be tested were defined by the mine’s waste rock classification system (Table 2.1). Waste rock contained in each field barrel part of the waste rock research program is associated with one tipping phase in the experimental waste rock piles. The subject of the current study is one of these field barrels, UBC2-3A, containing waste rock from pile 2, tipping phase 3, which is potentially acid-producing intrusive Class A waste rock.  2.2.2 Experimental Design of Field Barrel Study All field barrels were constructed using one-meter tall, 60-cm in diameter plastic barrels (Figure 2.1). The tops of the field barrels are open to the atmosphere with an outflow spout located at the base to allow drainage to exit freely into 20-L collection buckets (Figure 2.1). Samples were collected on a bi-weekly or monthly basis, unless when there was no discharge from the field barrels, which commonly occurred during the dry season (Peterson, 2014).    Figure 2.1. a) Field barrels and their collection buckets at the mine site and b) top view of field barrel UBC2-3A   17  Field parameters were measured including specific conductance, pH, and temperature, and samples were collected and analyzed at an external laboratory for major ions and total metals including Ag, Al, As, Ba, B, Be, Bi, Ca, Cd, Cl, Co, Cr, Cu, F, Fe, Hg, K, L, Mg, Mn, Mo, Na, Ni, N, Pb, P, Sb, Se, Si, Sn, SO4, Sr, Ti, V and Zn. The field barrel considered in this study (UBC2-3A) was constructed in 2008-2009 and contains class A intrusive igneous quartz monzonite waste rock with elevated sulfide and Zn concentrations (Table 2.1). This material is characterized by relatively high sulfide and low carbonate content and is considered potentially acid generating (Table 2.2). Compositional information on relevant parameters of intrusive waste rock contained in other field barrels is also provided in Table 2.2.   Table 2.2. Summary of unmodified Sobek ABA test, solid phase elemental analysis results and water:rock ratio of field barrels for intrusive waste rock type (Modified from Peterson, 2014)  Unit UBC2-0A UBC2-1A UBC2-1B UBC2-2A UBC2-3A Rock Type - Intrusive Intrusive Intrusive Intrusive Intrusive Total S % 0.62 0.20 4.26 0.64 1.56 Total C % 0.17 0.15 0.09 0.08 0.05 Total Ca % 1.3 0.8 5.5 1.0 1.5 Bulk NP tCaCO3/1000t 29.0 12.0 8.0 8.0 7.0 AP tCaCO3/1000t 19.4 6.3 133.1 20.0 48.8 NP/AP* - 1.49 1.90 0.06 0.40 0.14 water:rock** kg/kg 0.14 0.14 0.14 0.14 0.14 *NP represents unmodified Sobek (Sobek et al., 1978) neutralization potential. **water:rock: average water to rock ratio in wet season. The average moisture content is adapted from Pile 2 average moisture content observed in wet season. Data presented in Peterson (2014).  2.2.3 Solid Phase Analysis and Acid Base Accounting  The mineralogical and elemental solid-phase composition of the waste rock, was analyzed by Peterson (2014) and ALS labs in Lima, Peru (results presented in Peterson (2014)). The analysis included solid-phase major element and trace metal concentrations using whole rock digestion  18  and inductively-coupled plasma mass spectrometry (ICP-MS), acid-base accounting (ABA), including maximum potential acidity (AP) and neutralization potential (NP) using the unmodified Sobek method (Sobek et al., 1978) without siderite correction, and total solid phase S and C by Leco furnace (Peterson, 2014) (Table 2.2).   Field barrel UBC2-3A was selected for this study due to its rapid transition from neutral to acidic conditions.  This was despite the fact that it did not have the lowest NP/AP ratio among the Pile 2 field barrels (Table 2.2) which industry standards would have us believe is the factor that should lead to the most rapid acidification. This suggests that some of the NP measured under static conditions is not available under kinetic field-barrel conditions. In addition, the drainage from this field barrel contained the highest Cu and Zn concentrations.  Mineralogical composition of field barrel UBC2-3A was determined using X-ray diffraction (XRD) and relative proportions of the minerals (Table 2.3) were determined using Rietveld refinement using the Topas v.3.0 software (Peterson, 2014). The dominant minerals detected by XRD are quartz [SiO2], orthoclase [KAlSi3O8] and plagioclase feldspars [NaAlSi3O8-CaAl2Si2O8]. The dominant sulfides are pyrite [FeS2] and chalcopyrite [CuFeS2] with trace molybdenite [MoS2]. Carbonate minerals were not detected by XRD in the intrusive rock, except for siderite [FeCO3], which was present at very low weight percentages in some field barrels. However, siderite was not detected in UBC2-3A field barrel material. Actinolite [Ca2(Mg,Fe)5Si8O22(OH)2] and oligoclase [(Ca,Na)(Al,Si)4O8] were ignored as a contributors to neutralization. Although identified by quantitative XRD, melanterite was not included in the conceptual model. This mineral has a high solubility, leading to very high sulfate concentrations,  19  which were not observed in the field barrel drainage. The mineralogical composition of field barrel is UBC2-3A is presented in Table 2.3.   Table 2.3. Results of quantitative XRD analyses for field cell UBC2-3A (Modified from Peterson, 2014, ND = non detected)  Mineral Abundance [wt%] Actinolite 1.04 Albite low 1.04 Andradite 8.54 Biotite 1M 2.00 Chalcopyrite 2.42 Diopside 2.67 Ferrihydrite ND Kaolinite ND Magnetite 0.74 Melanterite 0.18 Molybdenite 2H 0.04 Muscovite 2M1 0.86 Oligoclase 6.24 Orthoclase 34.19 Pyrite 2.73 Pyrrhotite  ND Quartz 35.24 Siderite ND Wollastonite 2.07  2.2.4 Description of Numerical Model  The drainage from the field barrel was simulated using the MIN3P code, a three-dimensional multicomponent finite volume reactive transport model for variably saturated media based on the global-implicit solution method (Mayer, 1999; Mayer et al., 2002a). This code includes Richards equation for the solution of variably-saturated flow and solves mass balance equations for advective-diffusive solute transport and diffusive gas transport. Geochemical reactions are  20  described by a partial equilibrium approach using equilibrium-based law-of-mass-action relationships for fast reactions, and a generalized kinetic framework for reactions that are relatively slow in comparison to the transport time scale. The model formulation includes aqueous complexation, hydrolysis, redox reactions and mineral dissolution-precipitation reactions. The thermodynamic database in MIN3P is based on the database of WATEQ4F (Ball and Nordstrom, 1991) and MINTEQA2 (Allison et al., 1990). The MIN3P database also allows the specification of kinetically controlled intra-aqueous and dissolution-precipitation reactions.   2.2.5 Scenario-based Modeling of Waste Rock Weathering in Field Barrel UBC2-3A To address the objectives of this chapter, five simulations are presented that are based on the five scenarios summarized in Table 2.4. It was necessary to conduct this study via a scenario-based approach, because solid phase data was insufficient to adequately constrain the modeling. Primary sulfides, carbonates, and silicate minerals, as well as secondary phases provide important controls on pH and dissolved metals in drainage from the field barrel. When quantitative data was available for any of these minerals, it was used to constrain the model. If adequate data was not available, the presence, volume fraction and effective reaction rate of the mineral were considered variables in the scenario modeling.   The conceptual model for all three simulations consisted of the following primary buffering phases, namely calcite and wollastonite. The initial approach was to constrain the volume fraction of calcite based on static NP testing results and then based on solid phase elemental analysis (Table 2.2). In both scenarios, the abundance of wollastonite was constrained by quantitative XRD-results (Table 2.3). These scenarios are entitled “Calcite from NP” and  21  “Calcite from solid phase analysis”, respectively. The next scenario also considered the same abundance of wollastonite, but calcite content was calibrated to improve agreement with observed drainage-water chemistry. This scenario was named “Calcite calibrated”. Two additional simulations are presented to demonstrate the profound effect of wollastonite and calcite dissolution on the effective neutralization potential and the evolution of drainage water chemistry. These simulations are directly based on the scenario “Calcite calibrated” by removing either wollastonite (“without wollastonite”) or calcite (“without calcite”).   Table 2.4. Summary of scenario-based models for field barrel UBC2-3A. Scenario Description Initial Volume Fraction (wt %) Calcite Wollastonite Calcite from NP Calcite volume fraction estimated from bulk NP (unmodified Sobek), wollastonite volume fraction from Rietveld analysis 0.70 2.07 Calcite from solid phase analysis Calcite volume fraction estimated from solid phase composition analysis, wollastonite volume fraction from Rietveld analysis 0.42 2.07 Calcite calibrated Calcite volume fraction calibrated to data, wollastonite volume fraction from Rietveld analysis 0.06 2.07 without wollastonite Calcite volume fraction calibrated to data, wollastonite eliminated 0.06 - without calcite Calcite eliminated, wollastonite volume fraction from Rietveld analysis - 2.07  In addition, secondary gypsum, gibbsite, ferrihydrite, malachite, brochantite, antlerite, smithsonite and k-jarosite were included in the conceptual model due to the high probability of  22  their formation based on either geochemical speciation calculations of the drainage water or identification in mineralogical analysis.   Table 2.5. Mineral dissolution-precipitation, aqueous oxidation and gas dissolution-exsolution reactions  Mineral Reaction    Primary Minerals log Kim  1) pyrite* FeS2 (s) + H2O + 7/2O2 (aq) → Fe2+ + 2SO42- + 2H+ - 61.488 2) chalcopyrite CuFeS2  (s) +  4O2  (aq) → Cu2+ + Fe2+ + 2SO42-  -35.27 3) sphalerite ZnS (s) + 2O2 (aq) → Zn2+ + SO42-  -11.618 4) magnetite Fe2+Fe23+O4(s) + 8H+ → 2Fe3+ + Fe2+ + 4H2O 3.7370 5) calcite CaCO3 (s) ↔ Ca2+  + CO32-  -8.475 6) wollastonite CaSiO3 (s) + 2H+ + H2O → Ca2+ + H4SiO4(aq) 12.996 7) biotite-ph  K (Mg2Fe) (AlSi3O10) (OH)2 (s) + 10H+ → K+ + 2Mg2++ Fe2++ Al3++ 3H4SiO4(aq)  - 8) orthoclase  KAl3Si3O8 (s) + 4H+  +4H2O → K+ + Al3++ 3H4SiO4(aq)  - 9) albite NaAl3Si3O8 (s) + 4H+  +4H2O → Na+ + Al3++ 3H4SiO4(aq)  - 10) muscovite-ph KAl3Si3O10(OH)2 (s) + 10H+ → K++ 3Al3+ + 3H4SiO4(aq)  -   Secondary Minerals   11) gibbsite Al(OH)3 + 3H+ ↔ Al3+ + 3H2O  8.110 12) gypsum CaSO4 .2H2O ↔  Ca2+ + SO42- + 2H2O  -4.580 13) ferrihydrite Fe(OH)3 (am) + 3H+ ↔  Fe3+ + 3H2O  4.891 14) Malachite Cu2 CO3 (OH)3 + 2H+ ↔ 2Cu2++ 2H2O + CO32-  -5.18 15) brochantite  Cu4(SO4) (OH)6 + 6H+ ↔  4Cu2+ + 6H2O + SO42-  15.34 16) antlerite Cu3(SO4) (OH)4 + 4H+ ↔  3Cu2+ + 4H2O + SO42-  8.29 17) smithsonite  ZnCO3  ↔ Zn2+ + CO32-  -10.0 18) k-jarosite  K Fe3(SO4)2 (OH)6 + 6H+ ↔ K+ + 3Fe3+ + 2SO42- + 6H2O -9.210  19) silica-am  SiO2 (am) + 2H2O ↔ H4SiO4 (aq)  -2.710  Aqueous Oxidation Reduction  20) Fe(II)/Fe(III) Fe2+ + 14O2  (aq)  + H+ ↔  Fe3+ + 1/2H2O 8.50 21) SO42-/HS- HS- + 2O2  (aq)  ↔ SO42- + H+ 138.51  23   Mineral Reaction    Gas Dissolution Exsolution  22) O2 (g)/O2(aq)  O2  (g) ↔ O2  (aq) -2.898 23) CO2(g) /CO2(aq)  CO2  (g) + H2O  ↔  CO32-+ 2H+ -18.149  Minerals considered in these simulations are summarized in Table 2.5. In the “Calcite from NP” simulation, the volume fraction of calcite was estimated at 0.7 wt% using the bulk neutralization potential data reported from ABA analysis (Table 2.2). For the “Calcite from Solid phase” simulation, the volume fraction of calcite was calculated to be 0.42 wt% from the solid phase composition analysis.    Figure 2.2. Conceptual model of acid rock drainage generation and pH buffering in the field barrel  Sulfide mineral weathering, acid neutralization reactions and reactive transport in the field barrel UBC2-3A were simulated as a one-dimensional vertical profile (Figure 2.2). The main reaction processes occurring in the field cell are sulfide mineral oxidation, dissolution and precipitation of gangue mineral phases, precipitation and re-dissolution of secondary mineral phases, as well as  24  hydrolysis and aqueous complexation (Peterson, 2014). Transport processes include advective-diffusive transport in the water phase. The partial pressure of oxygen was fixed at atmospheric levels to reflect the well-ventilated conditions in the field barrel.   Considering the strong seasonal climate at the site, the hypothesis is that effluent concentrations and mass loadings from the field barrel are substantially affected by the variability of precipitation rates between wet and dry seasons. It is anticipated that during the dry season (Figure 2.3a), lower precipitation and higher evaporation result in longer residence times and lead to precipitation of secondary minerals within the field barrel. At the start of the wet season (Figure 2.3b), the upper portion of the field barrel, which contains mostly fine particles, starts to wet up. Increasing moisture content is expected to promote the re-dissolution of soluble precipitates and activate piston flow, leading to an advance of the wetting front in the field barrel (Figure 2.3c and d). Drainage water arriving at the bottom of the field barrel was sampled. Geochemical equilibrium may not have been reached between the fast-moving pore water and the solid phase under field condition for some solid phases, in particular silicate minerals. For all scenarios considered here, the physical properties of the waste rock contained within the field barrel were assumed homogeneous and isotropic.   25   Figure 2.3. Conceptual model of different stages of field barrel life in wet and dry seasons  2.2.5.1 Physical Parameters The length of the model domain was one meter, consistent with field barrel dimensions, and the simulations were performed using 100 control volumes in vertical direction. Horizontal flow components due to heterogeneities within the field barrels were neglected and the field barrel was modeled as a spatially uniform porous medium, with soil-water characteristic functions that did not vary with location. Particle-size-distribution (ASTM D 5519–94) and bulk-density (ASTM D 5030–89) were analyzed on the waste rock (Blackmore et al., 2014; Golder, 2010). The UBC2-3A waste rock is relatively homogeneous with a particle size distribution (PSD) similar to other waste rock of the same type (Figure 2.4). The calculated uniformity coefficient (Cu or D60/D10 [-]) for UBC2-3A waste rock is greater than 167. This value is indicative of well-graded material (Morin et al., 1991). The simulations were performed for a time period of 2,200 days (approximately 6 years since the start of the field barrel program) with a maximum time step of one day.  The flow boundary condition at the top of the field barrel was set to a second type (Neumann), specified flux condition. In the wet season, the inflow boundary condition was set equal to the  26  estimated daily recharge in the associated experimental-scale pile. This assumption was made due to lack of daily drainage volume data from the field barrel scale study. Evaporation, and therefore recharge at the crown of the experimental scale pile were estimated by a water-balance approach. Using daily rainfall data, daily evaporation/recharge was estimated as that which gave the best match to the observed outflow hydrograph of discharge from the base of the pile. More details on the estimation of evaporation and recharge at the pile scale can be found in Javadi et al. (2012). Using evaporation from the pile experiment for the field barrel may have resulted in underestimation of daily recharge at the field barrel scale. In the dry season, the inflow boundary condition was set equal to zero which is consistent with the field data, since there is minimal drainage volume recorded from the field barrels during dry season. Drainage only occurs early during the dry season and is attributed to drain down of residual wet season recharge. The outflow boundary condition was set to a first type (Dirichlet) boundary with a hydraulic head of –2m, because the discharge point in the collection bucket was located below the base of the field barrel and to ensure that unsaturated conditions were maintained throughout the field barrel, consistent with conditions in the field.   27   Figure 2.4. Particle size distribution curve for the field barrel UBC2-3A material.  The soil hydraulic function parameters for the field barrel (Table 2.6) were adapted from the parameters calculated for the experimental pile containing the same waste rock material. In the absence of direct measurements, residual saturation (Sr) and the soil hydraulic function parameters α = 7 m-1 and n = 1.65 for the van Genuchten model (Wösten and Van Genuchten, 1988) were estimated from material-specific soil water characteristic curves (see Javadi et al., 2012 for more details). The soil water characteristic curves were calculated using the SoilVision Software (Speidel, 2011). The average porosity of the waste rock material was measured to be 0.34 (Blackmore et al., 2014) and saturated hydraulic conductivity was calibrated to be equal to 6.7 10-4  ms-1 (Javadi et al., 2012). Literature values for the free phase diffusion coefficients in water (Da = 2.3810-9 m2/s) was used (Mayer et al., 2002a). The effect of dispersion on solute transport was neglected. All physical input parameters are summarized in Table 2.6. 0.010.11101001000Percentage Passing (%)Particle size (mm)UBC2-3A 28   Table 2.6. Physical input parameters for flow and reactive transport simulations in field barrel UBC2-3A (see Javadi et al., 2012 for more details) Parameter Symbol Unit Value Reference Porosity ϕ - 0.34 Speidel (2011) Residual saturation Sr - 0.36 Speidel (2011) Recharge rate qr ms-1 transient Calibrated, as a fraction of rainfall data Hydraulic conductivity Kzz ms-1 6.710-4 Calibrated based on ring-infiltrometer data (Blackmore et al., 2014),  van Genuchten soil  hydraulic function parameters α m-1 7 Speidel (2011) n - 1.65 Speidel (2011) Free phase diffusion  coefficient in aqueous phase Da m2 s-1 2.3810-9 Mayer et al. (2002)  The parameters presented in Table 2.6 were estimated by calibrating the daily hydrograph and cumulative outflow of the Pile 2 Lysimeter D and were adapted for field barrel UBC2-3A (details presented in Chapter 3). The flow calibration on the pile scale was possible due to existence of hourly outflow volumes; However, such resolution of data did not exist for the field barrel scale. As a result, the estimation of the flow related parameters would not be accurate using the field barrel flow data. It is important to consider that the evaporation is higher at the pile scale than on the field barrel scale due to presence of slopes and berm in piles.   2.2.5.2 Reaction Network and Geochemical Parameters 2.2.5.2.1 Pyrite Oxidation and Sulfide Mineral Weathering Reactions  Pyrite and chalcopyrite were detected in the waste rock using XRD analysis and were included in the simulations based on measured concentrations. Although sphalerite was not detected in XRD-analyses, Mineral Liberation Analyzer (MLA) studies (St. Arnault, in progress) revealed  29  the presence of trace amounts in intrusive waste rock, including material UBC2-3A. Sphalerite was therefore considered as a primary mineral phase in the model. The relatively high concentrations of zinc in the effluent from the field barrel (ranging from 10 to 400 mgL-1 from 2007 to 2013) provide further evidence for the presence of a zinc source in the waste rock. Galena was also not among the sulfide minerals that were identified by XRD. Since lead concentrations in the effluent solution were relatively low (0.001 to 2.5 mg L-1 from 2007 to 2013), galena was not included in the model. Although molybdenite was identified, the concentration of Mo in aqueous phase stayed below 0.1 mgL-1 for the duration of simulations and only in the final wet season it increased to below 0.3 mgL-1 in UBC2-3A, and therefore was not included in the present simulations. The reaction stoichiometries of the sulfide weathering reactions considered in the simulations are summarized in Table 2.5.  A wide range of laboratory-based abiotic empirical rate laws exist for aqueous oxidation of pyrite by ferric ion and dissolved oxygen (Jerz and Rimstidt, 2004; Lowson, 1982; McKibben and Barnes, 1986; Moses et al., 1987; Wiersma and Rimstidt, 1984; Williamson and Rimstidt, 1994). Meanwhile, the kinetic oxidative dissolution of pyrite and other sulfide minerals is a complex process and the rates obtained in the laboratory are not necessarily applicable to field conditions. Variation in physical and chemical factors such as flushing rate, flushing frequency, particle size distribution, degree of liberation, and rate of secondary mineral precipitation-dissolution strongly affect effective reaction rates and the evolution of weathering (Sapsford et al., 2009). It is therefore often more practical to calibrate effective reaction rates to match the observed data in the field.    30  The observed pH values in effluent from the field barrel are consistently below 7 starting with the first wet season, and subsequently drop to lower pH-values accompanied by increasing metal concentrations. In order to reproduce field observations of pH trends and metal release, the weathering rates of sulfide minerals were assumed pH-dependent with higher oxidation rates at lower pH-values. This formulation captures the acceleration of weathering rates due to the presence of acidophilic sulfur oxidizing bacteria under acidic pH conditions (Blowes et al., 2003) and is consistent with microbial catalysis of ferrous iron oxidation under low pH-conditions, which can remarkably enhance rates of ferric iron production, and consequently sulfide mineral oxidation (Nordstrom and Southam, 1997). Dockrey et al. (2014) conducted microbiological investigations, confirming the presence of acidophilic iron and sulfur oxidizer bacteria for samples collected from field barrel UBC2-3A. To reproduce observed drainage water chemistry, a combination of zero-order and Monod-type rate expressions were used for the minerals pyrite, chalcopyrite, and sphalerite, accounting for pH-dependence of these oxidative dissolution reactions (Table 2.7). When the activity of hydrogen ion is substantially below 10-3 (mol L-1), or in other words when pH >> 3, sulfide mineral oxidation rates are assumed to be dominated by a zero-order rate expression as shown in Table 2.7. For the condition where the activity of the hydrogen ion is around or above 10-3 (mol L-1), or pH < 3, the reaction rate is dominated by a fractional order term dependent on the activity of the hydrogen ion [H+]. In the equations presented in Table 2.7, 𝑅𝑝𝑦𝑟𝑖𝑡𝑒𝑚  and 𝑅𝑝𝑦𝑟𝑖𝑡𝑒−𝑝𝐻𝑚  are the reaction rates for pyrite oxidation for circum-neutral and acidic ranges (mol dm-1 bulk s-1), 𝑘𝑝𝑦𝑟𝑖𝑡𝑒𝑚,𝑒𝑓𝑓 and 𝑘𝑝𝑦𝑟𝑖𝑡𝑒−𝑝𝐻𝑚,𝑒𝑓𝑓 are the effective reaction rate constants (mol dm-1 bulk s-1) and ks is the half saturation constant for H+ (mol L-1 H2O). Effective rate constants were calibrated for each mineral in an attempt to reproduce observed pH declines and metal release rates. The reactions were defined as surface-controlled  31  reactions. The composite rate of pyrite oxidation was calculated as 𝑅𝑝𝑦𝑟𝑖𝑡𝑒𝑚 + 𝑅𝑝𝑦𝑟𝑖𝑡𝑒−𝑝𝐻𝑚 . The effective reaction rates for chalcopyrite, sphalerite and wollastonite were determined using the same approach.  Table 2.7. Reaction rate expressions used for primary mineral weathering (combined reaction paths) Mineral Rate Expression Pyrite 𝑅𝑝𝑦𝑟𝑖𝑡𝑒𝑚 = 𝐾𝑝𝑦𝑟𝑖𝑡𝑒𝑚,𝑒𝑓𝑓(1 −𝐼𝐴𝑃𝑝𝑦𝑟𝑖𝑡𝑒𝐾𝑝𝑦𝑟𝑖𝑡𝑒𝑚 ) + 𝐾𝑝𝑦𝑟𝑖𝑡𝑒−𝑝𝐻𝑚,𝑒𝑓𝑓([𝐻+]𝑘𝑠 + [𝐻+]) Chalcopyrite 𝑅𝑐ℎ𝑎𝑙𝑐𝑜𝑝𝑦𝑟𝑖𝑡𝑒𝑚 = 𝐾𝑐ℎ𝑎𝑙𝑐𝑜𝑝𝑦𝑟𝑖𝑡𝑒𝑚,𝑒𝑓𝑓(1 −𝐼𝐴𝑃𝑐ℎ𝑎𝑙𝑐𝑜𝑝𝑦𝑟𝑖𝑡𝑒𝐾𝑐ℎ𝑎𝑙𝑐𝑜𝑝𝑦𝑟𝑖𝑡𝑒𝑚 ) + 𝐾𝑐ℎ𝑎𝑙𝑐𝑜𝑝𝑦𝑟𝑖𝑡𝑒−𝑝𝐻𝑚,𝑒𝑓𝑓([𝐻+]𝑘𝑠 + [𝐻+]) Sphalerite 𝑅𝑠𝑝ℎ𝑎𝑙𝑒𝑟𝑖𝑡𝑒𝑚 = 𝐾𝑠𝑝ℎ𝑎𝑙𝑒𝑟𝑖𝑡𝑒𝑚,𝑒𝑓𝑓(1 −𝐼𝐴𝑃𝑠𝑝ℎ𝑎𝑙𝑒𝑟𝑖𝑡𝑒𝐾𝑠𝑝ℎ𝑎𝑙𝑒𝑟𝑖𝑡𝑒𝑚 ) + 𝐾𝑠𝑝ℎ𝑎𝑙𝑒𝑟𝑖𝑡𝑒−𝑝𝐻𝑚,𝑒𝑓𝑓([𝐻+]𝑘𝑠 + [𝐻+]) Wollastonite 𝑅𝑤𝑜𝑙𝑙𝑎𝑠𝑡𝑜𝑛𝑖𝑡𝑒𝑚 = 𝐾𝑤𝑜𝑙𝑙𝑎𝑠𝑡𝑜𝑛𝑖𝑡𝑒𝑚,𝑒𝑓𝑓(1 −𝐼𝐴𝑃𝑤𝑜𝑙𝑙𝑎𝑠𝑡𝑜𝑛𝑖𝑡𝑒𝐾𝑤𝑜𝑙𝑙𝑎𝑠𝑡𝑜𝑛𝑖𝑡𝑒𝑚 ) + 𝐾𝑤𝑜𝑙𝑙𝑎𝑠𝑡𝑜𝑛𝑖𝑡𝑒−𝑝𝐻𝑚,𝑒𝑓𝑓([𝐻+]𝑘𝑠 + [𝐻+]) Muscovite 𝑅𝑚𝑢𝑠𝑐𝑜𝑣𝑖𝑡𝑒 = −𝑆𝑚𝑢𝑠𝑐𝑜𝑣𝑖𝑡𝑒(𝑘1[𝐻+]0.08 + 𝑘2[𝐻+]−0.1) Biotite 𝑅𝑏𝑖𝑜𝑡𝑖𝑡𝑒 = −𝑆𝑏𝑖𝑜𝑡𝑖𝑡𝑒(𝑘1[𝐻+]0.25) Albite 𝑅𝑎𝑙𝑏𝑖𝑡𝑒 = −𝑆𝑎𝑙𝑏𝑖𝑡𝑒(𝑘1[𝐻+]0.49 + 𝑘2[𝐻+]−0.3) Orthoclase  𝑅𝑜𝑟𝑡ℎ𝑜𝑐𝑙𝑎𝑠𝑒 = −𝑆𝑜𝑟𝑡ℎ𝑜𝑐𝑙𝑎𝑠𝑒(𝑘1[𝐻+]0.5 + 𝑘2[𝐻+]−0.45) 𝑘𝑠: half saturation constant (mol L-1 H2O) 𝑘𝑚𝑖𝑛𝑒𝑟𝑎𝑙𝑚,𝑒𝑓𝑓 and 𝑘𝑚𝑖𝑛𝑒𝑟𝑎𝑙−𝑝𝐻𝑚,𝑒𝑓𝑓: effective rate constants for pyrite, chalcopyrite, sphalerite and wollastonite (mol L-1 bulk s-1) 𝑆𝑚𝑖𝑛𝑒𝑟𝑎𝑙: reactive surface area (m2 mineral L-1 bulk)      32  2.2.5.2.2 Acid Neutralization  The dissolution of carbonate minerals, principally calcite, commonly contribute significantly to pH-buffering, if these phases are present. According to Equation 2-1, at pH <≈ 6.3, one mole CaCO3 equivalent neutralizes two moles of aqueous H+ (Morin and Hutt, 2001). However, at ≈6.3<pH<≈10.3, the reaction occurs based on Equation 2-2: 𝐶𝑎𝐶𝑂3 + 2𝐻+ ↔ 𝐶𝑎2+ + 𝐻2𝐶𝑂3 ↔ 𝐶𝑎2+ + 𝐻2𝑂 + 𝐶𝑂2(𝑔)  Equation 2-1 𝐶𝑎𝐶𝑂3 + 𝐻+ ↔ 𝐶𝑎2+ + 𝐻𝐶𝑂3−  Equation 2-2 The fact that pH in drainage from the field barrel remained circum-neutral for a period of time after initiation of the experiment suggests that calcite was initially present in the waste rock, although it was not detectable in XRD analyses (Peterson, 2014). MLA analysis (St. Arnault, 2018, in progress) confirms that calcite and other carbonate phases are present at trace amounts in intrusive waste rock. In addition, gas partial pressure data collected from the same waste rock material contained in experimental Pile 2 (Lorca et al., 2016) showed elevated concentrations of CO2 gas (above 1% (v/v)), which is indicative of  dissolution of carbonate minerals (possibly calcite).   For the simulations, the initial amount of calcite in the model was estimated using two methods: (1) based on the bulk NP value reported from unmodified Sobek acid base accounting (ABA) (Table 2.2), and (2) total calcium and total carbon content from solid phase elemental analysis (Table 2.2). The initial weight percentage of calcite estimated based on the Sobek method was equal to 0.7 wt%. This value is estimated based on the relationship of the solid mineral CaCO3 and the aqueous acidity neutralized by dissolution of calcite at  pH <≈ 6.3 (Equation 2-1) (Morin  33  and Hutt, 2001). The assumption was that the bulk NP measured in the field barrel was provided by calcite. Since the relative importance of wollastonite is not known at this stage, the contribution of this mineral to NP was ignored for this scenario. However, the role of wollastonite is evaluated in the next section. The initial weight percentage of calcite estimated using calcium and carbon content from solid phase analysis was equal to 0.42 wt%. There was less total C in the sample than total Ca, as a result, the total C was considered as a limiting factor for calculating the volume fraction of calcite. It was assumed that all carbon measured in the solid phase analysis was inorganic and was present as carbonate in calcite. The excess Ca was considered to be from Ca-bearing silicate minerals such as wollastonite [CaSiO3]. The excess bulk NP not attributable to calcite was interpreted to be contributed from wollastonite.  difference between estimated calcite from bulk NP and solid phase composition analysis was considered to be due contributions from other mineral phases (e.g. wollastonite). Notably, sampling variability might also contribute to differences between the results of the two methods. The estimated volume fractions for calcite were used in Scenarios “Calcite from NP” and “Calcite from solid phase”.   There were three other Ca-bearing minerals which were detected by XRD: wollastonite (2.07 wt%), diopside (2.67 %wt) and andradite (8.54 wt%) (Table 2.3). Diopside and andradite were assumed non-reactive for the six-year period of the current study (2007-2013), due to their very slow reaction rates, and therefore were not considered in the model. On the other hand, wollastonite is a silicate mineral that is considered to weather more rapidly, similar to anorthite (Jambor, 2003). Based on the existing literature (Fernández-Caliani et al., 2008; Jambor, 2003; Jambor et al., 2002), wollastonite is also known to provide an extraordinarily high NP. However,  34  the relative importance of calcite and wollastonite in retaining pH above neutral in a waste rock material that contains both minerals is not well known. In both natural weathering and in lab studies a preferential release of Ca relative to Si has been observed (Brantley and Chen 1995, Peters et al. 2001). Xie and Walther (1994) noted that wollastonite brought into contact with pure water resulted in a rapid and appreciable pH rise within minutes. Conversely, the reactivity of wollastonite at pH = 5 is lower by a factor of 200 or more relative to the reactivity of calcite (Jambor, 2003). Here, the reactivity of wollastonite in comparison to calcite is examined in more detail. The complete, stoichiometric dissolution of wollastonite is shown in Equation 2-3.  𝐶𝑎𝑆𝑖𝑂3(𝑠) + 2𝐻+ + 𝐻2𝑂 → 𝐶𝑎2+ + 𝐻4𝑆𝑖𝑂4(𝑎𝑞)  Equation 2-3 The reaction rates of silicate minerals including wollastonite, muscovite, biotite, albite, orthoclase are considered to be pH-dependent (Error! Reference source not found.). For wollastonite, a reaction pathway for pH < 3 was added to the database. The initial values for effective reaction rates for abovementioned minerals were estimated constrained by literature values for silicate weathering (Mayer et al., 2002a) and were later calibrated in an attempt to match the drainage quality data obtained from the field barrel (Table 2.8). The reactive surface areas for biotite, oligoclase, albite, and muscovite were calibrated to observed drainage chemistry (Table 2.8). The reaction stoichiometry and equilibrium constants of the dissolution-precipitation are summarized in Table 2.5.    35   Table 2.8. Initial volume fraction, effective rate, and calibrated surface area for primary and secondary minerals (ND= not detected)  Mineral Mineral Content Kim, Kim,eff Si   calibrated Primary Minerals wt (%) Volume Fraction mol L-1 s-1 m2L-3 bulk 1) pyrite 2.73 1.12 X 10-2 1.2 X 10-10 - 2) chalcopyrite 2.42 1.09 X 10-2 1.5 X 10-11 - 3) sphalerite ND ND 5.0 X 10-12 - 4) magnetite 0.74 2.71 X 10-3 10-11 - 5) calcite 0.7, 0.42,  0.06 4.89 X 10-3, 2.94 X 10-3, 4.19 X 10-4 10-7 - 6) wollastonite 2.07 1.38 X 10-2 0.5 X 10-10 - 7) biotite-ph 2.00 1.29 X 10-2 10-10.97 10 8)orthoclase 34.19 2.56 X 10-1 10-9.93 100 9) albite 1.04 7.52 X 10-3 10-9.69 0.5 10) muscovite-ph 0.86 5.78 X 10-3 10-12.60 10  Secondary Minerals    11) gibbsite - - 10-6 - 12) gypsum - - 10-7 - 13) ferrihydrite - - 10-8 - 14) Malachite - - 10-7 - 15) brochantite  - - 10-7 - 16) antlerite - - 10-7 - 17) smithsonite - - 10-7 - 18) k-jarosite - - 10-9 - 19) silica-am - - 10-6 -   36  The initial weight percentage of minerals were converted to volume fractions, i.e. the volume of bulk aquifer occupied by the specific mineral phase divided by the bulk volume of the aquifer (Equation 2-4). This quantity has been chosen, since it is convenient for reactive transport simulations (Mayer et al., 2017):  𝜑𝑖 =10−2 𝐺𝑖𝛾𝑏𝛾𝑖 Equation 2-4 where 𝜑𝑖 is the mineral volume fraction, 𝐺𝑖 is the weight percentage of the mineral relative to bulk weight of the sample (-), 𝛾𝑏 is the bulk density of the sample (g cm-3) and 𝛾𝑖 is the density of mineral phase (g cm-3).  2.2.5.2.3 Secondary Mineral Formation Figure 2.5 shows the observed aqueous concentrations of Ca, SO4 and pH in the field barrel drainage solution collected over the six years of study (2007-2013) and Figure 2.6 presents the saturation indices (SI) predicted from the aqueous chemistry analysis of UBC2-3A field barrel effluent throughout the wet season. The data shown represent wet season conditions, because the principal effluent discharge from field barrels and sample collection only occurs in the wet season. Figure 2.5 shows that the concentrations of Ca and SO4 during the first part of the experiment are correlated with substantially higher concentrations at the beginning of the wet season than towards the end of the wet season. During the latter part of the experiment, SO4 concentrations increase substantially, while Ca concentrations decline. The saturation index of gypsum [CaSO4∙2H2O] (Figure 2.6) is near equilibrium (SI = 0) during the wet season of 2007 and then oscillates between 0 and -1 until the end of the experiment.    37   Figure 2.5. Calcium and sulfate variations over time compared to pH in UBC2-3A field barrel  The computed saturation indices suggest that secondary copper hydroxy-sulfate minerals such as brochantite and antlerite are important phases controlling dissolved Cu-concentrations. Speciation calculations for drainage from the field barrel (Figure 2.6) show that the SI of secondary copper hydroxy-sulfate mineral antlerite [Cu3(SO4)(OH)4] oscillates between -4 and 0.8 between 2007 and 2008, when circum-neutral conditions prevail. In 2009, after pH declined to values between 4.8 and 5.9, the SIs increased to supersaturated values (SI ≈1). Starting with the 2011 wet season, the SI of antlerite is supersaturated at the onset of wet season and then decreases to close to equilibrium conditions (-0.5<SI<0.5). A similar trend can be seen for brochantite [Cu4SO4(OH)6] and copper hydroxy-carbonate minerals such as malachite [Cu2CO3(OH)2] and azurite [Cu3(CO3)2(OH)2].   38   Figure 2.6. Equilibrium phases predicted from geochemical modeling of UBC2-3A field barrel  Figure 2.6 shows that jarosite [KFe3+3(OH)6(SO4)2] remained undersaturated during the 2007 and 2008 wet seasons but became supersaturated at the start of the 2009 wet season when pH declined to 5.5. Jarosite remained supersaturated for the rest of the simulation period when pH declined from 4.8 to 2. Ferrihydrite [Fe(OH)3] and gibbsite [Al(OH)3] were mostly undersaturated or close to equilibrium in 2007 and 2008. In 2009, the solution became either close to saturation or supersaturated with respect to these phases and starting in 2010 consistent supersaturated conditions developed and prevailed until the end of the experiment. Speciation simulations also demonstrated that smithsonite [ZnCO3] and rhodochrosite [MnCO3] were undersaturated throughout the simulation period (Figure 2.6). Precipitation and dissolution of  39  secondary minerals were considered to be reversible and their effective rate coefficients were set to achieve quasi-equilibrium conditions (Table 2.8).  2.2.5.2.4 Intra-aqueous and gas exsolution-dissolution reactions  The reaction stoichiometry and equilibrium constants of the oxidation-reduction reactions are summarized in Table 2.5. All relevant complexation and hydrolysis reactions were also considered (not shown) to ensure that mineral solubilities are represented adequately.  2.2.5.3 Initial and Boundary Conditions  The initial chemical composition of pore water and recharge into the field barrel is summarized in Table 2.9. The recharge water and background pore water have pH values of 5.5 and 6, respectively, and are both dilute and in equilibrium with atmospheric O2 and CO2. The composition of the recharge water is representative of rainwater. The concentration of all ions in initial waste rock pore water were assumed to be low because the waste rock was fresh and recently extracted from the mine. The simulation period corresponds to 2200 days (or 6.03 years) after decommissioning of the field barrels, using a maximum time step of one day.  Table 2.9. Chemical composition of recharge water and initial waste rock pore water in the model Component Concentration (mol L-1) Recharge Water Waste Rock pCO2 3.17 X 10-4 3.17 X 10-4 SO42- 1.0 X 10-10 1.0 X 10-10 H4SiO4 1.0 X 10-10 1.0 X 10-10 K+ 1.0 X 10-10 1.0 X 10-10 Mg2+ 1.0 X 10-10 1.0 X 10-10 Ca2+ 1.0 X 10-10 1.0 X 10-10  40  Component Concentration (mol L-1) Recharge Water Waste Rock Zn2+ 1.0 X 10-10 1.0 X 10-10 Pb2+ 1.0 X 10-10 1.0 X 10-10 Cu2+ 1.0 X 10-10 1.0 X 10-10 Mn2+ 1.0 X 10-10 1.0 X 10-10 Na+ 1.0 X 10-10 1.0 X 10-10 Al3+ 1.0 X 10-10 1.0 X 10-10 Cl- 1.0 X 10-10 1.0 X 10-10 pH 5.5 6.0 pO2 (atm) 0.21 0.21 Fe3+ 1.0 X 10-10 1.0 X 10-10 Fe2+ 1.0 X 10-10 1.0 X 10-10 HS- 1.0 X 10-10 1.0 X 10-10  2.3 Results and Discussion 2.3.1 Effective Neutralization Potential and Role of Calcite 2.3.1.1 Calcite Estimated from Bulk NP (0.7 wt%) and Solid Phase Analysis (0.42 wt%) Figure 2.7 shows the results of three simulations compared with the field data. Figure 2.7 and Figure 2.8 demonstrate the dependence of drainage pH on the calcite volume fraction. The predicted pH in “Calcite from NP” and “Calcite from Solid phase” simulations is far from the measured pH. Similarly, the concentration of SO4, Cu, and Zn are underpredicted after 600 days, due to neutral pH prevailing. Ca concentrations are overpredicted for the first 200 days, which is due to presence of excess calcium from calcite, gypsum and wollastonite dissolution. Reactive transport modeling shows that as long as calcite is available for reaction and its dissolution rate exceeds the rate of acid production, pH will remain neutral. These conditions are met for the “Calcite from NP” and “Calcite from Solid phase” simulations (Figure 2.8).  41    42  Figure 2.7. Calcite amount calculated from NP (0.7 wt%), solid phase elemental analysis (0.42 wt%) and calibrated (0.06 wt%). Plots compare the pH, SO4, Cu, Zn and Ca from data and model. The colored squares are the drainage data from field barrel.   Figure 2.8 shows that the simulations based on the “Calcite from NP” and “Calcite from Solid phase” conceptual models overpredict the available NP inferred from field observations. Therefore, in the next simulation the initial amount of calcite was decreased. The scenario “Calcite calibrated” is the simulation in which the volume fraction of calcite is calibrated to better match observed drainage water composition. In this case, the calcite weight fraction was equal to 0.06 wt%, more than an order of magnitude lower than determined via ABA. The initial volume fraction of calcite was determined using sensitivity analysis as described in detail in Section 2.3.1.2. Upon depletion of calcite in the “Calcite calibrated” scenario at 500 days, pH becomes acidic.   In general, the main neutralizing minerals in mine waste rock are considered to be carbonate minerals including calcite, and secondary carbonate minerals such as siderite, smithsonite, malachite, and rhodochrosite (Blowes and Ptacek, 1994). In the process of neutralization of acidity, calcite is the first mineral to become depleted and dolomite-ankerite and siderite deplete later (Blowes and Ptacek, 1994). Siderite dissolution does not produce any net alkalinity, because it is often followed by the oxidation of ferrous iron and ferric iron precipitation (Blowes et al., 2003) (Equation 2-5, Equation 2-6, and Equation 2-7). Siderite was detected in XRD analysis in the field barrels containing intrusive material. Field barrel UBC2-3A however did not have siderite detected.   43    Figure 2.8. Comparison of calcite, gypsum and wollastonite abundance, in the middle of the field barrel (control volume = 50) as a function of time for the three simulations  The assumption in this study, that all carbon measured in the solid phase analysis was inorganic and was present as carbonate in calcite mineral, was based on the fact that siderite was not detected in UBC2-3A field barrel. However, the presence of siderite cannot be ruled out due to sampling variability. The siderite correction was not conducted for the ABA via the Sobek method in this study. Lack of information regarding the presence of siderite might have contributed to the uncertainty in calculating initial calcite volume fractions.  44  𝐹𝑒𝐶𝑂3 + 𝐻+ ↔ 𝐹𝑒2+ + 𝐻𝐶𝑂3−  Equation 2-5 𝐹𝑒2+ +12𝑂2 + 2𝐻+ → 𝐹𝑒3+ + 𝐻2𝑂  Equation 2-6 𝐹𝑒3+ + 3𝐻2𝑂 → 𝐹𝑒(𝑂𝐻)3 + 3𝐻+  Equation 2-7  2.3.1.1.1 Seasonal Influences on Secondary Mineralogy The simulation results suggest that the seasonal variation in the concentration of calcium and sulfate is controlled by precipitation and dissolution of gypsum. During the dry season, gypsum precipitates within the field barrel (Figure 2.9). Gypsum formation occurs due to low water to rock ratio and long residence times. During the wet season, there is continuous supply of fresh low-salinity recharge and residence times are short (Langmuir, 1997), which causes dissolution of gypsum.  Figure 2.9. Left: Precipitation of secondary mineral presumably gypsum in the holes punctured on the walls of field barrel UBC2-3A; Right: precipitation of secondary iron oxyhydroxides and hydroxysulfates close to the bottom of field barrel UBC2-3A (images by E. Skierszkan in May 2016)   45  2.3.1.2 Processes Controlling pH and Metal Attenuation: Calcite Estimated by Calibration (0.06 wt%)  2.3.1.2.1 Assessment of Geochemical Evolution, Long-term Trends and Seasonal Influences The focus of the “Calcite calibrated” simulation was to develop a conceptual model that would reproduce the pH evolution in field barrel drainage observed in the field and determine the effective carbonate neutralization potential. After three years, the concentration of SO4 exceeds Ca-concentrations, indicating the depletion of available calcite; at the same time first signs of the formation of net acidity become visible (Figure 2.5). The concentration of Ca (Figure 2.5) in drainage was at the highest level (16 mmol/L) near the start of data collection at about 100 days and then declined to 4  mmol/L at the end of that wet season, reflecting that calcite dissolution approached completion. The modeling results for the “Calcite calibrated” scenario (Figure 2.10 Right) show that gypsum precipitates in the dry season and re-dissolves in the following wet season for the first three years of the lifetime of the field barrel. The simulation results show dissolution of gypsum, brochantite and antlerite at about 600 days following the pH decrease at the end of second wet season (Figure 2.10 Right). The dissolution of these sulfate-bearing secondary minerals is responsible for the release of the excess SO4 that was observed in the following wet season (Figure 2.5). In the fifth year, Ca-concentrations rise at the onset of wet season, which is attributed to the dissolution of a Ca-bearing primary mineral (likely wollastonite), triggered by pH decreasing to about 4 or dissolution of a secondary phase such as gypsum that has precipitated during the preceding dry season (Figure 2.10 Right).    46    Figure 2.10. Left: pH from data and model for“Calcite calibrated” simulation (0.06 wt%). The colored squares are the drainage data from field barrel. Right: Abundance of calcite and selected secondary minerals (gibbsite, gypsum, ferrihydrite, malachite, brochantite, antlerite, k-jarosite and SiO2 phase), expressed as volume fraction, at the outflow boundary of field barrel as a function of time for “Calcite calibrated” simulation.  Immediately after initiation of the field barrel experiment in 2007-2008, drainage-water pH was slightly alkaline (pH = 8) (Figure 2.10). The pH decreased rapidly from 8 to 6.4 in the middle of the first wet season. Preliminary simulations revealed that CO2 gas does not control pH, therefore, since the annual pH variations in the wet season are not pCO2 related on the field barrel scale, they are likely due to water flowing along various flow path lengths and accessing materials with different acidity/alkalinity. The mixing process within the field barrel can possibly explain the slight fluctuations. The pH stayed at the same level for another wet season from about 470 to 630 days (2008-2009) (Figure 2.5). This constant pH during both wet seasons implies that calcite continued to remain at equilibrium as a pH-neutralizing mineral. Sulfide oxidation processes continued to occur during the dry seasons, prompting continued calcite  47  dissolution and increased Ca concentration. The simulation results (Figure 2.10 Right) demonstrate that at about 1200 days, gypsum dissolves at the start of the wet season, which subsequently results in a decrease of Ca concentrations after the first flush. The simulation results confirm the formation of gypsum as a secondary mineral and its dissolution at the start of each wet season.   In all wet seasons, the pH at the start of wet season is higher than the pH at the end of wet season, which indicates that dissolution of buffering minerals is effective during the preceding dry season. Precipitation of jarosite started following the depletion of carbonate minerals at 600 days and its volume fraction increased with a higher rate when pH decreased to about 2.3. The evolution of the field barrel through time and pH decreasing to below 3 results in precipitation of secondary minerals in the lower section of the field barrel (Figure 2.9).   2.3.1.2.2 Determination of Effective Carbonate NP Comparing the volume fraction of calcite from the “Calcite calibrated” simulation and calcite estimated from bulk NP provides the ratio of available to total NP that is equal to 9% of bulk NP. This result indicates that the bulk NP value measured by unmodified-Sobek method cannot be effectively used for prediction of onset of acidity in intrusive material with low carbonate content. This is due to aggressiveness of Sobek method and release of NP from non-carbonate minerals (Jambor, 2003) such as wollastonite. For such low carbonate content, the contribution of more slowly dissolving and less effective non-carbonate phases towards NP are difficult to identify and quantify. A similar result is obtained for the “Calcite from Solid phase” scenario, which similarly overpredicts the available NP. In this case, the available NP obtained is equal to  48  14 percent of the NP calculated from solid phase composition analysis represented in “Calcite from Solid phase” conceptual model. This finding reveals that, the NP estimated from solid phase composition is also not a conservative estimate for available NP. The excess carbonate content may have been introduced due to siderite, which does not contribute to NP.   2.3.2 Contribution of Wollastonite and Calcite to Neutralization Potential 2.3.2.1 Contribution of Wollastonite The simulation result from the scenario without wollastonite demonstrates that weathering of wollastonite could explain the source of Ca for gypsum precipitation after depletion of calcite. Based on the Jambor et al. (2002) study, wollastonite produces relatively high NP values (>20 kg CaCO3 equivalent per tonne of material), close to carbonates. Most minerals such as pyroxene, amphibole, and feldspar groups, have NP values considerably lower than 20 kg CaCO3 equivalent per tonne of material (Jambor et al., 2002). To test the effect of wollastonite being in equilibrium with UBC2-3A field barrel effluent, geochemical speciation calculations were performed using PHREEQC with the Minteq.v4 database (modified after Fernández-Caliani et al., (2008)). The pH of the solution increased from an initial value of 2.53 to 4.12 and equilibrium speciation predicted supersaturation conditions for secondary minerals including goethite, jarosite and schwertmannite. The saturation indices for ferrihydrite were close to equilibrium. This simulation suggests that wollastonite can buffer the pH of UBC2-3A field barrel drainage values of around 4, but not to values > 6, as for calcite. On the other hand, the result of this simulation does not provide any information on the reaction rate of wollastonite compared to rate of acidity production and over the time of study. A reactive transport simulation is beneficial in this context.  49   To investigate the interaction of the reaction rate of wollastonite and the rate of acid production coupled with flow in mine waste rock, two reactive transport scenarios were set up. The objective of the “without wollastonite” scenario was to determine the influence of wollastonite on drainage chemistry, specifically on pH and concentration of components such as Ca, SO4 and Si over time. In this scenario, the mineral wollastonite was eliminated from the conceptual model. Figure 2.11 shows the pH from two reactive transport simulations, “with wollastonite” and “without wollastonite” compared to observed data.   Figure 2.11. Left: pH trend over time for data and model for simulation with wollastonite mineral “Calcite calibrated” (green line) and without wollastonite mineral “without wollastonite” (blue line); Right: Ca concentration trend over time for data and model for simulation with wollastonite “Calcite calibrated” (green line) and without wollastonite (blue line).  In both scenarios, the first major decrease in pH, at about 500 days (Figure 2.11), corresponds to the depletion of calcite, and the second major decrease, at about 600 days, in the absence of wollastonite (i.e. for the “without wollastonite” scenario), corresponds to depletion of gibbsite  50  (Figure 2.12). Gibbsite dissolution maintains the pH of pore water near 4.0. In the presence of wollastonite (in the “with wollastonite” scenario), gibbsite is supersaturated until 1195 days (Figure 2.10 Right) and pH remains at about 4.0 during that period (Figure 2.11 Left). pH abruptly decreases to about 2.4 upon depletion of gibbsite. Similarly, Fernández-Caliani et al., (2008) reported in an acid-rock drainage, pH = 2.1 context, the incongruent dissolution of wollastonite and leaving a residual amorphous silica-rich phase that preserved the prismatic morphology of the parent wollastonite. More mineralogical analysis is required to document the changes in wollastonite that have occurred in this field barrel. The Ca released into solution from wollastonite weathering results in a gradual pH increase over the next three years and precipitation of gypsum. Fernández-Caliani et al., (2008) also noted the pH increase from 2.1 to 3.5 with subsequent precipitation of gypsum as well as poorly crystallized Fe-Al oxy-hydroxides and oxy-hydroxysulfates whose components were derived from the acid rock drainage solution. In Figure 2.12, there is a clear increasing trend of the secondary SiO2 volume fractions when pH decreases to about 2.4 due to enhanced reaction rates of wollastonite and aluminosilicate minerals including biotite, orthoclase, albite, and muscovite.   In the conceptual model that includes wollastonite (Figure 2.10 Left), the simulation indicates precipitation of gypsum at the column outlet in every dry season and dissolution in the wet season after 1195 days. The precipitation of gypsum was observed in the samples collected from the field barrel in the dry season (Figure 2.9) and resulted in higher concentrations of Ca at the onset of wet season and lower concentrations at the end of wet season. Weathering of wollastonite provides Ca for gypsum precipitation in each dry season in the scenario that included wollastonite (“Calcite calibrated” simulation) in Figure 2.10 (Right). The dissolution of  51  gypsum in each following wet season releases Ca, which is consistent with the observed data (Figure 2.11 Right). Meanwhile, in the “without wollastonite” simulation the Ca concentration decreases to trace levels at 550 days upon depletion of calcite and gypsum and it does not appear to re-precipitate in the following dry seasons (Figure 2.12). The weathering of wollastonite in the “with wollastonite” scenario provides the buffering required to maintain pH at about 4.0, which results in a closer prediction of Ca concentrations in the field barrel drainage. This set of simulations demonstrates that while the fast-reacting minerals such as calcite determine the short-term chemistry, the slow-reacting minerals such as wollastonite affect the long-term chemistry of waste rock drainage.   Figure 2.12. Abundance of calcite and selected secondary minerals (gibbsite, gypsum, malachite, antlerite, k-jarosite and SiO2 phase), expressed as volume fraction, at the outflow boundary of field barrel as a function of time in the “without wollastonite” simulation.   52  2.3.2.2 Contribution of Calcite Based on the result of the previous scenario “without wollastonite”, wollastonite weathering results in buffering at pH about 4 and produces more consistent ion concentrations with the field data, therefore, the wollastonite mineral was re-introduced to the conceptual model. On the other hand, calcite was not detected in XRD and in the “Calcite calibrated” scenario, the volume fraction of calcite was estimated to be as low as 0.06 wt%. As a result, in the next scenario “without calcite”, the calcite was eliminated from the conceptual model to assess the sensitivity of the results towards the presence of calcite at trace concentrations. The objective of this scenario was to evaluate whether wollastonite could be the sole source of neutralization potential in this field barrel in case calcite was present in trace amounts or was unavailable for reaction, due to formation of secondary coatings and passivation.   The results demonstrate the sensitivity of pH and Ca concentration in the field barrel drainage to the calcite content. Figure 2.13 (Left) shows that in absence of calcite (“without calcite” scenario), pH decreases to about 2.4 from the start of the simulation, which is inconsistent with the field observations that demonstrate pH levels between 6 and 8 until depletion of calcite at 600 days. In this scenario, wollastonite weathering increases the pH and maintains it at about 4 after 1500 days. This late buffering of wollastonite occurs due to the fact that, the ability of the mineral wollastonite to buffer the pH highly depends on the ratio of the wollastonite dissolution rate to the sulfide mineral oxidation rate at pH<4.   53   Figure 2.13. Left: pH trend over time for data and model for simulation with wollastonite and calcite minerals “Calcite calibrated” scenario (green line) and with wollastonite and without calcite minerals “without calcite” scenario (blue line). Right: Ca concentration versus time for data and model for simulations with wollastonite and calcite minerals “Calcite calibrated” (green line) and with wollastonite and without calcite minerals “without calcite” (blue line).  The dissolution rate of sulfide minerals decrease over time (results not shown here). At 1500 days, the overall weathering rate of sulfide minerals becomes sufficiently low so that wollastonite weathering can more effectively buffer pH. Figure 2.13 (right) shows that in the absence of calcite, predicted Ca concentrations in the first wet season, between 100 and 200 days, are lower than observed data, and the conceptual model that includes calcite (“Calcite calibrated”), is in better agreement with the measured Ca concentration for the first wet season. However, the magnitude of the predicted Ca peak is higher than observed data between 300 and 500 days, which is due to gypsum dissolution Figure 2.10, Right).   The prediction of Cu concentration in the effluent solution substantially affected by elimination of calcite from the conceptual model as a primary mineral (Figure 2.14 Right). In the “without  54  calcite” conceptual model, the predicted Cu concentration more strongly deviates from measured copper concentrations. This discrepancy indicates that the simulation does not predict the retention of copper until about 1500 days, as occurring in the field barrel. The Cu concentration is too high especially at the onset of wet season from start of simulation until about 1500 days. Furthermore, the simulation predicts that in the absence of calcite, malachite, the secondary carbonate minerals that Cu is mostly associated with, does not precipitate (Figure 2.14 Left). This is in contrast with the results from the conceptual model that included calcite, “Calcite calibrated”, (Figure 2.10 right) which indicated precipitation of malachite until 600 days. However, even in the “Calcite calibrated” conceptual model there is excess copper released, from 600 days following the dissolution of malachite to 1500 days, in comparison to observed data (Figure 2.14 Right). The Cu hydroxy-sulfate minerals antlerite and brochantite also dissolve at 600 days (Figure 2.12). Data from the field experiment show increasing copper concentrations only after 1500 days. This behavior points towards the precipitation of another secondary mineral in the field barrel in addition to malachite that retains copper until 1500 days and releases the copper when pH decreases to below 4 after 1500 days. Peterson (2014) observed formation of a predominantly amorphous precipitate in the same intrusive material contained in this field barrel in Pile 2 during the transition from neutral to acidic condition.   55   Figure 2.14. Left: Abundance of selected secondary minerals (gibbsite, gypsum, malachite, antlerite, k-jarosite and SiO2 phase), expressed as volume fraction, at the outflow boundary of field barrel as a function of time in “without calcite” conceptual model; Right: Cu concentration versus time for data and model for simulation with wollastonite and calcite minerals “Calcite calibrated” (green line) and with wollastonite and without calcite minerals “without calcite” (blue line)  Synchrotron analysis (Peterson, 2014) suggested that copper in this precipitate is mostly associated amorphously with sulfate, and to a lesser degree with the crystalline carbonates malachite and azurite. The properties of this secondary amorphous precipitate does not have a known structure and therefore it was not included in the conceptual model and the reactive transport simulations. Including such an amorphous phase may improve the agreement of model and observed data, particularly for Cu concentrations. The simulation results suggest that wollastonite cannot be the only mineral that provides neutralization potential in this field barrel and although calcite was not observed during mineralogical analyses, observational and modeling results of drainage water composition provide string evidence of its presence in this material type, albeit at low concentrations.  56  2.3.3 Uncertainties and limiting factors As seen in the “Calcite calibrated” simulation, the pH trend captured by the model is lower than the observed values in the field between 700 and 1700 days. This results in an overestimation of the concentrations of the components of interest during that period. There are several potential causes for this discrepancy including uncertainties in the effluent volume measurement in the field throughout the experiment. This uncertainty in the drainage volume measurement is higher between 700-1700 days due to lower frequency of data collection at the mine site. It is also challenging to calibrate weathering rates to match field conditions. For example, reactive surface areas are difficult to characterize. In addition, although material properties were assumed homogeneous, natural waste rock is physically and chemically heterogeneous. In addition, there are uncertainties regarding the role of physical and chemical heterogeneity of the waste rock material. In addition, the current solution is likely a non-unique representation of this problem. We investigated various plausible scenarios, and calibrated them to observations of several outflow parameters. We believe that the calibrated parameters provide a good description of the modeled system.  2.4 Summary and Conclusion The purpose of the current study was to evaluate conceptual models that adequately describe transition of pH from neutral to acidic conditions and how secondary minerals and silicate minerals buffer acidity in a low carbonate waste rock environment at the field barrel scale. The results of a separate mineralogical study (Peterson, 2014) provided constraints on the minerals included in the model. The six-year evolution of drainage quality from the field barrel is complex and is affected by precipitation and dissolution of various secondary minerals and the  57  enhancement of sulfide weathering rates with declining pH. A representative conceptual model that adequately approximates the field-observed pH and the concentration of sulfate, calcium, copper and zinc requires inclusion of calcite and wollastonite dissolution and precipitation/dissolution of secondary minerals gibbsite, malachite, ferrihydrite, smithsonite, antlerite, brochantite and gypsum. The simulation results indicate that secondary mineral precipitation and dissolution controls the release of components such as sulfate, copper, zinc and calcium to the effluent solution and implies that the estimation of weathering rates cannot be directly derived from drainage chemistry.  In field barrel UBC2-3A, the observed pH and relatively high solute concentrations compared to other field barrels containing intrusive material, demonstrating that the effective reaction rates of acid generating minerals, especially pyrite, did not decrease due to passivation throughout the six years of study. In fact, obtaining improved fits with observational data required to include biotic sulfide oxidation rates that increase under acidic pH-conditions. Therefore, using the shrinking core model was not required during the first six years of lifetime of this high sulfide low carbonate field barrel with fast transition from neutral to acidic conditions. Reactive transport modeling results suggest the occurrence of seasonal formation and dissolution of gypsum in the field barrel. The simulation results suggest that the annual seasonal variation in concentrations of calcium and sulfate can be explained by precipitation and dissolution of gypsum. In the dry season, gypsum precipitates within the field barrel. In the wet season, abundant supply of low-salinity recharge results in dissolution of gypsum.    58  The last two simulations illustrate the role of calcite dissolution for acid neutralization at pH-values around 6.3 and the role of wollastonite in buffering at pH 4. The simulation results based on the conceptual model including calcite estimated from bulk NP yielded neutral-pH conditions for the entire duration of the field experiment, which was inconsistent with field observations. This finding indicates that bulk NP determined from ABA is not a good representation for the effective neutralization potential in this rock type and substantially overestimates the available NP under field conditions. Similar simulation results were obtained by estimating the calcite volume fraction using calcium and carbon from solid phase elemental analysis. The conceptual model without wollastonite shows that wollastonite weathering provides calcium for gypsum precipitation after the depletion of calcite. Furthermore, this conceptual model suggested that within this intrusive material, wollastonite contributes to pH buffering at pH values around 4. In addition, the incongruent dissolution of wollastonite was not considered in the model, which might affect the release rate of calcium to the effluent solution. The final two simulations, based on the elimination of wollastonite and calcite from the conceptual model, confirm that although dissolution of wollastonite can neutralize acidity, its rate of dissolution and consequent acid neutralization is slow compared to carbonate minerals in this rock type. Furthermore, wollastonite is not the sole source of NP in the intrusive waste rock, and despite the fact that calcite was not detected in XRD, its presence is required to maintain pH above 6.3.   It is also important to point out that some of the high concentration in drainage at the start of annual wet season at 1530 and 1925 days, exhibit a single elevated concentration, and are represented by a single data point. Increasing sampling frequency throughout the wet season, especially at the onset of wet season, for the field barrels that have exhibited rapid pH transition  59  from neutral to acidic conditions would benefit the development of an improved understanding of metal accumulation and release in such experiments.     60  Chapter  3: Evaluating preferential flow in an experimental waste rock pile using unsaturated flow and solute transport modeling  3.1 Introduction For waste-rock piles containing reactive minerals, the quality of discharge is affected by a combination of geochemical and hydrologic processes. To better characterize and monitor metal release and attenuation, it is essential to investigate and determine the controlling flow and solute transport processes. Particularly important, is the partitioning between relatively slow matrix flow and relatively fast preferential flow (Nichol et al., 2005). The geological characteristics of ore deposits, mine extraction methods, and the approach for construction (e.g. end dumping), provide key controls on the hydrologic characteristics of a waste-rock pile. The parameters that are predominant in controlling the hydrologic properties of waste-rock piles are (Smith and Beckie, 2003): (1) the particle size distribution of the material, and (2) the proportion and spatial arrangement of matrix-supported and matrix-free zones that are created during dump construction.   To investigate fluid flow through waste rock, it is useful to distinguish between “soil-like” and “rock-like” behavior. Based on a study by Dawson et al. (1998), infiltration behavior depends on the sand-size content (<2mm diameter) of the waste material. A sand-size content of about 20% has been used to define a boundary between soil-like and rock-like behavior. In a soil-like waste-rock pile, the hydraulic properties of the porous medium are controlled by the finer-grained particles, i.e. the matrix, while in rock-like material, point-to-point contacts between coarse rock  61  fragments take on a greater role in determining the fluid flow behavior (Smith and Beckie, 2003).   Hydraulic conductivity and soil-water characteristic curves depend on particle size distribution and porosity. Water retention generally increases as particle size and porosity decrease (Aubertin et al., 2003). Saturated hydraulic conductivity (Ks) tends to increase with the average size of the particles (Mbonimpa, M et al., 2002). This trend may be offset by a decrease in porosity, which can occur when the proportion of coarse particles is high enough (Fala et al., 2005). Although fine-grained waste-rock has a significant impact on the bulk hydraulic conductivity and moisture content of a pile, the particle size distribution cannot be considered in isolation from the role played by the heterogeneous structure created during construction of the pile such as coarse rubble zones at the base of the pile, or the presence of large rock fragments (Smith and Beckie, 2003). During high rainfall events, these structures may locally focus flow such that water can enter into coarse-grained zones which then form preferential flow paths(e.g. Pruess, K., 1999). The consequence of preferential flow is that a portion of the infiltrating water moves at rates that are significantly faster than the rest of the infiltrating water. With the occurrence of preferential flow, solutes can reach a given depth in less time than predicted by calculations assuming a uniform wetting front. The particle size and structural characteristics of a waste rock pile also influence the ingress of oxygen into a pile. The rate at which oxygen is re-supplied (by diffusive or advective transfer) is a controlling factor in determining the sites and rates of sulfide oxidation. Together, these processes provide fundamental controls for sulfide mineral weathering and metal release from mine waste rock (Smith and Beckie, 2003).    62  These complexities make it difficult to assess fluid flow and reactive transport processes in waste rock in a quantitative fashion, and lead to challenges when predicting long-term weathering and metal release. Despite these difficulties, several studies have been conducted to investigate unsaturated flow processes in mine waste rock (e.g.: Fala et al., 2005). In addition, flow and reactive transport simulations were carried out to investigate the nature of interactions between flow, solute transport, and geochemical reactions, and the effect of these processes on sulfide mineral oxidation and drainage water quality. For example, Lefebvre et al., 2001a, 2001b evaluated the role of oxygen ingress and heat generation on sulphide mineral weathering in waste rock piles. Linklater et al. (2005) conducted a modeling study using the SULFIDOX code at the Aitik mine site in Sweden to investigate the coupling between transport processes and weathering reactions. Molson et al., (2005) investigated the role of capillary barrier effects on sulfide oxidation and metal transport in mine waste rock. However, most previous efforts did not address the role of matrix and preferential flow on basal discharge and water quality.  The objective of this paper is to investigate the behavior of water flow within an experimental waste rock pile composed of relatively fine-grained materials and to identify whether fast flow pathways are of importance in this pile. We use a model based on the well-established matrix-flow formulation described by Richards equation to simulate flow and transport observations collected in the field experiment. The extent of preferential flow can be assessed by comparing the flow and tracer dynamics produced by the matrix-flow model with observations from the field.  Discrepancies between simulations and observations will be used to refine the conceptual understanding of the pile hydrology in fine-grained waste rock.    63  3.2 Pile 2 Experiment Pile 2 is one of five 36 m (L) x 36 m (W) x 10 m tall instrumented test piles constructed at the Antamina Mine in Peru and designed to study the physical and chemical processes controlling drainage and mass loadings from mine waste rock (see Hirsche et al., 2012 for a project overview). Approximately 20,000-25,000 tonnes of waste rock were placed in each pile by end dumping in three tipping phases (Bay et al., 2009; Hirsche et al., 2012). Pile 2 is composed of a relatively fine-grained intrusive waste rock material in which matrix flow is hypothesized to dominate.  All drainage from the pile is captured by basal lysimeters and conveyed to tipping bucket flow meters which continuously monitor flow rates.   To gain insight into transport processes, a conservative bromide tracer was applied to the crown (flat surface at the top) of each test pile (Blackmore et al., 2012). The concentration of applied tracer was 1895 mg/L of bromide (Peterson, 2014). Bromide tracer was applied using a sprinkler system on Pile 2 on January 20, 2010 for 4.5 hours at a rate of 6 mm/hr, corresponding to a five-year rainfall precipitation event at the Antamina Mine site. Tracer samples were collected from pile outflow at time intervals that varied from 15 minutes (immediately following tracer application) to weekly. The sprinkler system was adjusted to obtain uniform distribution of tracer on the surface of the pile confirmed by the monitoring results of measuring cups placed at regular intervals on the crown throughout tracer application (Peterson, 2014). Surface run off was not observed during the time of tracer application; although some ponding could be seen, especially close to the berm. Ponded water subsequently infiltrated into the pile (Peterson, personal communication).   64  3.3 Conceptual Model   Considering the fine-grained nature of the waste-rock (Peterson et al., 2012), Pile 2 is conceived to consist of a homogeneous fine-grained matrix material in which unsaturated flow can be represented by a single characteristic curve in a Richards equation-based model. This simple approach was adopted here to specifically focus on testing the hypothesis of matrix-dominated flow behaviour in Pile 2. Agreement between simulation and field results for outflow and tracer arrival times would illustrate that this conceptual model is a reasonable representation for the hydrologic response of the pile. Homogeneity is a pragmatic initial choice that can be relaxed if supported by an examination of model residuals. To simplify the initial analysis, the truncated-pyramid geometry of the pile (Figure 1a) is represented as an area-weighted composite of five, one-dimensional columns (Figure 1 b).  The total surface area of the 10 – m high pile is subdivided into five elevation intervals (Figure 1a). The surface area falling within each elevation interval is assigned to the one-dimensional column of the corresponding height (Figure 1 b). Flow is independently simulated in each one-dimensional column, and then the area-weighted composite is formed to determine the total pile outflow. This approach considerably simplifies the simulations but restricts the model to consideration of one-dimensional vertical flow. Unsaturated flow and tracer transport is simulated with the flow and reactive transport computer code MIN3P (Mayer et al., 2002b).    65        Figure 3.1. a) Conceptual depiction of pile geometry and simulation approach, Ai corresponds to exposed area of each level; b) Cross section containing five soil profiles 2-10m, each profile represents one level of the pile.  3.4 Field and Model Parameters Particle size analysis was performed for each tipping phase in Pile 2 (see Peterson et al., 2012 for particle size distributions (PSDs)). Although the results show variability between different tipping phases, the average particle size is relatively fine-grained with an average D20 of 1mm (i.e., 20% of the material is finer than 1mm). The average pile porosity (ϕ) was determined based on porosity measurements in field cell samples (Speidel, 2011). In absence of direct measurements, residual saturation (Sr) and the soil hydraulic function parameters α and n for the van Genuchten model (Wösten and Van Genuchten, 1988) were estimated from soil water characteristic curves calculated using the SoilVision program (see Blackmore et al., 2012, Table 1). Saturated hydraulic conductivity was measured at the surface of pile 2, using fixed ring infiltrometer tests (Blackmore, 2015, Table 1).   The heights of the one-dimensional solution domains ranged from 2 m to 10 m – allowing a representation of the slopes and the crown of the pile (Figure 1). Each column was discretized  66  into uniform cells of 5 cm length in vertical direction. A fixed water table was assigned at the base of the pile.  The initial condition was set to a hydraulic head of -10m relative to the bottom of the pile, extending from the base to the top of each column, and representing relatively dry initial conditions.  Simulations were run over a time period of 4 years with a maximum time step of 0.01 days.  The physical parameters used in the model simulations are summarized in Table 1.  Table 3.1. Table 3.2. Physical input parameters for unsaturated flow and tracer test Parameter Symbol Unit Value Reference Dimension of solution domain  (composite model) Lz m 10, 8, 6, 4, 2  model parameter Porosity ϕ - 0.34 Speidel (2011) Residual saturation Sr - 0.36 Speidel (2011) Recharge rate qr m/s transient Calibrated, as a fraction of precipitation data Hydraulic conductivity Kzz m/s 1.3410-5 Based on ring-infiltrometer data (Blackmore, 2015), calibrated Van Genuchten soil  hydraulic function parameters α m-1 7 Speidel (2011) n - 1.65 Speidel (2011) Initial Br-1 concentration C0 Mg/L 1895  Tracer release time t C0 day 907  Free phase diffusion  coefficient in aqueous phase Da m2/s 2.410-9 Molson et al., (2008) Longitudinal dispersivity αl m 0.2 estimated  For tracer test simulations, bromide tracer (1895 mg/L) was applied to the surface of the 10m column only, to mimic the field tracer application to the crown of the pile on January 24, 2010  67  for 4.5 hours. At the time of tracer release, the water content in the pile and the outflow rate were representative for typical wet season conditions.  3.5 Modeling Approach Recharge was assigned as a fraction of daily precipitation measured at the UBC weather station located in close proximity to Pile 2.  For the initial simulations, evaporation was used as the sole calibration parameter in an attempt to match observed cumulative discharge at the base of the pile and the observed outflow hydrograph. Specific calibration targets included the matching of peak flows during the wet season, and draindown during the dry season. The pile was modeled as spatially uniform porous media, with soil-water characteristic functions that did not vary with location. The saturated hydraulic conductivity obtained from fixed ring infiltrometer tests on the compacted crown of the pile was initially used for the simulations. This value likely underestimates the whole - pile hydraulic conductivity substantially, since the pile surface is the most compacted and contains significantly more fine-grained material than the majority of the pile (Singurindy et al., 2012; Smith and Beckie, 2003).  In a second set of simulations, it was explored whether the model fit could be improved by including the saturated hydraulic conductivity in the calibration process. The resulting parameters that provided the best fit to flow data were then used to simulate the tracer test without any further model adjustments.     3.6 Results and Discussion 3.6.1 Hydrologic response and cumulative outflow Figure 2a presents the field-observed cumulative outflow for the basal lysimeter for a time period of four years (August 2007-August 2011). Observed cumulative outflow shows a strong seasonal  68  pattern with high discharge during the wet season and much reduced discharge during the dry season. This response is also clearly visible in the observed hydrograph (Figure 2b), which reveals a relatively rapid response of pile outflow to precipitation events.  In the wet season, maximum discharge exceeds 7 L/min, while flows are reduced to less than 1 L/min during the dry season.   Data collection for Pile 2 outflow started 380 days from the start of pile construction and the initial phase of wetting-up during construction and immediately after completion could not be captured. In contrast, the model simulations were initiated at the beginning of pile construction. This was necessary to capture the wetting up of the pile in the model runs, a prerequisite to reproduce the hydrologic response of the pile in Years 2-4 of the simulation period. To allow a comparison between observed and simulated data, the simulated cumulative outflow had to be corrected by subtracting predicted outflow at T = 380 days (Figure 2a). To ensure transparency of this approach, simulation results for the uncorrected and corrected cumulative outflow curves are presented in Figure 2a.   A best fit between observed and simulated cumulative outflow (Figure 2a) could be obtained by setting the fraction of daily precipitation that enters as recharge to 0.65 during the wet season and 0.1 during the dry season. This implies that 52% of precipitation ends up as recharge over the simulation period. Using this recharge pattern an excellent agreement could be obtained for the first two “water years” with observational data (8/2008-7/2009 and 8/2009-7/2010). Between 8/2008 and 7/2009, the total discharge into the basal lysimeter was approximately 1050 m3 for observed and simulated data. In the subsequent year 950 m3were released from the bottom of the  69  pile. In the following water year (8/2010-7/2011), substantial differences can be observed between observed and cumulative outflows. Observations suggest that the cumulative outflow was reduced to approximately 800 m3, while simulations using the same parameters as for the previous water years suggest an outflow of >1000m3. These differences can be explained by the clogging of the collection system due to precipitate formation (see Peterson et al., 2012 for details), which led to an intermittent shutdown of drainage water collection in the beginning of 2011 (Figure 2b) and likely caused a reduction of flow prior to the complete sealing of the lysimeter drainage pipes. Flow resumed to normal levels after the pipes were cleaned (Figure 2b); however, these interruptions do not allow one to close the water mass balance for this year.    Although the cumulative discharge is well matched with this simulation, the model was not able to reproduce basal discharge patterns (Figure 2b), yielding a delayed response, lower peak flows (Figure 2b) and lower cumulative flows (Figure 2a) than observed during the wet season. For the dry season, the model predicts a slower drain down and more sustained flows than indicated by observations (Figure 2a, b). This behaviour can be attributed to preferential flow; however, it may also be due to an underestimation of the representative saturated hydraulic conductivity used in the simulations. It is well known that the process of end-dumping leads to a gradation of grain size with depth, with the coarsest material accumulating near the bottom of the pile, while the most fine-grained material is retained near the pile surface (Smith and Beckie, 2003). In addition, compaction occurs due to track traffic at the pile surface during the process of end-dumping. Together, these processes result in the lowest hydraulic conductivities near the surface of the pile, which are captured by the ring infiltrometer measurements. In the absence of measured hydraulic conductivity within the pile, it makes sense to recalibrate the model with a  70  higher uniform hydraulic conductivity, before invoking a more complex model that accounts for a gradation of hydraulic conductivity with depth, or matrix and preferential flow.     71   Figure 3.2. Observed and simulated response to precipitation events for base case simulation (K = 1.34 x 10-5 m/s) a) Cumulative discharge b) Outflow hydrograph and precipitation.   72   Figure 3.3. Observed and simulated response to precipitation events calibrated saturated hydraulic conductivities a) Cumulative discharge b) Outflow hydrograph and precipitation.  Figure 3 presents results from the recalibrated model for a range of uniform saturated hydraulic conductivities that are 10, 50 and 100 times higher than the saturated hydraulic conductivity measured using ring infiltrometry. All simulations provide a significant improvement of the model fit in comparison to the base case simulation (Figure 2). Despite the apparent simplicity of the model, a nearly perfect match is obtained for cumulative discharge during the first two water years (Figure 3a). The onset of pile outflow in response to the wet season now closely matches observations (Figure 3b). Although the model seems to slightly underpredict peak flows, it is able to capture short term fluctuations in pile discharge in response to very wet and dry periods. The model is also able to closely match the observed draindown during the dry season. These  73  results are encouraging, and at first sight suggest that matrix flow dominates the hydrogeologic behaviour of this waste rock pile.        3.6.2 Tracer test and solute transport modeling Figure 4 illustrates the field-observed and simulated tracer breakthrough at the base of pile 2, together with the observed and simulated hydrograph for the simulations with Ks = 6.7 x 10-4 m/s. The time of tracer application is indicated by an arrow. Tracer data between February 27th and April 9th 2010 was not collected and it was linearly interpolated between the two end points.   Figure 3.4. Field-observed and simulated tracer breakthrough at the base of pile 2, depicted with observed and simulated hydrograph    74  Breakthrough of bromide at the base of the pile was observed 1.5 months following tracer application, with sustained concentrations in the following time period. Despite the good fit between observations and simulations for the hydrologic response of the pile, the model was not able to predict this breakthrough. This discrepancy indicates that preferential flow does occur in this waste rock pile, despite its fine-grained nature. Although tracer concentrations remained below 5 mg/L, about 12% of the applied bromide was recovered at the base of the pile after 10 months. In contrast, it takes more than one year for the tracer to arrive at the base in the model simulations that do not include preferential flow. Tracer breakthrough may also be affected by an uneven distribution of recharge across the top of the pile, which is not captured by the model. The redistribution of precipitation on the crown of the pile has been observed during heavy rain events, leading to local ponding on the pile surface and areas of enhanced recharge. This complexity is not captured by the model.   3.7 Conclusions and Outlook Numerical modeling of flow and solute transport allows investigation of fluid flow patterns that govern drainage quantity from waste rock piles and affect water quality and mass loadings. In this paper, we used a simple 1D-composite model with only two spatially uniform calibration parameters (recharge and saturated hydraulic conductivity) to simulate discharge for a time period of four years and the response to a tracer test.  The model was able to closely match cumulative discharge and the response of the hydrograph to wet and dry seasons and allowed us to distinguish distinct infiltration rates in the wet and dry seasons. However, the uniform flow and transport model failed to adequately reproduce the response to a tracer test, providing a strong indication for the occurrence of preferential flow in this waste rock pile, despite its soil- 75  like nature. The key information gained from this exercise is that matching the outflow hydrograph and cumulative discharge alone is insufficient to characterize solute transport and residence times in this waste rock pile. This is in accord with results from subsurface hydrology, where it is known that tracer data provide complementary information not present in flow data (Harvey and Gorelick, 1995). Our finding has implications for prediction of metal release and attenuation processes within waste rock and provides the motivation for the development of a model that accounts for matrix and preferential flow.      The findings from Chapters 2 and 3 demonstrate the strong role of preferential flow even in a soil-like waste rock pile on the field barrel scale and the pile scale, respectively. To fully investigate the geochemical evolution within the pile, a model is required that can simulate the reactive transport in a preferential flow dominated porous media. Such a code did not exist, therefore, the MIN3P-THCm-DP model was developed based on the existing MIN3P code. Details of the model development and verification are provide in the next chapter (Chapter 4).        76  Chapter  4:  Implementation and verification of mobile-immobile, dual-porosity and dual-permeability models in MIN3P to simulate flow and solute transport in the vadose zone  4.1 Introduction  4.1.1 Background and Concepts An important aspect in the study of variably saturated soils is the estimation of water and solute travel time. In homogeneous soils, flow and solute transport tends to be uniform, resulting in stable moisture infiltration fronts. However, observations at field sites demonstrate that water infiltration and solute transport fronts are not uniform, but rather travel with different velocities through various parts of the soil. These processes cannot be described by classical models of uniform flow and solute transport (Hendrickx, 2001; Köhne et al., 2006; Pot et al., 2005). Unstable or preferential flow often occurs in soils with a significant fraction of coarse-grained material (Dekker and Ritsema, 1996; Heijs et al., 1996).  Tracer tests are one of the methods that can provide evidence for such phenomena (Hsieh et al., 2001). Non-equilibrium preferential flow is important in various fields such as hydrogeology, hydrology, petroleum engineering and waste disposal site construction (Köhne et al., 2009). For example, at the Exploratory Studies Facility at Yucca Mountain, Nevada, water with an elevated chlorine-36 signature (i.e. water less than 50 years old) was detected several hundred meters below the surface (Fabryka-Martin et al., 1998). It would take hundreds to thousands of years for water to reach that depth based on a standard uniform flow model in a homogeneous medium,  77  providing clear evidence of preferential flow at this site. Other examples include long tails resulting from the slow-release of organic material from soils composed of fine-grained and coarse-grained layers containing lignite,  as well as remediation of contaminants at former military and industrial sites, where transport takes place through layers with different hydraulic and chemical properties (Köhne et al., 2009).  4.2 The mobile-immobile and dual-porosity concept The dual-porosity concept for porous media was first suggested for the investigation of fractured rocks in petroleum reservoirs (Barenblatt et al., 1960; Bibby, 1981; Duguid and Lee, 1977) and was later adopted for describing solute transport in mobile and immobile pore regions of structured soils.   The assumption in dual-porosity models is that water flow is restricted to preferential-flow regions (also called fractures, mobile region, or inter-aggregate pores) and immobile water present in the matrix region (also called immobile region or intra-aggregate pores). These two-region type flow and transport models have water partitioned between mobile (θmo) and immobile (θim) pore regions (θ = θmo+ θim) (Simunek and van Genuchten, 2008).   In this method, a set of coupled water flow and solute transport equations based on Richards equation is used, one equation describing flow in the mobile (preferential flow) region and the second equation accounting for the mass balance in the immobile (matrix) region. The main difference between mobile-immobile and dual-porosity models is that the mobile-immobile model does not consider water exchange between the two regions but does allow the exchange of  78  solute. The flow equations for the dual-porosity model can be described by the following equations (The following equations are developed as one-dimensional for the purpose of simplicity):  𝜕𝜃𝑚𝑜(𝜓𝑚𝑜)𝜕𝑡=𝜕𝜕𝑧(𝐾(𝜓𝑚𝑜) [𝜕𝜓𝑚𝑜𝜕𝑧+ 1]) − Γ𝑤 − 𝑆𝑚𝑜(𝜓𝑚𝑜) Equation 4-1  𝜕𝜃𝑖𝑚(𝜓𝑖𝑚)𝜕𝑡= Γ𝑤 − 𝑆𝑖𝑚(𝜓𝑖𝑚) Equation 4-2  where 𝜃𝑚𝑜(𝜓𝑚𝑜) is the water content in the mobile pore region as a function of pressure head 𝜓𝑚𝑜 in the mobile pore region, 𝑡 is time, 𝑧 is elevation, and 𝐾(𝜓𝑚𝑜) is the hydraulic conductivity as a function of pressure head in the mobile region. The water content in the mobile pore region is defined by 𝜃𝑖𝑚(𝜓𝑖𝑚) as a function of pressure head 𝜓𝑖𝑚 in the immobile pore region. 𝑆𝑖𝑚 and 𝑆𝑚𝑜 are sink terms for the immobile and mobile pore regions [T-1], respectively. Γ𝑤 is the water transfer rate between the two pore domains [T-1] with two different common formulations. In the first formulation, the water transfer rate is proportional to the effective saturation of mobile and immobile pore regions using a first-order mass transfer equation (Simunek et al., 2003):    Γ𝑤 =𝜕𝜃𝑖𝑚𝜕𝑡= 𝜔(𝑆𝑒𝑚𝑜 − 𝑆𝑒𝑖𝑚) Equation 4-3   79  where 𝜔 is a first-order rate coefficient [T-1], and 𝑆𝑒𝑚𝑜and 𝑆𝑒𝑖𝑚 are the effective saturations of mobile and immobile pore regions, respectively. This formulation for Γ𝑤 does not require a water retention function for the immobile (matrix) region and only requires the knowledge of residual and effective saturation of the immobile pore region. The second formulation for Γ𝑤 is based on the difference in pressure heads in the mobile and immobile pore regions (Gerke and van Genuchten, 1993a).   The dominant concept underlying “physically based” hydrological flow models in the vadose zone is the Darcy-Richards equation. The Darcy-Richards equation holds at larger scales of application and the parameter values are constant in time and space for a given soil horizon. However, field tracer tests show that the Darcy-Richards approach fails to explain some of the observed phenomena (Beven and Germann, 2013). In spite of these shortcomings, the Darcy-Richards equation remains popular because: (1) it provides a practical foundation to describe flow processes in partially saturated media, and (2) with modification, it allows for preferential-flow processes to be taken into account (Beven and Germann, 2013).  When applying the Richards equation, one has to be aware that although the equation might be valid at the experimental scale, it might not be valid under field conditions, particularly if the soil is heterogeneous and fluxes are subject to preferential flow effects. The main assumption when applying the Richards equation is that the soil is homogeneous at the resolution of the simulation grid-blocks (Beven and Germann, 2013). As a result, some authors (e.g. Beven and Germann, 2013) have suggested that the Richards approach for field conditions should not be considered physically based, but instead should be considered as a convenient conceptual approximation.  80   Extensions of the Darcy-Richards and solute transport equations accounting for non-uniform flow and transport processes in heterogeneous soils include various dual-domain approaches (Simunek and van Genuchten, 2008), describing the effects of non-ideal flow behavior. Common approaches include dual-porosity and dual-permeability (Simunek and van Genuchten, 2008). In these approaches, the effect of soil heterogeneity is captured by two co-existing continua, accounting for regions of preferential flow, matrix flow, and/or immobile regions.  A crucial component in dual-domain models is the mass-transfer term governing the exchange of water between the two co-existing sub-domains. Several empirical and semi-empirical expressions are used to represent mass transfer in current models. Generally speaking, water communication between the two flow domains is a transient, nonlinear process (Vogel et al., 2010).  Among the approaches suggested for the mass-transfer term, Gerke and van Genuchten (1993) have presented a first-order algebraic approximation of the inter-domain transfer (e.g. Gerke and van Genuchten, 1993b, 1996), which is still considered a reasonably adequate and computationally highly efficient method as it: (1) is independent from micro-scale geometry, (2) limits model parameters in both domains to a reasonable number, (3) and has been verified extensively. This approach has been used in codes such as HYDRUS (Simunek and van Genuchten, 2008; Simunek et al., 2012).    81  The saturation-based formulation results in fewer parameters in the dual-porosity model. By setting the residual saturation of the mobile region to zero, the number of parameters is reduced by one and drops to an even lower number. The saturation-based formulation considers the same retention properties for both regions and has to be used with caution (Simunek et al., 2003). The pressure head-based formulation provides a more realistic approach to the water transfer rate between the two pore regions (Gerke and van Genuchten, 1993a)The formulation for this approach is similar to the one used in dual-permeability models and is described in more detail when introducing the dual-permeability formulation below. For the mobile-immobile formulation, the water transfer rate is set to zero, implying that water flow is restricted to the mobile region only and that saturation remains constant in the immobile region.  The governing equations for solute transport in dual-porosity media are defined by the following equations:   𝜕𝜃𝑚𝑜𝑐𝑚𝑜𝜕𝑡=𝜕𝜕𝑧(𝜃𝑚𝑜𝐷𝑚𝑜𝜕𝑐𝑚𝑜𝜕𝑧) −𝜕𝑞𝑚𝑜𝑐𝑚𝑜𝜕𝑧− 𝜙𝑚𝑜 − Γ𝑠 Equation 4-4  𝜕𝜃𝑖𝑚𝑐𝑖𝑚𝜕𝑡= −𝜙𝑖𝑚 + Γ𝑠 Equation 4-5  Γ𝑠 = 𝜔𝑚𝑖𝑚(𝑐𝑚𝑜 − 𝑐𝑖𝑚) + Γ𝑤𝑐∗ Equation 4-6  where 𝑐𝑚𝑜 and 𝑐𝑖𝑚 are concentrations of solute [ML-3] in mobile and immobile pore regions, respectively. 𝐷𝑚𝑜 is the dispersion coefficient in the mobile region [L2T-1] and 𝑞𝑚𝑜 is the water  82  flux in mobile pore region [LT-1].  𝜙𝑚𝑜 and 𝜙𝑖𝑚 are the sink-source terms for both regions. Γ𝑠 is the mass transfer term [ML-3T-1] between mobile and immobile pore regions composed of the sum of an apparent first-order advective mass transfer term and a diffusive mass transfer term. 𝜔𝑚𝑖𝑚 is the mass transfer coefficient [T-1] for diffusive mass exchange. Equations 4-4 and 4-5 describe the solute transport in mobile and immobile pore regions, respectively. Equation 4-6 defines the mass transfer rate between mobile and immobile domains. In terms of solute transport, the major difference between mobile-immobile and dual-porosity models appears in Γ𝑠. In mobile-immobile models, the advective term (i.e. the term including Γ𝑤) is set to zero. In dual-porosity models 𝑐∗ is equal to 𝑐𝑚𝑜 for Γ𝑤> 0 and 𝑐𝑖𝑚for Γ𝑤< 0 (Simunek and van Genuchten, 2008).  4.3 The dual-permeability concept The dual-permeability approach is an extension of the dual-porosity approach, allowing for water flow and solute transport in both co-existing continua. While dual-porosity models assume that water in the immobile region is stagnant, dual-permeability models allow for water flow in this region as well. The two co-existing continua are commonly used to describe matrix flow (slow) and preferential-flow (fast) regions. This model has two water retention functions, one for the matrix and one for the preferential-flow region; and two hydraulic conductivity functions, Km(𝜓m) for matrix and Kf(𝜓f) for preferential flow. 𝜓m and 𝜓f are the pressure heads in the matrix and the preferential-flow region, respectively (Hsieh et al., 2001).  In this formulation, Darcy-type flow is considered in both preferential-flow and matrix regions, and the transfer of water and solute between the two pore regions is described by a first-order  83  coupling term (Gerke and van Genuchten, 1993a; Simunek and van Genuchten, 2008). The one-dimensional vertical flow of water in preferential-flow and matrix regions is described by the equations 4-7 and 4-8, respectively:   𝜕𝜃𝑓(𝜓𝑓)𝜕𝑡=𝜕𝜕𝑧[𝐾𝑓(𝜓𝑓) (𝜕𝜓𝑓𝜕𝑧+ 1)] −Γ𝑤𝑤𝑓− 𝑆𝑓(𝜓𝑓) Equation 4-7  𝜕𝜃𝑚(𝜓𝑚)𝜕𝑡=𝜕𝜕𝑧[𝐾𝑚(𝜓𝑚) (𝜕𝜓𝑚𝜕𝑧+ 1)] +Γ𝑤1 − 𝑤𝑓− 𝑆𝑚(𝜓𝑓) Equation 4-8  Γ𝑤 = 𝛼𝑤(𝜓𝑓 − 𝜓𝑚) Equation 4-9  𝛼𝑤 =𝛽𝑎2𝛾𝑤𝐾𝑎 Equation 4-10  where 𝜃𝑓 and 𝜃𝑚 refer to water contents for the two separate (preferential-flow and matrix) regions such that 𝜃 = 𝑤𝜃𝑓 + (1 − 𝑤𝑓)𝜃𝑚, t is time (T), 𝑧 is elevation (L), and 𝐾(𝜓𝑓) and 𝐾(𝜓𝑚) are the hydraulic conductivity as a function of pressure head in the preferential-flow and matrix regions.  Γ𝑤 is the water transfer rate (T-1), S is the sink term (T-1), and  𝑤𝑓 is the ratio of volume of preferential-flow region and total domain. In equation 4-9, 𝛼𝑤 is a first-order transfer coefficient for water (L-1 T-1) defined in equation 4-10. 𝛽, a and 𝛾𝑤 are geometrical and empirical coefficients, and 𝐾𝑎 is the hydraulic conductivity (Gerke and van Genuchten, 1993a, 1993b). Subscripts f and m refer to preferential-flow and matrix pore regions respectively.  84  Solute transport in the dual-permeability approach is based on the advection-dispersion equations in both matrix and preferential-flow pore regions. There are various formulations that are suggested for the first-order solute mass transfer coefficient αs, which are discussed by several researchers (van Genuchten and Dalton, 1986; Gerke and van Genuchten, 1996, 1993a).   𝜕𝜕𝑡(𝜃𝑓𝑐𝑓) =𝜕𝜕𝑧(𝜃𝑓𝐷𝑓𝜕𝑐𝑓𝜕𝑧− 𝑞𝑓𝑐𝑓) − 𝜙𝑓 −Γ𝑠𝑤𝑓 Equation 4-11  𝜕𝜕𝑡(𝜃𝑚𝑐𝑚) =𝜕𝜕𝑧(𝜃𝑚𝐷𝑚𝜕𝑐𝑚𝜕𝑧− 𝑞𝑚𝑐𝑚) − 𝜙𝑚 +Γ𝑠1 − 𝑤𝑓 Equation 4-12  𝛤𝑠 = αs(1 − 𝑤𝑓)𝜃𝑚(𝑐𝑓 − 𝑐𝑚) + {Γw𝑐𝑓Γw𝑐𝑚 Γw ≥ 0Γw < 0 Equation 4-13  𝛼𝑠 =𝛽𝑎2𝐷𝑎 Equation 4-14  In the above equations, 𝜃𝑓 and 𝜃𝑚 refer to water contents for the two separate (preferential-flow and matrix) regions, c is the solute concentration (ML-3), t is time (T), 𝑧 is elevation (L), D is the dispersion coefficient (L2 T-1), Γ𝑠 is the solute mass transfer term (ML-3T-1). 𝑤𝑓 is the ratio of volume of preferential-flow region and total domain. 𝑞𝑓 and 𝑞𝑚 are the volumetric fluid flux density in preferential-flow region and matrix, respectively. 𝜙𝑓 and 𝜙𝑚 are the source-sink terms that account for various zero- or first-order or other reactions in both regions (ML-3T-1). The exchange term 𝛤𝑠 includes both advective and diffusive/dispersive transport as described in equation 4-13. When Γw ≥ 0 water flow direction is from preferential-flow region to matrix. 𝛼𝑠  85  (T-1) is the solute transfer coefficient (T-1), Da is the effective ionic or molecular diffusion coefficient (L2T-1) of the matrix block near the interface (Gerke and van Genuchten, 1993a) as described in equation 4-14.  𝛽, and a are geometrical and empirical coefficients. The variables in these equations refer to two overlapping domains of matrix and preferential-flow regions (Simunek and van Genuchten, 2008).   Figure 4.1. Conceptual physical nonequilibrium models for water flow and solute transport: a) uniform flow, b) mobile-immobile, 3) dual-porosity, and d) dual-permeability model. The dark blue and red arrows indicate the water flow and solute transport, respectively. The horizontal arrows demonstrate the water and solute transfer between the two pore regions.   4.4 Literature review on the existing codes with preferential-flow approach Review of the approaches and models representing preferential flow has been presented in several studies including but not limited to Beven and Germann (2013), Diamantopoulos and Durner (2012), Gerke, (2006), Kohne et al. (2009), Simunek and van Genuchten (2008),  86  Simunek et al. (2003). The modeling tools for preferential flow and solute transport include a wide range of complexity. There have been several models that use the Darcy-Richards equation. Beven and Germann (2013) categorized the main approaches to modeling preferential flow: 1. Single continuum: in this approach, preferential flow is considered as a modified relative conductivity curve close to saturation. This method is implemented in the HYDRUS code (Simunek and van Genuchten, 2008). 2. Mobile-immobile: in this approach, one of the pore regions is considered to be immobile and the second pore region is a Darcy-Richards domain. There is a first-order transfer term for exchange of solute between the two pore regions. This method is implemented in the HYDRUS code. 3. Dual-porosity: in this approach, “simple volume filling or a kinematic equation” is used for the preferential flows. The transfer between the immobile or Darcy-Richards matrix is treated separately. This method is implemented in kinematic model of Beven and Germann (1981), PREFLO model of Workman and Skaggs (1990), the MACRO model of  (Jarvis et al., 1991, 1994, 1997; Larsson and Jarvis, 1999; Larsson et al., 1999), and SWAP model of (van Dam et al., 2008). 4. Dual-permeability: in this approach, preferential flow is simulated by high permeability regions in a Darcy-Richards domain (this method is implemented into the DUAL code (Gerke and van Genuchten, 1993a)) or in fractured rocks that the matrix pore region is represented by blocks and fractures are demonstrated as Darcy-Richards flow regions that exchange water with matrix. This method is implemented in the HYDRUS code.  87  While most of the models mentioned above successfully described preferential flow in some contexts, they also had deficiencies (Beven and Germann, 2013) due to their dependence on Richards equation and thus following its assumption of equilibrium gradients and homogeneous soil properties. These models cannot always reproduce all of the events of water flow and solute transport into macro-porous soil.  4.5 Objectives of current implementation There are several studies that investigate water flow and tracer solute transport in preferential-flow domains, and in particular, structured soils. The number of similar studies that focus on chemical reactions in macroporous soils with heterogeneous soil properties, especially mine waste rock, is very limited. Reactive transport is largely influenced by the presence of preferential-flow paths within a soil medium, and geochemical reactions are affected due to limited residence time of the pore water in soil (Hsieh et al., 2001). The objective of this chapter is to add the capability to MIN3P-THCm code to describe: (1) flow, (2) conservative solute transport, and (3) reactive transport in porous systems with significant local pressure disequilibrium.  4.6 Development of mobile-immobile, dual-porosity and dual-permeability code MIN3P-THCm-DP 4.6.1 Existing MIN3P, MIN3PDUAL and MIN3P-THCm code MIN3P is a general three-dimensional multicomponent reactive transport code for variably saturated porous media developed by Dr. K. U. Mayer (Mayer, 1999; Mayer et al., 2002). This code includes generalized formulation for kinetically-controlled intra-aqueous and mineral  88  dissolution-precipitation reactions was developed and incorporated into MIN3P code, in addition to geochemical equilibrium expressions for hydrolysis, aqueous complexation, oxidation-reduction, ion exchange, surface complexation, and gas dissolution-exsolution reactions. All kinetically-controlled reactions can be described by either reversible or irreversible processes. Different reaction mechanisms for dissolution precipitation reactions are considered in the code and a large number of rate expression reported in literature can be incorporated into the model through the related database.   A general dual-porosity multi-component reactive transport approach, implementing a first-order mass transfer model (FOMT), was developed based on the existing MIN3P code by L. Cheng from University of Sheffield (Cheng, 2006) and was named MIN3PDUAL. The code was used to assess the fate and transport of MTBE after a spill accident at a petroleum filling station in a Chalk aquifer in the UK. This development used the same overall data structure of MIN3P but expanded it with added terms for secondary (immobile) porosity. The change in Jacobian matrix structure is shown in Figure 4.2. This change resulted in a Jacobian matrix with a size four times larger than the single-porosity Jacobian and thus leads to a significant increase in memory and computational requirements. Therefore, this development was difficult to adapt in the future versions of the code and the functions for this development have not been carried forward into the current version of MIN3P-THCm (Mayer et al., 2017).  89   Figure 4.2. Jacobian matrix structure in MIN3P and MIN3PDUAL (Cheng, 2006)  Later, several extensions were added to MIN3P code including heat transport, one-dimensional hydromechanical coupling, multicomponent diffusion, and reactive transport in highly saline solution (Amos and Mayer, 2006; Bea et al., 2012; Henderson et al., 2009; Rasouli et al., 2015). The new version is renamed MIN3P-THCm and is under continuous verification and quality control (Mayer et al., 2017).  4.6.2 Conceptual model The conceptual model of the existing MIN3P code (Mayer et al., 2002) is presented in Figure 4.3, which describes the uniform flow model. In this conceptual model, the representative elemental volume (REV) of the variably saturated porous media consists of mobile aqueous and gas phases and an immobile solid phase. In Figure 4.3, Qa,a, Qa,g, Qa,s, and Qs,s, are the source-sink terms for the aqueous, gaseous and solid phases, respectively. In same figure, Qa,in, Qg,in, Qa,out and Qg,out are external sources and sinks due to advection, diffusion and dispersion transport processes.   90  In the model, the aqueous phase includes inorganic and organic dissolved species and the solvent water. The gas phase consists of atmospheric gases and water vapor, as well as other gases such as methane, hydrogen sulfide, hydrogen gas and organic compounds in gaseous form. The solid phase includes minerals and surface species. Reactions in this model are either homogeneous (occur within a single phase), or heterogeneous (occur in two or more phases). Homogeneous reactions include hydrolysis, complexation, and aqueous oxidation-reduction reactions in aqueous phase and mineral alteration in the solid phase. Heterogeneous reactions include mineral dissolution-precipitation, oxidation-reduction reactions, ion exchange, adsorption, and gas exchange (Mayer, 1999; Mayer et al., 2002).    Figure 4.3. The conceptual model of the physicochemical system (Mayer et al., 2002)  4.6.3 Governing equations Variably-saturated flow equations: the following equations represent mass conservation for water in the existing uniform flow version of MIN3P. The governing equations for the non-uniform flow models (mobile-immobile, dual-porosity and dual-permeability) are presented later  91  in this chapter. With the assumptions of water being an incompressible fluid, no hysteresis and a passive air phase, the mass conservation equation for the water phase is (Mayer 1999):  𝑆𝑎𝑆𝑠𝜕ℎ𝜕𝑡+ ϕ𝜕𝑆𝑎𝜕𝑡− ∇. [𝑘𝑟𝑎𝐾∇ℎ] − 𝑄𝑎 = 0        Equation 4-15  Where a is the aqueous phase, Sa is the saturation of the aqueous phase (m3 m-3), 𝑆𝑠 is the specific storage coefficient (m-1), ℎ is the hydraulic head (m), t is time (S), ϕ is the porosity (m3m-3), kra is the relative permeability of the porous medium with respect to the aqueous phase (dimensionless), 𝐾 is the saturated hydraulic conductivity tensor (ms-1) , and 𝑄𝑎 is source or sink term (s-1). The nonlinear functions defining the water retention curves (Sw-ψ) and relative permeability functions (Krw-ψ) are given by (Wösten and Van Genuchten 1988) and can be found in Mayer et al., (2002).   Reactive Transport Formulation: the following equations represent the mass - conservation equation for a component in the existing uniform flow version of MIN3P. The governing equations for the non-uniform flow models (mobile-immobile, dual-porosity and dual-permeability) are presented later in this chapter. The mass-conservation equation for a component Aj, written in terms of total component concentration Tj, takes the following form (Lichtner 1985; Mayer 1999):   92   𝜕𝜕𝑡[𝑆𝑎𝜙𝑇𝑗𝑎] +𝜕𝜕𝑡[𝑆𝑔𝜙𝑇𝑗𝑔] + ∇. [𝑞𝑎𝑇𝑗𝑎] − ∇. [𝑆𝑎𝜙𝐷𝑎∇𝑇𝑗𝑎] − ∇. [𝑆𝑔𝜙𝐷𝑔∇𝑇𝑗𝑔]− 𝑄𝑗𝑎,𝑎 − 𝑄𝑗𝑎,𝑠 − 𝑄𝑗𝑎,𝑒𝑥𝑡 − 𝑄𝑗𝑔,𝑒𝑥𝑡 = 0       𝑗 = 1, 𝑁𝑐 Equation 4-16  In this equation, Sg is the saturation of the gaseous phase [m3 gas m-3 void], Tj a [mol L-1 H2O] is the total aqueous component concentration for component Aj c, Tj g [mol L-1 gas] is the total gaseous concentration for component Aj c. qa is the Darcy flux vector, while Da and Dg are the dispersion tensors for the aqueous and gaseous phase, respectively. Qj a,a [mol dm-3 porous medium] and Qj a,s [mol dm-3 porous medium] are internal source and sink terms toward the total aqueous component concentrations due to intra-aqueous kinetic reactions and kinetically controlled dissolution/precipitation reactions. Qj a,ext [mol dm-3 porous medium] and Qj g,ext [mol dm-3 porous medium] are external source and sink terms for the aqueous and gaseous phase, respectively (Mayer, 1999).  4.6.4 Boundary conditions In MIN3P and MIN3P-THCm codes, the boundary conditions that have been specified for variably saturated flow problems are Dirichlet (specified hydraulic head/pressure), Cauchy (specified flux), free exit boundary condition and seepage face.  Boundary conditions for reactive transport include Dirichlet (specified concentration), Neuman (free exit boundary), Cauchy (specified mass flux), and ‘mixed’ boundary condition which is  93  specified mass flux and fixed concentraion for gaseous species on dummy node outside of solution domain.  4.7 MIN3P-THCm-DP code MIN3P-THCm-DP code is an extension of MIN3P-THCm with addition of mobile-immobile, dual-porosity and dual-permeability capabilities. This option can be turned off and the code can then be used as the original MIN3P-THCm. The data structure has remained the same. The input file has been modified to include the new parameters for preferential flow. The output files have kept the same structure.   4.7.1 Conceptual model To incorporate dual-domain models into MIN3P, the original conceptual model is modified to have two overlapping pore regions: the mobile/preferential-flow region and immobile/matrix region. Each of these pore regions consists of aqueous, solid and gas phases and the mass exchange between the aqueous phases of the two pore regions is described by a first-order transfer coefficient. The conceptual model for the MIN3P-THCm-DP model is shown in Figure 4.4.   Figure 4.4a shows the conceptual model for the mobile-immobile and dual-porosity model. The water content in the immobile pore region is constant over time and water flow and solute transport occurs within the mobile region. Solute exchange between the two pore regions is by diffusion. In the dual-porosity model, the mobile-immobile model is extended to include both  94  water and solute transfer between the two pore regions. Solute can move into and out of the immobile domain by both diffusion and advection processes.    Figure 4.4. Conceptual model of MIN3P-THCm-DP model   The dual-porosity approach implemented in MIN3P for formulation of Γ𝑤, is based on the difference in the head between mobile and immobile pore regions. The dual-permeability model (Figure 4.4b), considers the movement of water and solute in both pore regions (preferential-flow and matrix regions) and therefore requires two water retention functions for preferential-flow and matrix pore regions. In the preferential-flow region, water flows relatively faster compared to the matrix pore region. Similar to the dual-porosity model, the dual-permeability model considers the transfer of both water and solute between the two pore regions.   95  4.7.2 Governing equations In implementing dual-permeability equations in MIN3P-THCm, it must be noted that different types of dual-permeability approaches may be used to describe flow and transport in structured media. Several assume similar governing equations to describe flow in the fracture and matrix regions, while others use different formulations for the two regions. The formulation of the dual-porosity and dual-permeability used in this thesis is based on the approach presented in (Gerke and van Genuchten, 1993a) in which Richards equation is applied to each of two pore regions. Local porosities of fracture and matrix pore systems are defined as the following equations:  ϕ =𝑉𝑝𝑉𝑡    ϕ𝑓 =𝑉𝑝,𝑓𝑉𝑡,𝑓  ϕ𝑚 =𝑉𝑝,𝑚𝑉𝑡,𝑚 Equation 4-17  𝑉𝑝 = 𝑉𝑝,𝑓 + 𝑉𝑝,𝑚  𝑉𝑡 = 𝑉𝑡,𝑓 + 𝑉𝑡,𝑚 Equation 4-18  Volumetric weighting factor: 𝑤𝑓 =𝑉𝑡,𝑓𝑉𝑡  Equation 4-19  where w is the ratio of the volumes of the fracture (inter-aggregate) and the total pore systems (Gerke and van Genuchten, 1993a) (Gerke and van Genuchten, 1996).  The three porosities are related as: ϕ = 𝑤𝑓ϕ𝑓 + (1 − 𝑤𝑓)ϕ𝑚 Equation 4-20  The (local) volumetric water content of preferential-flow and matrix regions (L3L-3) is given by the following equations:  96  𝜃𝑓 =𝑉𝑤,𝑓𝑉𝑡,𝑓 𝜃𝑚 =𝑉𝑤,𝑚𝑉𝑡,𝑚 Equation 4-21  Water content of bulk soil:  𝜃 = 𝑤𝑓𝜃𝑓 + (1 − 𝑤𝑓)𝜃𝑚 Equation 4-22  Average bulk soil hydraulic conductivity:  𝐾 = 𝑤𝑓𝐾𝑓 + (1 − 𝑤𝑓)𝐾𝑚 Equation 4-23  𝑖𝑓 ℎ = ℎ𝑚 = ℎ𝑓 equilibrium assumption by Peters and Klavetter (1988) the water flow and solute transport in both pore regions are described by a coupled pair of Richards equations for dual-permeability (equations 4-24 and 4-25):  𝑆𝑎𝑓𝑆𝑠𝑓𝜕ℎ𝑓𝜕𝑡+𝑤𝑓ϕ𝑓𝜕𝑆𝑎𝑓𝜕𝑡− ∇. [𝑤𝑓𝑘𝑟𝑎𝐾𝑓∇ℎ𝑓] − 𝑤𝑓𝑄𝑎𝑓 = −Γ𝑤        Equation 4-24  𝑆𝑎𝑚𝑆𝑠𝑚𝜕ℎ𝑚𝜕𝑡+ (1 − 𝑤𝑓)ϕ𝑚𝜕𝑆𝑎𝑚𝜕𝑡− ∇. [(1 − 𝑤𝑓)𝑘𝑟𝑎𝐾𝑚∇ℎ𝑚]− (1 − 𝑤𝑓)𝑄𝑎𝑚 = −Γ𝑤       Equation 4-25  For mobile-immobile and dual-porosity models, the equations for the dual-permeability model are simplified to equations 4-26 and 4-27 for the two pore regions. This simplification assumes that in these models the water flow only occurs in the mobile region:  𝑆𝑎𝑓𝑆𝑠𝑓𝜕ℎ𝑓𝜕𝑡+𝑤𝑓ϕ𝑓𝜕𝑆𝑎𝑓𝜕𝑡− ∇. [𝑤𝑓𝑘𝑟𝑎𝐾𝑓∇ℎ𝑓] − 𝑤𝑓𝑄𝑎𝑓 = −Γ𝑤        Equation 4-26  97   𝑆𝑎𝑚𝑆𝑠𝑚𝜕ℎ𝑚𝜕𝑡+ (1 − 𝑤𝑓)ϕ𝑚𝜕𝑆𝑎𝑚𝜕𝑡− (1 − 𝑤𝑓)𝑄𝑎𝑚 = −Γ𝑤     Equation 4-27  where a is the aqueous phase, 𝑆𝑎𝑓 and 𝑆𝑎𝑚 are the saturation of the aqueous phase (m3 m-3) of the preferential-flow region and matrix respectively, 𝑆𝑠𝑓 and 𝑆𝑠𝑚 are the specific storage coefficient (m-1) of the preferential-flow region and matrix respectively, ℎ𝑓 and ℎ𝑚 are the hydraulic head (m) of the preferential-flow region and matrix respectively, t is time (S), ϕ𝑓 and ϕ𝑚 are the porosities (m3m-3) of preferential-flow and matrix regions respectively, kra is the relative permeability of the porous medium with respect to the aqueous phase (dimensionless), 𝐾𝑓 and 𝐾𝑚 are saturated hydraulic conductivity tensors (ms-1) for preferential-flow and matrix regions respectively, and 𝑄𝑎𝑓 and 𝑄𝑎𝑚 are source or sink terms (s-1) in preferential-flow and matrix regions respectively. The nonlinear functions defining the water retention curves (Sw-ψ) and relative permeability functions (Krw-ψ) are given by (Wösten and Van Genuchten 1988) and can be found in Mayer et al., (2002). Γ𝑤 is the space and time dependent exchange term (s-1) describing the transfer of water between the two pore regions (equations 4-9 and 4-10).  The water contents θf and θm have different meanings in dual-permeability model than they would for dual-porosity model where they represented water content of total pore space (i.e. θ = θmo+ θim). In the dual-permeability model they refer instead to water contents of two separate pore regions (matrix and preferential flow), described as θ = wfθf + (1-wf) θm = θF+ θM. where θF and θM are the absolute water contents in the matrix and preferential-flow pore regions, respectively (Simunek and van Genuchten, 2008).  98   The following equations represent mass conservation for a component in the dual-permeability model in the preferential-flow region and matrix respectively:   𝜕𝜕𝑡[𝑆𝑎𝑓𝑤𝑓𝜙𝑓𝑇𝑗𝑎𝑓] +𝜕𝜕𝑡[𝑆𝑔𝑓𝑤𝑓𝜙𝑓𝑇𝑗𝑓𝑔] + ∇. [𝑤𝑓𝑞𝑎𝑓𝑇𝑗𝑎𝑓]− ∇. [ 𝑆𝑎𝑓𝑤𝑓𝜙𝑓𝐷𝑎∇𝑇𝑗𝑎𝑓] − ∇. [𝑆𝑔𝑓𝑤𝑓𝜙𝑓𝐷𝑔∇𝑇𝑗𝑓𝑔] − 𝑄𝑗𝑓𝑎,𝑎− 𝑄𝑗𝑓𝑎,𝑠 − 𝑤𝑓𝑄𝑗𝑓𝑎,𝑒𝑥𝑡 − 𝑄𝑗𝑓𝑔,𝑒𝑥𝑡 = −Γ𝑠                  𝑗 = 1, 𝑁𝑐 Equation 4-28  𝜕𝜕𝑡[𝑆𝑎𝑚𝑤𝑚𝜙𝑚𝑇𝑗𝑎𝑚] +𝜕𝜕𝑡[𝑆𝑔𝑚(1 − 𝑤𝑓)𝜙𝑚𝑇𝑗𝑚𝑔 ] + ∇. [(1 − 𝑤𝑓)𝑞𝑎𝑚𝑇𝑗𝑎𝑚]− ∇. [ 𝑆𝑎𝑚(1 − 𝑤𝑓)𝜙𝑚𝐷𝑎∇𝑇𝑗𝑎𝑚]− ∇. [𝑆𝑔𝑚(1 − 𝑤𝑓)𝜙𝑚𝐷𝑔∇𝑇𝑗𝑚𝑔 ] − 𝑄𝑗𝑚𝑎,𝑎 − 𝑄𝑗𝑚𝑎,𝑠− (1 − 𝑤𝑓)𝑄𝑗𝑚𝑎,𝑒𝑥𝑡 − 𝑄𝑗𝑚𝑔,𝑒𝑥𝑡 = −Γ𝑠                  𝑗 = 1, 𝑁𝑐 Equation 4-29  The governing equation for the mobile region in the mobile-immobile and dual-porosity models is the same as the equation for the preferential-flow region in dual-permeability model, whereas the equation for the immobile region is the simplified from the equation for matrix in dual-permeability model (equations 4-30 and 4-31):   99  𝜕𝜕𝑡[𝑆𝑎𝑓𝑤𝑓𝜙𝑓𝑇𝑗𝑎𝑓] +𝜕𝜕𝑡[𝑆𝑔𝑓𝑤𝑓𝜙𝑓𝑇𝑗𝑓𝑔] + ∇. [𝑤𝑓𝑞𝑎𝑓𝑇𝑗𝑎𝑓]− ∇. [ 𝑆𝑎𝑓𝑤𝑓𝜙𝑓𝐷𝑎∇𝑇𝑗𝑎𝑓] − ∇. [𝑆𝑔𝑓𝑤𝑓𝜙𝑓𝐷𝑔∇𝑇𝑗𝑓𝑔] − 𝑄𝑗𝑓𝑎,𝑎− 𝑄𝑗𝑓𝑎,𝑠 − 𝑤𝑓𝑄𝑗𝑓𝑎,𝑒𝑥𝑡 − 𝑄𝑗𝑓𝑔,𝑒𝑥𝑡 = −Γ𝑠                  𝑗 = 1, 𝑁𝑐 Equation 4-30  𝜕𝜕𝑡[𝑆𝑎𝑚(1 − 𝑤𝑓)𝜙𝑚𝑇𝑗𝑎𝑚] +𝜕𝜕𝑡[𝑆𝑔𝑚(1 − 𝑤𝑓)𝜙𝑚𝑇𝑗𝑚𝑔 ]− ∇. [ 𝑆𝑎𝑚(1 − 𝑤𝑓)𝜙𝑚𝐷𝑎∇𝑇𝑗𝑎𝑚]− ∇. [𝑆𝑔𝑚(1 − 𝑤𝑓)𝜙𝑚𝐷𝑔∇𝑇𝑗𝑚𝑔 ] − 𝑄𝑗𝑚𝑎,𝑎 − 𝑄𝑗𝑚𝑎,𝑠− (1 − 𝑤𝑓)𝑄𝑗𝑚𝑎,𝑒𝑥𝑡 − 𝑄𝑗𝑚𝑔,𝑒𝑥𝑡 = −Γ𝑠                  𝑗 = 1, 𝑁𝑐 Equation 4-31  In these equations, 𝑆𝑔𝑓 and 𝑆𝑔𝑚 are the saturation of the gaseous phase [m3 gas m-3 void] in the preferential-flow region and matrix, respectively, Tjf a and Tjm a [mol L-1 H2O] are the total aqueous component concentration for component Aj c in the preferential-flow region and matrix, respectively, Tjf g and Tjm g [mol L-1 gas] are the total gaseous concentration for component Aj c in the preferential-flow region and matrix, respectively. qaf and qam are the Darcy flux vector, while Da and Dg are the dispersion tensors for the aqueous and gaseous phase, respectively. Qjf a,a and Qjm a,a [mol dm-3 porous medium] and Qjf a,s and Qjm a,s [mol dm-3 porous medium] are internal source and sink terms toward the total aqueous component concentrations due to intra-aqueous kinetic reactions and kinetically controlled dissolution/precipitation reactions in preferential-flow region and matrix, respectively. Qjf a,ext and Qjm a,ext [mol dm-3 porous medium] and Qjf g,ext and Qjm g,ext [mol dm-3 porous medium] are external source and sink terms for the aqueous and gaseous phase, in preferential-flow region and matrix.  100  4.7.3 Boundary conditions The boundary conditions that have been specified for variably saturated and reactive transport are similar to MIN3P-THCm code. The boundary condition on soil profile can be specified on preferential-flow region, matrix or on both pore regions based on the problem. For a Cauchy (specified flux) boundary condition specified on the profile, the actual surface flux is calculated by weighting the flux by wf, where wf is the ratio of the volumes of the fracture (inter-aggregate) to the total pore system and is entered by the user in the input file.  4.7.4 Input file The structure of input file for MIN3P-THCm-DP is similar to MIN3P-THCm code. To incorporate the mobile-immobile, dual-porosity and dual-permeability approaches, one data block is added which is named ‘Section 11B: physical parameters - dual-permeability’. To set up a simulation for MIN3P-THCm-DP code, some of the original data blocks required modification, which are described in detail in the appendix.  4.7.5 Output files The output files for the current version of MIN3P-THCm-DP are similar to the original MIN3P-THCm files. The spatial data for flow variables such as pressure head, water content, and saturation, and the output data for concentration, are given for each pore domain in the same output file. TECPLOT headers are included in each file and are used for plotting purposes using TECPLOT software.   101  4.8 Verification of MIN3P-THCm-DP  To ensure the accuracy of MIN3P-THCm-DP, it was verified against established results obtained from HYDRUS-1D code (Simunek and van Genuchten, 2008). HYDRUS-1D is a software package for simulating water, heat and solute transport in one-dimensional variably-saturated porous media. The governing flow and transport equations are solved numerically using Galerkin-type linear finite element schemes for spatial discretization. Finite-difference methods were used to approximate temporal derivatives. A fully implicit finite-difference scheme with Picard linearization was used to solve the Richards equation, while a Crank–Nicholson finite-difference scheme was used for solving the advection–dispersion equations (Simunek and van Genuchten, 2008).   Both HYDRUS-1D and MIN3P-THCm-DP codes are based on the Richards equation approach proposed by Gerke and Genuchten (1993a, 1993b) for modeling flow and solute transport in dual-domain systems (Simunek et al., 2012). Both codes use a dual-permeability flow model consisting of two mobile regions, one representing the matrix and one the preferential-flow pore region. In MIN3P-THCm-DP, the dual-permeability model can be simplified to mobile-immobile and dual-porosity models in which one fraction of the water content is mobile and another fraction immobile. The solute transport equations also consider nonlinear nonequilibrium reactions between the solid and liquid phases. While the HYDRUS-1D code is accessible and sufficient for single-component modeling of solute transport in non-uniform flow systems, it is limited in its ability to account for the chemical or biological reactions that occur in dual-domain systems such as generation of acid rock drainage in mine waste rock piles. The MIN3P-THCm-DP code, while less user-friendly, overcomes these limitations and has the capability of  102  performing multi-component reactive transport simulations in non-equilibrium preferential-flow problems.   The MIN3P and MIN3P-THCm codes have been carefully verified using a collection of benchmarks (Mayer et al., 2017). For verification of MIN3P-THCm-DP, a series of verification examples were set up and listed in Table 4.1. The physical input parameters for each pore region are shown in Table 4.2, and the parameters defining the solute transfer term between the two-pore regions are summarized in Table 4.3.   In all verification scenarios, the specified-flux boundary condition on top of the domain is only applied on mobile/preferential-flow regions in order to comply with published examples in HYDRUS-1D (Gerke and van Genuchten, 1993a). To verify MIN3P-THCm-DP results against HYDRUS-1D code, in each verification scenario, the pressure head, water content, and concentration in each pore region, as well as the water transfer rate between the two regions, are compared between the two simulations.   When comparing the water content results between MIN3P-THCm-DP and HYDRUS-1D codes, it is important to note that in the HYDRUS-1D code the water contents θf and θm have different meanings in the dual-porosity model, where they represent water contents of the total pore space (i.e. θ = θmo+ θim), versus the dual-permeability model, where they refer to the water contents of two separate pore regions (matrix and preferential flow), described as θ = wfθf + (1-wf) θm = θF+ θM. The θF and θM are the absolute water contents in the matrix and preferential-flow pore regions, respectively (Simunek and van Genuchten, 2008). Therefore, in the dual-permeability  103  approach, in HYDRUS-1D the water content is weighed internally by wf  in the source code (HYDRUS-1D water content output results are the water content multiplied with wf  and 1- wf  for  preferential-flow and matrix regions, respectively). In MIN3P-THCm-DP the water contents meanings are consistent between the dual-permeability and dual-porosity models and they represent the absolute water contents in preferential-flow and matrix pore regions. As a result, for comparison purposes between the MIN3P-THCm-DP and HYDRUS-1D, the water-content data from MIN3P-THCm-DP must be divided by wf  and 1- wf  for the preferential-flow region and matrix, respectively. In the dual-porosity approach, the water content results are absolute values and weighing them is not required.   Both MIN3P-THCm-DP and HYDRUS-1D codes were set up to use implicit scheme for temporal discretization and upstream weighting for spatial discretization of governing equations for solute transport.  Table 4.1. Summary of dual-porosity, dual-permeability verification scenarios. All verifications are performed against HYDRUS-1D code. Verif.Scen.a Sim. No.b Code Approach Processes in each pore region Mass transfer processes on interface Description A 1 HYDRUS-1D Dual-porosity Water flow and solute transport in mobile region Solute diffusion  Dual-porosity with advective transfer turned off (only diffusive transfer) 2 HYDRUS-1D Dual-permeability (mimic dual-porosity) Water flow and solute transport in P.F.c region Solute diffusion  Dual-permeability with Ks of matrix set to zero to mimic dual-porosity and advective transfer turned off (only diffusive transfer) B 3 HYDRUS-1D Dual-porosity Water flow and solute transport in mobile region Solute advection  Dual-porosity with diffusive transfer turned off (only advective transfer) 4 HYDRUS-1D Dual-permeability (mimic dual-Water flow and solute transport in P.F. region Solute advection Dual-permeability with Ks of matrix set to zero to mimic dual-porosity and diffusive transfer  104  Verif.Scen.a Sim. No.b Code Approach Processes in each pore region Mass transfer processes on interface Description porosity) turned off (only advective transfer) C 5 MIN3P-THCM-DP Dual-permeability (mimic dual-porosity) Water flow and solute transport in P.F. region Solute advection and diffusion Dual-permeability with Ks of matrix set to zero to mimic dual-porosity advective and diffusive transfer 6 HYDRUS-1D Dual-permeability (mimic dual-porosity) Water flow and solute transport in P.F. region Solute advection and diffusion Dual-permeability with Ks of matrix set to zero to mimic dual-porosity advective and diffusive transfer D 7 MIN3P-THCM-DP Dual-permeability Water flow and solute transport in both regions Solute advection and diffusion Dual-permeability with advective and diffusive transfer 8 HYDRUS-1D Dual-permeability Water flow and solute transport in both regions Solute advection and diffusion Dual-permeability with advective and diffusive transfer aVerif. Scen.: Verification scenario bSim. No.: Simulation number cP.F.: Preferential flow   105  Table 4.2. Physical input parameters for the HYDRUS-1D and MIN3P simulations     Time step preferential flow region/ mobile Matrix/ immobile Top B.C.* Initial Condition Dispersivity Simulation No. Type domain size (z) Final time Min Max θr θs α n Ks I θr θs α n Ks I Flow Transport Flow Transport Mat. Frac.  [-] [cm] [d] [d] [d] [-] [-] [1/cm] [-] [cm/d] [-] [-] [-] [-] [-] [cm/d] [-] [cm/d] [mmol/cm3] [cm] [cm] [cm] [cm] 1 Dual por 40 0.08 1E-8 1 0 0.025 0.1 2 100 0.5 0 0.475 0.005 1.5 - - -50 1 -1000 0 0 1 2 Dual perm 40 0.08 1E-8 1 0 0.5 0.1 2 2000 0.5 0 0.5 0.005 1.5 1E-15 0.5 -50 1 -1000 0 0 1 3 Dual por 40 0.08 1E-8 1 0 0.025 0.1 2 100 0.5 0 0.475 0.005 1.5 - - -50 1 -1000 0 0 1 4 Dual perm 40 0.08 1E-8 1 0 0.5 0.1 2 2000 0.5 0 0.5 0.005 1.5 1E-15 0.5 -50 1 -1000 0 0 1 5 Dual perm 40 0.08 1E-8 1 0 0.5 0.1 2 2000 0.5 0 0.5 0.005 1.5 1E-15 0.5 -50 - -1000 - - 1 6 Dual perm 40 0.08 1E-8 1 0 0.5 0.1 2 2000 0.5 0 0.5 0.005 1.5 1E-15 0.5 -50 - -1000 - 0 - 7 Dual perm 40 0.08 1E-8 1 0 0.5 0.1 2 2000 0.5 0 0.5 0.005 1.5 1.0526 0.5 -50 - -1000 - 0 - 8 Dual perm 40 0.08 1E-8 1 0 0.5 0.1 2 2000 0.5 0 0.5 0.005 1.5 1.0526 0.5 -50 - -1000 - 0 - *B.C.: boundary condition     106  Table 4.3. Input parameters for mass transfer between the two pore regions for the HYDRUS-1D and MIN3P-THCm-DP simulations  4.8.1 Verification scenario A)  This verification scenario consists of two simulations: simulations 1 and 2, set up in the HYDRUS-1D code using the dual-porosity model with mass transfer driven by the pressure head gradient, and the dual-permeability model, respectively. The objective of this verification scenario is: (1) to compare two simulations, both in HYDRUS-1D, with only diffusive mass transfer between the two pore regions, to check the simplification of the dual-permeability model to the dual-porosity model in HYDRUS-1D code; (2) to determine whether the dual-porosity model with mass transfer driven by the pressure head gradient, and the dual-permeability model in HYDRUS-1D code, give the same results for outflow concentrations when both models only have diffusive solute mass transfer between the two Simulation No. wf β γ a Ksa Diffus Wa Da (MassTr) omegab Alphac  [-] [-] [-] [cm] [cm/d] [cm2/d] [cm2/d] [1/d] [1/d] 1 - - - - - - - 0 1.5 2 0.05 3 0.4 1 0 0 0.5 - - 3 - - - - - - - 0.01 0 4 0.05 1 1 1 0.01 0 0 - - 5 0.05 3 0.4 1 0.01 - - - - 6 0.05 3 0.4 1 0.01 - 0.5 - - 7 0.05 3 0.4 1 0.01 0 0.5 - - 8 0.05 3 0.4 1 0.01 0 0.5 - - a DiffusW [cm2d-1]: molecular diffusion coefficient in free water bomega (ω) [1/d]: mass transfer coefficient on interface for dual-porosity in HYDRUS-1D code cAlpha [1/d]: mass transfer coefficient for solute exchange between mobile and immobile liquid regions. This parameter is similar to ω in dual-porosity model  107  pore regions, and the dual-permeability code is modified (by setting Ks in z-direction to a small number) to represent a dual-porosity pore system; and, (3) to check the modification required for parameters that define the diffusive mass transfer between the two pore regions in both approaches. All verification scenarios are based on the examples provided in (Gerke and van Genuchten, 1993a; Simunek et al., 2003).  4.8.1.1 Simulation 1: HYDRUS-1D dual-porosity with diffusive solute transfer between the two pore regions (Mobile-immobile) Simulation 1 is a 1D transient dual-porosity problem with a specified-flux (Cauchy) boundary condition of 50 cm/d (at z = 40 cm) and a specified-pressure head (Dirichlet) boundary condition on the outflow (z = 0 cm). Water was exclusively applied on the mobile pore region at the surface. The parameters selected for the verification scenarios are selected based on a simulation presented in Gerke and Genuchten, (1993a) and also used in HYDRUS-1D code example projects provided with the code. The hydraulic function properties of mobile and immobile pore regions were described using van Genuchten functions (van Genuchten, 1980). The hydraulic parameters of mobile and immobile regions are representative of relatively coarse- and fine-grained soil material, respectively. The porosity is set to 0.025 (weighed by wf = 0.05) in the mobile region and 0.475 (weighed by 1- wf) in the immobile pore region. The domain is discretized into 325 cells.  There is water flow exclusively in the mobile region in the z-direction, and the transport process within the mobile region is advection in the vertical direction. The soil function parameters for each pore region, boundary condition, and initial condition for flow and solute  108  transport are given in Table 4.2. The solute mass transfer coefficient characterizing diffusive solute exchange between the mobile and immobile zones of the matrix domain (Alpha) is given in Table 4.3. This parameter is set to 1.5 [1/d]. The chemical system consists of one conservative component that does not go through any chemical reactions.  4.8.1.2 Simulation 2: HYDRUS-1D dual-permeability mimicking dual-porosity with diffusive solute transfer between the two pore regions (Mobile-immobile) Simulation 2 is a 1D transient dual-permeability problem with a specified flux (Cauchy) boundary condition of 50 cm/d (at z = 40 cm) and a specified pressure head (Dirichlet) boundary condition on the outflow (z = 0 cm). Water was exclusively applied on the preferential-flow pore region at the surface. The hydraulic function properties of preferential-flow and matrix pore regions were described using van Genuchten functions (van Genuchten, 1980). The hydraulic parameters of preferential-flow and matrix regions are representative of relatively coarse and fine-grained soil material, respectively. The porosity is set to 0.5 in the preferential-flow region and 0.5 in the matrix pore region. The domain is discretized into 325 cells.   The saturated hydraulic conductivity (Ks) of the preferential-flow region is set to a very small value (1×10-15 m/s) to mimic the dual-porosity model; thus, there is water flow exlusively in the preferential-flow region in the z-direction, and the transport process within the preferential-flow region is advection in the vertical direction. The soil function parameters for each pore region, boundary condition and initial condition for flow and transport are given in Table 4.2. We assume rectangular aggregates (β = 3) with an average matrix block  109  size of 2 cm (a = 1 cm) (Gerke and van Genuchten, 1993a). The γw parameter was set to 0.4 as suggested by Gerke and Genuchten (1993b). The apparent hydraulic conductivity of the transfer term was calculated using 𝐾𝑎 = 0.5[𝐾𝑎(ℎ𝑓) + 𝐾𝑎(ℎ𝑚)]. The hydraulic parameters for the transfer term were assumed to be the same as for the matrix, except for the saturated hydraulic conductivity, which was decreased by a factor of 100 (Gerke and van Genuchten, 1993a). The chemical system consists of one conservative component.  4.8.1.3 Results Figure 4.5 and Figure 4.6Figure 4.6 demonstrate that the two approaches have different output concentrations and solute mass transfer rates. The solute mass transfer term Γs (T-1) has two parts: diffusive and advective, as presented in equation 4-6 for dual-porosity, and in equation 4-13 for dual-permeability model. The Γs in dual-porosity and dual-permeability models is calculated based on the following equations:  Γ𝑠 = 𝜔𝑚𝑖𝑚(𝑐𝑚𝑜 − 𝑐𝑖𝑚) + Γ𝑤 × 𝑐∗ (equation 4-6) Dual-porosity  Γ𝑠 = 𝛼𝑠(1 − 𝑤𝑓)𝜃𝑚(𝑐𝑓 − 𝑐𝑚) + Γ𝑤 × 𝑐∗ (equation 4-13) Dual-permeability  The advective parts are similar and dependent on the water mass transfer rate (Γ𝑤) and the solute concentration in one of the pore regions (𝑐∗). To compare the diffusive part of the solute mass transfer term between the two models, first, the advective mass transfer between mobile and immobile domain was turned off and only diffusive mass transfer was allowed. The diffusive part in the dual-permeability equation has two extra terms (1 − 𝑤𝑓), which is the ratio of volume of matrix to the total volume, and 𝜃𝑚, which is the water content  110  (saturation) of the matrix. Therefore, it was expected that the diffusive part of the solute mass transfer from the dual-permeability and dual-porosity models would differ. The results obtained from Figure 4.5 and Figure 4.6 confirm this hypothesis and show that HYDRUS-1D treats diffusive solute mass transfer between the two pore regions differently in dual-porosity and dual-permeability models.    Figure 4.5. HYDRUS-1D: The pink plot: concentration of tracer in mobile domain using dual-porosity (mobile-immobile, pressure head mass transfer) with zero advective mass transfer and only diffusive mass transfer between the two pore regions. The blue plot: concentration of tracer in preferential-flow domain using dual-permeability (no flow in matrix to mimic dual-porosity) with zero advective mass transfer and only diffusive mass transfer between the two pore regions. Both results are plotted for 0.01 day output time.   111   Figure 4.6. HYDRUS-1D: The pink plot: solute mass transfer rate of tracer between mobile and immobile domains using dual-porosity (mobile-immobile, pressure head mass transfer) with zero advective mass transfer and only diffusive mass transfer on interface. The blue plot: solute mass transfer rate of tracer between preferential-flow region and matrix domains using dual-permeability (no flow in matrix to mimic dual-porosity) with zero advective mass transfer and only diffusive mass transfer between the two pore regions. Both results are plotted for 0.01 day output time.  4.8.2 Verification scenario B) This verification scenario consists of two simulations: simulations 3 and 4, set up in HYDRUS-1D code using the dual-porosity model with mass transfer driven by the pressure head gradient, and the dual-permeability model, respectively. The objective of this verification scenario is: (1) to compare two simulations both in HYDRUS-1D with only advective mass transfer between the two pore regions, to check the simplification of the dual-permeability model to the dual-porosity model in HYDRUS-1D code, and, (3) to check the  112  modifications required for parameters that define the advective mass transfer between the two pore regions to have a consistent representation in both approaches.  4.8.2.1 Simulation 3: HYDRUS-1D dual-porosity with advective solute transfer between the two pore regions  Simulation 3 is a 1D transient dual-porosity problem with a specified flux (Cauchy) boundary condition of 50 cm/d (at z = 40 cm) and a specified pressure head (Dirichlet) boundary condition on the outflow (z = 0 cm). Water was exclusively applied on the mobile pore region at the surfacce. The hydraulic function properties of the the mobile and immobile pore regions were described using van Genuchten functions (van Genuchten, 1980). The hydraulic parameters of mobile and immobile regions are representative of relatively coarse and fine-grained soil material, respectively. The porosity is set to 0.025 (weighed by wf = 0.05) in the mobile region and 0.475 (weighed by 1- wf) in the immobile pore region. The domain is discretized into 325 cells.  Water flows exclusively in the mobile region in the z-direction and the transport process within the mobile region is advection in the vertical direction. The soil function parameters for each pore region, boundary condition, and initial condition for flow and transport are given in Table 4.2. The water-transfer coefficient characterizing advective solute exchange between the mobile and immobile zones of the matrix domain (ω) (i.e. water transfer coefficient in dual-porosity model with mass transfer driven by the pressure head gradient in HYDRUS-1D) is given in Table 4.3. This parameter must be set equal to the saturated hydraulic conductivity of the interface (Ka) in the dual-permeability model (Simulation 4), which is equal to 0.01 cm/d to  113  have the same advective mass transfer in both simulations. The chemical system consists of one conservative component.  4.8.2.2 Simulation 4: HYDRUS-1D dual-permeability mimicking dual-porosity with advective solute transfer between the two pore regions Simulation 4 is a 1D transient dual-permeability problem with a specified-flux (Cauchy) boundary condition of 50 cm/d (at z = 40 cm) and a specified-pressure head (Dirichlet) boundary condition on the outflow (z = 0 cm). Water was exclusively applied on the preferential-flow pore region at the surface. The hydraulic function properties of the preferential-flow and matrix pore regions were described using van Genuchten functions (van Genuchten, 1980). The hydraulic parameters of preferential-flow and matrix regions are representative of relatively coarse- and fine-grained soil material, respectively. The porosity is set to 0.5 in the preferential-flow region and 0.5 in the matrix pore region. The domain is discretized into 325 cells.   The saturated hydraulic conductivity (Ks) of the preferential-flow region is set to a very small value (1×10-15 m/s) to mimic the dual-porosity model; thus, there is water flow exclusively in the preferential-flow region in the z-direction. The transport process within the preferential-flow region is advection in the vertical direction. The soil function parameters for each pore region, boundary condition, and initial condition for flow and transport are given in Table 4.2. The chemical system consists of one conservative component.   114  4.8.2.3 Results  The advective solute mass transfer rate, in both dual-porosity and dual-permeability approaches, have the same equation (Γ𝑤 × 𝑐∗). The Γ𝑤 parameter is the water transfer rate between the two domains and 𝑐∗ is the concentration of conservative component in either one of the domains that has the higher hydraulic head. In the dual-porosity model, Γ𝑤 is calculated using equation 4-3. In the dual-permeability model, Γ𝑤 is calculated using equations 4-9 and 4-10. To make the dual-permeability and dual-porosity models give the same advective solute mass transfer between the two pore domains, Γ𝑤 (i.e. Γ𝑤 =𝛽𝛾𝑤𝑎2(ℎ𝑓 − ℎ𝑚)) is required to be the same for both simulations (i.e. equations 4-3 and 4-9 must give the same result). For this purpose, parameters a, β, and γw are required to be set to be equal to one in the dual-permeability model.  Figures 9-13 demonstrate the concentration of tracer, solute transfer rate, pressure head, water content, and water transfer rate for output times of 0.01, 0.04 and 0.08 days. The results from simulations 3 and 4, with only advective solute transfer between the two pore regions, show very good agreement. The comparison of between the two simulations results indicates that the dual-permeability model, with only advective mass transfer between the two pore regions, degenerates to the dual-porosity model in HYDRUS-1D code.   115   Figure 4.7.  HYDRUS-1D: The pink plot: concentration of tracer in mobile domain using dual-porosity (mobile-immobile, head mass transfer) with zero diffusive mass transfer and only advective mass transfer between the two pore regions. The blue plot: concentration of tracer in preferential-flow region using dual-permeability (no flow in matrix to mimic dual-porosity) with zero diffusive mass transfer and only advective mass transfer between the two pore regions.   116   Figure 4.8. HYDRUS-1D: The pink plot: solute mass transfer rate of tracer between mobile and immobile domains using dual-porosity (mobile-immobile, pressure head mass transfer) with zero diffusive mass transfer and only advective mass transfer between the two pore regions. The blue plot: solute mass transfer rate of tracer between the preferential-flow region and matrix using dual-permeability (no flow in matrix to mimic dual-porosity) with zero diffusive mass transfer and only advective mass transfer between the two pore regions.   117   Figure 4.9. HYDRUS-1D: The blue plot: pressure head in mobile domain using dual-porosity (mobile-immobile, pressure head mass transfer) with zero diffusive mass transfer and only advective mass transfer between the two pore regions. The pink plot: pressure head of tracer in preferential-flow region (also called fracture) and matrix domains using dual-permeability (no flow in matrix to mimic dual-porosity) with zero diffusive mass transfer and only advective mass transfer between the two pore regions.   118   Figure 4.10. HYDRUS-1D: The blue plot: water content in mobile and immobile domains using dual-porosity (mobile-immobile, pressure head mass transfer) with zero diffusive mass transfer and only advective mass transfer between the two pore regions. The pink plot: water content in preferential-flow region (also called fracture) and matrix using dual-permeability (no flow in matrix to mimic dual-porosity) with zero diffusive mass transfer and only advective mass transfer between the two pore regions.   119   Figure 4.11. HYDRUS-1D: The blue plot: water mass transfer rate of tracer between mobile and immobile domains using dual-porosity (mobile-immobile, pressure head mass transfer) with zero diffusive mass transfer and only advective mass transfer between the two pore regions. The pink plot: water mass transfer rate of tracer between the preferential-flow region (also called fracture) and matrix using dual-permeability (no flow in matrix to mimic dual-porosity) with zero diffusive mass transfer and only advective mass transfer between the two pore regions.  4.8.3 Verification scenario C)  This verification scenario consists of two simulations: simulations 5 and 6, using dual-permeability model mimicking dual-porosity, set up in MIN3P-THCm-DP and HYDRUS-1D codes, respectively. The objective of this verification scenario is to compare the two simulations, to check the simplification of the dual-permeability model to the dual-porosity model in MIN3P-THCm-DP and HYDRUS-1D codes, with both diffusive and advective solute transport between the two pore regions switched on.   120  4.8.3.1 Simulation 5: MIN3P-THCm-DP dual-permeability mimicking dual-porosity with advective mass transfer between the two pore regions Simulation 5 is a 1D transient dual-permeability mimicking dual-porosity problem with a specified-flux (Cauchy) boundary condition of 50 cm/d (at z = 40 cm), and a specified-pressure head (Dirichlet) boundary condition on the outflow (z = 0 cm). Water was exclusively applied on the preferential-flow region at the surfacce. The hydraulic function properties of preferential-flow and matrix regions were described using van Genuchten functions (van Genuchten, 1980). The hydraulic parameters of the preferential-flow and matrix regions are representative of relatively coarse and fine-grained soil material, respectively. The porosity is set to 0.5 in the preferential-flow region and 0.5 in the matrix pore region. The domain is discretized into 325 cells.   The saturated hydraulic conductivity (Ks) of the preferential-flow region is set to a very small value (1×10-15 m/s) to mimic the dual-porosity model; thus, water flows exclusively in the preferential-flow region in the z-direction. The transport process within the preferential-flow region is advection in the vertical direction. The soil function parameters for each pore region, boundary condition, and initial condition for flow and transport are given in Table 4.2. We assume rectangular aggregates (β = 3) with an average matrix block size of 2 cm (a = 1 cm). The γw parameter was set to 0.4 as suggested by (Gerke and van Genuchten, 1993b). The wf  parameter is set to 0.05 (Table 4.3). The apparent hydraulic conductivity of the transfer term was calculated using 𝐾𝑎 = 0.5[𝐾𝑎(ℎ𝑓) + 𝐾𝑎(ℎ𝑚)]. The hydraulic parameters for the transfer term were assumed to be the same as for the matrix, except for the saturated  121  hydraulic conductivity which was decreased by a factor of 100 (Gerke and van Genuchten, 1993a). The chemical system consists of one conservative component.  4.8.3.2 Simulation 6: HYDRUS-1D dual-permeability with no mass transfer between the two pore regions Simulation 6 and simulation 5 have similar parameters, boundary conditions, and initial conditions. These parameters include soil hydraulic functions, and water and solute transfer parameters between the two pore regions, as shown in Table 4.2 and Table 4.3. The only difference is that this simulation is set up in HYDRUS-1D code.   4.8.3.3 Results One of the main differences between this verification scenario and the verification scenarios A and B is that, in this scenario both simulations are set up in the dual-permeability model and therefore the water content in both simulations is weighed by the wf  parameter. wf is equal to 0.05 in both simulations. Therefore, the water contents for the two separate pore regions (matrix and preferential flow) are implemented in MIN3P-THCm-DP code to be described in terms of the bulk soil volume, i.e. θ = wfθf + (1-wf) θm.  The pressure head and water content for both cases are shown in Figure 4.12 and Figure 4.13, respectively. Figure 4.14 shows the water transfer rate for both codes at 0.08 day output time. The concentration plot is shown in Figure 4.15. Overall, there is very good agreement between the two codes. Slight differences are observed in water-transfer term results. The  122  reason for this discrepancy is the differences in the time stepping. There are also slight differences in concentration plots.    Figure 4.12. HYDRUS-1D: The blue plots: pressure head in matrix and preferential-flow (also named fracture) domains using dual-porosity (pressure head mass transfer) with advective and diffusive solute transfer between the two pore regions. MIN3P-THCm-DP: The pink plots: pressure head in preferential-flow region (also named fracture) and matrix using dual-porosity (dual-permeability with no flow in matrix to mimic dual-porosity) with advective and diffusive solute transfer between the two pore regions.   123   Figure 4.13. HYDRUS-1D: The blue plots: water content in matrix and preferential-flow region (also named fracture) using dual-porosity (pressure head mass transfer) with advective and diffusive solute transfer between the two pore regions. MIN3P-THCm-DP: The pink plots: water content in the preferential-flow region (also named fracture) and matrix using dual-porosity (dual-permeability with no flow in matrix to mimic dual-porosity) with advective and diffusive solute transfer between the two pore regions.   124   Figure 4.14. HYDRUS-1D: The blue plot: water transfer rate between the two pore regions of matrix and preferential-flow region (also named fracture) using dual-porosity (pressure head mass transfer) with advective and diffusive solute transfer between the two pore regions. MIN3P-THCm-DP: The pink plots: water transfer rate between the two pore regions of preferential-flow region (also named fracture) and matrix using dual-porosity (dual-permeability with no flow in matrix to mimic dual-porosity) with advective and diffusive solute transfer between the two pore regions.   125   Figure 4.15. HYDRUS-1D: The blue plot: concentration of tracer in matrix and preferential-flow region (also named fracture) using dual-porosity (pressure head mass transfer) with advective and diffusive solute transfer between the two pore regions. MIN3P-THCm-DP: The pink plots: concentration of tracer in preferential-flow region (also named fracture) and matrix using dual-porosity (dual-permeability with no flow in matrix to mimic dual-porosity) with advective and diffusive solute transfer between the two pore regions.  4.8.4 Verification scenario D)  This verification scenario consists of two simulations: simulations 7 and 8, using the dual-permeability model set up in MIN3P-THCm-DP and HYDRUS-1D codes, respectively. The objective of this verification scenario is to compare two simulations, to check the dual-permeability model in MIN3P-THCm-DP and HYDRUS-1D codes with both diffusive and advective solute transport between the two pore regions. In this scenario, water flow and solute transport occurs in both preferential-flow and matrix pore regions.   126  4.8.4.1 Simulation 7: MIN3P-THCm-DP dual-permeability with diffusive and advective solute transfer between the two pore region Simulation 7 is a 1D transient dual-permeability problem with a specified flux (Cauchy) boundary condition of 50 cm/d (at z = 40 cm) and a specified pressure head (Dirichlet) boundary condition on the outflow (z = 0 cm). Water was exclusively applied on the preferential-flow pore region at the surface. The hydraulic function properties of preferential-flow and matrix regions were described using van Genuchten functions (van Genuchten, 1980). The hydraulic parameters of the preferential-flow and matrix regions are representative of the relatively coarse and fine-grained soil material, respectively. The porosity is set to 0.5 in the preferential-flow region and 0.5 in the matrix pore region. The domain is discretized into 325 cells.   The saturated hydraulic conductivity (Ks) of the preferential-flow region is set to 1.0526 cm/d to represent a slower water flow in a finer-grained porous medium; thus, there is water flow in both the preferential-flow and the matrix regions in the z-direction. The transport process within the preferential-flow and matrix regions is advection in the vertical direction. The parameters for soil function in each pore region, the boundary condition, and initial condition for flow and solute transport are given in Table 4.2. We assume rectangular aggregates (β = 3) with an average matrix block size of 2 cm (a = 1 cm). The γw parameter was set to 0.4 as suggested by Gerke and Genuchten (1993b). The wf  parameter is set to 0.05 (Table 4.3). The apparent hydraulic conductivity of the transfer term was calculated using 𝐾𝑎 = 0.5[𝐾𝑎(ℎ𝑓) + 𝐾𝑎(ℎ𝑚)]. The hydraulic parameters for the transfer term were assumed to be the same as for the matrix, except for the saturated hydraulic conductivity, which was  127  decreased by a factor of 100 (Gerke and van Genuchten, 1993a). The chemical system consists of one conservative component.  4.8.4.2 Simulation 8: HYDRUS-1D dual-permeability with diffusive and advective solute transfer between the two pore regions Simulation 8 and simulation 7 have similar parameters, boundary conditions, and initial conditions. These parameters include soil hydraulic functions, and water and solute transfer parameters between the two pore regions, as shown in Table 4.2 and Table 4.3. The only difference is that simulation 8 is set up in HYDRUS-1D code.  4.8.4.3 Results In this verification scenario both simulations are set up in the dual-permeability model and therefore the water content in both simulations is weighed by the wf  parameter. wf is equal to 0.05 in both simulations. Therefore, the water contents for the two separate pore regions (matrix and preferential flow) are implemented in MIN3P-THCm-DP code to be described in terms of the bulk soil volume, i.e. θ = wfθf + (1-wf) θm. Water flow and solute transport occur in both pore regions.  The pressure head and water content for both cases are shown in Figure 4.16 and Figure 4.17, respectively. Figure 4.18 shows the water transfer rate for both codes at 0.01 d, 0.04 d and 0.08 day output times. The concentration plot is shown in Figure 4.19. Overall, there is very good agreement between the two codes. Slight differences are observed in water transfer term results and concentration plots. The reason for the discrepancy is the oscillatory solution  128  that HYDRUS produces. MIN3P delivers a stable solution that provides confidence in the adequate implementation of the equations.     Figure 4.16. HYDRUS-1D: The dash line plots: pressure head in matrix and preferential-flow region (also named fracture) using dual-permeability with advective and diffusive solute transfer between the two pore regions. MIN3P-THCm-DP: The line plots: pressure head in preferential-flow region (also named fracture) and matrix using dual-permeability with advective and diffusive solute transfer between the two pore regions.   129   Figure 4.17. HYDRUS-1D: The dash line plots: water content in matrix and preferential-flow region (also named fracture) using dual-permeability with advective and diffusive solute transfer between the two pore regions. MIN3P-THCm-DP: The line plots: water content in the preferential-flow region (also named fracture) and matrix using dual-permeability with advective and diffusive solute transfer between the two pore regions.   130   Figure 4.18. HYDRUS-1D: The dash line plots: water transfer rate between the matrix and preferential-flow regions (also named fracture) using dual-permeability with advective and diffusive solute transfer between the two pore regions. MIN3P-THCm-DP: The line plots: water transfer rate between the matrix and preferential-flow region (also named fracture) using dual-permeability with advective and diffusive solute transfer between the two pore regions.   131   Figure 4.19. HYDRUS-1D: The dash line plots: concentration of tracer in matrix and preferential-flow region (also named fracture) using dual-permeability with advective and diffusive solute transfer between the two pore regions. MIN3P-THCm-DP: The line plots: concentration of tracer in preferential-flow region (also named fracture) and matrix using dual-permeability with advective and diffusive solute transfer between the two pore regions. F: is the abbreviation for fracture or preferential-flow region; and, M: is the abbreviation for matrix.  4.9 Summary A multi-component non-uniform flow and reactive transport model named MIN3P-THCm-DP was developed based on the existing MIN3P and MIN3P-THCm codes. This new model includes mobile-immobile, dual-porosity and dual-permeability in one-dimensional porous media systems. This model has the capability of simulating variably-saturated flow conditions in either steady-state/transients in addition to multi-component reactive transport in both preferential-flow region and matrix in dual-systems. The mass transfer between the  132  two pore regions is set as a first order mass transfer term. The accuracy of the code is successfully verified against the established code, HYDRUS-1D.    133  Chapter  5: Evaluation of Uniform and non-Uniform Flow and Solute Transport Models for Simulating Tracer Transport in Mine Waste Rock    5.1 Introduction Mining activities produce two types of waste streams: (1) uniformly-graded and fine-grained tailings and (2) non-uniformly-graded and often coarse-grained waste rock that consists of barren rock and below-grade ore material removed from open-pit operations. Waste rock is placed in piles with height ranging from tens to over 500 m either by end-dumping or push-dumping in several lifts which results in particle size grading in the piled waste rock. Normally, the finer-grained materials accumulate near the top of each lift that is later compacted by trucks to create a traffic surface. Coarser rock pieces and boulders preferentially accumulate at the bottom of the pile and create a rubble zone, imposing an increase in permeability towards the bottom of the pile. The complexity in the structure and variability in grain sizes can create zones with variable water transfer velocity within the waste rock that potentially lead to preferential flow. Unsaturated conditions that are typically present in the mine waste rock piles may also introduce further complexities. To improve the prediction of discharge volumes, concentrations and mass loadings, development of a sound understanding of flow and solute transport regime within the waste pile is necessary. This contributes directly to successful assessment of chemical evolution and temporal variations in water treatment needs.  134  The complexity of understanding the dynamics between flow, solute transport and chemical processes in the heterogeneous and macroporous mine waste rock originates from the coupled nature of these processes, making it impossible to characterize chemical evolution of pore water without understanding the nature of flow and solute transport.  The transport rate and concentration of solutes at the discharge point are affected by the flow regime within the waste rock pile. Water flow in an unsaturated waste rock pile is comprised of matrix flow and preferential flow. Richards equation has been found to be applicable to both the flow in the fine-grained matrix and the preferential (or macropore) flow in the coarse-grained material. Preferential flow can be modelled using three different dual-domain approaches including the mobile-immobile approach, the dual-porosity approach (modified mobile-immobile) and the dual-permeability approach. Among the approaches suggested for the mass-transfer term, Gerke and van Genuchten (1993) have presented a first-order algebraic approximation of the inter-domain water transfer (Γ𝑤) and mass transfer (Γ𝑠)  (e.g. Gerke and van Genuchten, 1993b, 1996). Preferential flow may cause the infiltration to bypass parts of the waste rock pile and may result in rapid solute transport to greater depths. The proportionality of preferential to matrix flow depends on several parameters including- but not limited to- the physical properties of waste rock such as particle size distribution (PSD) and hydrological conditions particularly the timing and magnitude of precipitation and infiltration events (Amos et al., 2015; Blackmore et al., 2014).  Extensive experimental and numerical modeling studies on the characterization of preferential flow and solute transport processes in structured and macroporous media at different scales can be found in the literature. Tracer tests have been used as the main  135  experimental method to infer preferential flow in soils (Germann et. al 1984, Kohne et al 2009, Beven and Germann, 2013). Numerical advancements include development of physically- based models for preferential flow and application of non-equilibrium solute transport to structured soils (Gerke, 2006; Jarvis, 2007; Simunek and van Genuchten, 2008; Simunek et al., 2003). In contrast, studies targeting understanding and modeling of preferential flow and solute transport in mine waste rock have been limited. There is still uncertainty in selection of the most representative flow model approach to capture the preferential characteristics of flow, solute transport and chemical processes in mine waste rock.   In this chapter, the results of a detailed comparative study of different numerical modeling approaches for simulating water flow and conservative solute transport through waste rock in an experimental waste rock pile in Antamina Mine, Peru are presented. The modeling approaches include uniform, mobile-immobile, dual-porosity and dual-permeability flow and solute transport. Please refer to Chapter 4 for the details on the implementation and verification of these modeling approaches in the existing reactive transport code MIN3P (Mayer et al., 2002). The current study builds on the previous modeling study of tracer transport in mine waste rock at the Antamina site conducted by Blackmore et al. (2014) for Piles 4 and 5. Blackmore et al.’s approach focused on using uniform and mobile-immobile modeling approaches at the column and experimental pile scales. The objectives of the current study are: 1) evaluate the suitability of uniform- and non-uniform flow and transport modeling approaches to reproduce measured discharge rates, concentrations and mass loadings from waste rock constrained by data from a conservative tracer test, 2) identify and  136  constrain the most sensitive parameters controlling flow rates, concentrations and mass loadings for each method, 3) identify and constrain sensitive parameters that are common to several or all methods, and 4) determine limitations of the approaches in reproducing field observations and evaluate reasons for the observed discrepancies. Extensive numerical modeling was conducted and selected simulation results are presented here to demonstrate the fundamental aspects of sensitivity of tracer breakthrough to spatial arrangement of preferential flow and matrix pore regions and solute transport parameters. A general schematic diagram of preferential flow stages are demonstrated in Figure 5.1.    Figure 5.1. The schematic diagram of the preferential and matrix flow phases in porous medium   137  5.2 Material and Methods 5.2.1 The Antamina Mine Waste Rock Research Site The Antamina Mine is located approximately 270 km northeast of Lima, Peru, with high-altitude Andean climate (between 4200 and 4700 m.a.s.l.) and mean annual temperature of 5.4-8.5 ͦ C. The average annual precipitation of 1200-1500 mm rainfall occurs mostly during a distinct wet season between October and April. Five instrumented experimental 36 m (l) × 36 m (l) × 10 m (h) waste rock piles (named Piles 1 to 5) were constructed at the mine site using the run-of-mine waste rock, dedicated to study the physical and chemical processes controlling drainage and mass loadings from mine waste rock (Peterson, 2014). Approximately 20,000-25,000 tonnes of waste rock were placed in each pile by end-dumping in three tipping phases, described in detail in Bay et al. (2009) and Hirsche et al. (2012). The waste rock was placed on a basal 1.5 m protective layer and three sloped layers (37 ͦ angle) of waste rock called tipping phases (Figure 5.2a). There are variations between the particle size distribution and material type between the tipping phases as each one came from a distinct zone of the mine (Peterson et al., 2012). The base of each pile is covered with a 36 m × 36 m impermeable geomembrane (Lysimeter D) and three smaller 4 m × 4 m interior Sub-lysimeters (named Sub-lysimeters A, B and C), illustrated in Figure 5.2.   All drainage from the piles is collected by the basal lysimeters and then conveyed to four tipping bucket flow meters, which provide continuous monitoring of flow rates. Each pile consists of several tipping phases (TP1, TP2 and TP3 in case of Pile 2 (Figure 5.2)). In this chapter, the monitoring data of Pile 2 Sub-lysimeter B is used for comparison with simulation results. The soil column above Sub-lysimeter B is called tipping phase 1 (TP1)  138  and is about 10m high. Pile 2 is classified as Class A intrusive waste rock based on Antamina’s waste rock classification system.  Please note that in Chapter 3, the data from lysimeter D was used to study the overall flow behavior of Pile 2 as it collects 97% of the total outflow. The solute transport, however, was found to be complex such that it could not be represented by simple single porosity model. This complexity requires utilizing preferential flow models that were developed and verified in Chapter 4. The drainage from all tipping phases of Pile 2 is collected and mixed in Lysimeter D. However, sub-lysimeters A, B and C collect drainage from either an individual tipping phase or two tipping phases at the most, and consequently their data is representative from drainage of the waste rock column directly above them without significant basal mixing of various flow paths-assuming vertical flow. To validate the applicability of the developed preferential flow models for conservative solute transport in the pile, the data of tracer concentration collected from sub-lysimeter B was selected for this study. The assumption of vertical flow is supported by the low bromide mass recovery from sub-lysimeter P2C located at the front of Pile 2 under the batter, where no tracer was applied directly above it (Figure 5.2). Therefore, sub-lysimeter C was not a good option for the purpose of this study, and either sub-lysimeters B or A could be used.   5.2.2 Tracer experiment description To gain insight into transport processes, conservative lithium bromide tracer with a concentration of 1895 mg/L of bromide was applied to the crown (flat surface at the top) of pile 2 (see Figure 5.2). Bromide was initially selected as tracer mainly because of its low tendency for sorption (Bowman, 1983)  which was later confirmed by laboratory experiments  139  on Pile 2 waste rock materials (Peterson, 2014). Bromide tracer was applied using a sprinkler system on Pile 2 on January 20, 2010 for 4.5 hours at a rate of 6 mm/hr, corresponding to a five-year rainfall precipitation event at the Antamina Mine site. Tracer samples were collected from pile outflow at time intervals that varied from 15 minutes (immediately following tracer application) to weekly. The sprinkler system was adjusted to obtain uniform distribution of tracer on the surface of the pile confirmed by the monitoring results of measuring cups placed at regular intervals on the crown throughout tracer application (Peterson, 2014). Surface run off was not observed during the time of tracer application; although some ponding could be seen, especially close to the berm. Ponded water subsequently infiltrated into the pile (Peterson, personal communication).  140    Figure 5.2. a) Schematic illustration of instrumentation lines, L1 to L6, Lysimeter D and Sub-lysimeters A, B, and C; b) Side view of experimental waste rock Pile 2 shows the three tipping phases (TP1, TP2 and TP3), Lysimeter D and Sub-lysimeters A, B and C and instrumentation lines, L1, L2 an L4; c) Application of bromide tracer using sprinkler system on the crown of the pile (all figures from Peterson, 2014).   5.2.3 Modeling approach  Unsaturated flow and tracer transport through waste rock is simulated using the MIN3P code (Mayer et al., 2002). MIN3P is a 3D finite-volume multicomponent reactive transport code  141  for variably-saturated porous media, that uses the global implicit method (GIM) to solve fully coupled transport and reaction governing equations. MIN3P applies the representative elementary volume (REV) approach for representing physiochemical attributes (Henderson, 2009).   An extension, named MIN3P-THCm-DP, was developed for simulation of the non-uniform flow and solute transport conditions including mobile-immobile, dual-porosity and dual-permeability approaches, all based on the Richards equation (Gerke and Genuchten, 1993a, 1993b). Details about the development and verification of the non-uniform flow capabilities are presented in Chapter 4 of this thesis.  5.2.4 Conceptual models  The conceptual models used in the current study are shown schematically in Figure 5.3. In addition to the uniform flow and solute transport models, we used dual-domain approaches in which the porous medium consists of two co-existing regions (Kohne et al., 2009): a preferential flow region with fast flow paths and a matrix pore region with lower or zero hydraulic conductivity. The multi-year transient recharge estimated from precipitation and evaporation data collected at Pile 2 was applied as inflow boundary condition to all models. The conceptual models for each set of simulations are:  Uniform-flow Model: In this conceptual model, the porous medium consists of a single domain and the recharge is applied on the whole domain, as shown in Figure 5.3a. Water flow and solute transport occur in a spatially uniform and single-porosity domain.   142  Mobile-immobile Model: In this conceptual model, the porous medium consists of two pore regions of mobile and immobile as shown in Figure 5.3b, and water flow and solute transport only occur within the mobile region. The immobile region initially takes in the tracer by diffusion from the mobile domain. The immobile region retains the tracer and later releases it back to the mobile region based on the concentration gradient between the two regions. The transient inflow boundary condition is applied only on top of the mobile region. In the mobile-immobile model, the only exchange between the two pore regions is diffusive transfer of tracer; i.e. the water transfer term between the regions is set to zero.   Figure 5.3. Conceptual models for water flow and solute transport in uniform and non-uniform flow models. Applied recharge condition are shown using the vertical light blue arrow atop each column. Water flow in the column is shown using the vertical dark blue arrow and tracer transport is represented by the vertical red arrow. The water transfer between the two pore regions is demonstrated by the horizontal dark blue arrow. The solute mass transfer between the two pore regions is represented by the horizontal red arrow. Dual-perm.: is the abbreviation for dual-permeability model, and P.F. is abbreviation for the preferential flow pore region.    143  Dual-porosity Model: In this conceptual model, the porous medium is composed of two pore regions of preferential flow and matrix, as shown in Figure 5.3c.  In comparison to the mobile-immobile model, the dual-porosity model has a first-order water transfer rate that controls the water flow between the preferential flow and matrix regions. Otherwise, the dual-porosity model is identical to the mobile-immobile model. The solute transfer between the two pore regions occurs via both molecular diffusion and advection (Simunek and van Genuchten, 2008). Recharge is applied only on top of the preferential flow region.  Dual-permeability 1 Model (100% of Recharge on Preferential Flow Region): In the dual-permeability conceptual model, the porous medium consists of two pore regions of preferential flow and matrix, as shown in Figure 5.3d. Water flow and solute transport can occur through both regions. In this conceptual model, the recharge is applied exclusively on top of the preferential flow region. The first-order mass transfer term between the two regions includes advection and/or diffusion. The water transfer and solute mass transfer terms determine the distribution of the water and solute in each pore region. Setting the water transfer and solute transfer terms to zero reduces the model to two uniform flow and solute transport regions with no interaction.   Dual-permeability 2 Model (100% of Recharge on Matrix Region): This conceptual model is identical to the dual-permeability 1 model with the difference that the recharge is only applied on top of the matrix region instead of the preferential flow region, as shown in Figure 5.3e.    144  Dual-permeability 3 Model (Recharge on both Matrix and Preferential Flow Regions): This conceptual model is identical to the dual-permeability 1 and 2 models with the difference that recharge is now applied on top of both preferential flow (𝑞𝑖𝑛𝑓−𝑃𝐹 = 55% of the recharge) and matrix (𝑞𝑖𝑛𝑓−𝑀 =45% of the recharge) regions, as shown in Figure 5.3f. The proportionality ratios of 55% and 45% were selected based on comparison of the modelled recovered tracer with field measurement.   5.2.5 Parameter estimation, initial and boundary conditions Parameter estimation for preferential flow models is challenging due to large number of parameters required for each pore region and interface, and lack of measurement methods especially in field scale studies (Arora et al., 2012; Jarvis et al., 2009; Köhne and Mohanty, 2005). Parametrization is even more difficult for heterogeneous material such as mine waste rock. The tipping phase 1 (TP1) in Pile 2 consists of two-internal layers composed of sub-tipping phases D1A and D1B each contributing 69% and 31% of the total waste rock volume in TP1, respectively (Personal communication with H. Peterson, 2018). The soil hydraulic parameters of sub-tipping phase 1 (D1A) were assigned to the simulated soil column. Figure 1.4a shows the particle size distribution of Pile 2 D1A.  The particle size fraction that controls the capillary flow in soil is the fraction which is finer than 4.75 mm (Yazdani et al., 2000).   In Figure 5.4, the blue diamonds show the measured PSD for Pile 2 D1A material. The particle size analysis was performed for above #200 mesh (0.074 mm) particle size. To estimate the PSD finer than 0.074 mm and identify soil class using USDA soil classification  145  triangle (Brown, 2003) shown in Figure 5.4, two methods are available. The first method (shown with (1) in Figure 5.4a) was used by Blackmore et al., (2014) and is based on “renormalizing PSD results to particles passing the #4 sieve (i.e., < 4.75 mm) and apportioning the renormalized volumes to sand-silt clay fractions”. Applying the first method, the PSD obtained for Pile 2 D1A shifts and scales as shown in Figure 5.4a by an arrow from the blue diamonds to the red circles. The second approach (shown with (2) in Figure 5.4a) is to extrapolate the trend of the data-points representing material finer than 10mm fraction size in PSD curve. In Figure 5.4a, the section of the measured data used for extrapolation is shown including the regression curve, the regression equation and the coefficient of determination (𝑅2 = 0.9999). Using the obtained regression equation, the PSD for sand, silt and clay is determined using the Wentworth grain size chart (4.75mm > sand > 0.62mm > silt > 0.004mm > clay > 0.001mm) (Wentworth, 1922), shown with white diamonds in Figure 5.4a. The second approach is used in this study. Applying these percentages to the USDA soil classification triangle (Brown, 2003) (Figure 5.4b), the Pile 2 D1A sub-tipping phase is classified as a sandy-loam.    146   Figure 5.4. a) Particle size distribution for Pile 2 sub-tipping phase 1 (D1A), the missing fine fraction is estimated  using two methods: (1) the red circles show results for method used by Blackmore et al., (2014), (2) the blue and white diamonds show results obtained with  the method of extrapolation of the PSD tail; b) Texture of the waste rock of Pile 2 sub-tipping phase 1 (D1A) represented over USDA soil texture triangle classes for the fine-grain particles (<4.75 mm size fraction). The blue circle shows the texture of the bulk material (sandy-loam). The texture of preferential flow (sand) and matrix (clay-loam) regions used in the conceptual models in this study are shown with pink and green colored areas on the triangle, respectively.  In Chapter 3, the sandy-loam material was selected for the bulk soil and the hydraulic parameters were calibrated for the uniform-flow single-porosity model using the drainage data collected from basal Pile 2 Lysimeter D (Javadi et al., 2012). For details on methodology and results please refer to Chapter 3. In this chapter, for preferential flow simulations two sets of soil hydraulic parameters were required for preferential flow and matrix pore regions instead of bulk parameters for sandy-loam soil. The parameters derived for preferential flow region and matrix represent a relatively coarse-grained, and fine-grained (1) (2)  147  soil, respectively. Since, the bulk soil was identified as sandy-loam, the preferential flow region and matrix were assumed to be represented best by sand and clay-loam, respectively (Figure 5.4b and Table 5.1).   Table 5.1. Parametrization and sensitivity analysis of uniform and preferential flow models, PF: Preferential Flow pore region, NA: Not Applicable. Conceptual Models Main Analysis Sensitivity Analysis Parameters PF Matrix Uniform flow NA Sand NA Mobile-immobile Sand Clay loam 𝐷𝑎, 𝐾𝑠𝑎, 𝑤𝑓 Dual-porosity Sand Clay loam 𝐷𝑎, 𝐾𝑠𝑎, 𝑤𝑓 Dual-permeability 1 Sand Clay loam 𝐷𝑎, 𝐾𝑠𝑎, 𝑤𝑓, 𝑞𝑖𝑛𝑓 Dual-permeability 2 Sand Clay loam 𝐷𝑎, 𝐾𝑠𝑎, 𝑤𝑓, 𝑞𝑖𝑛𝑓 Dual-permeability 3 Sand Clay loam 𝐷𝑎, 𝐾𝑠𝑎, 𝑤𝑓, 𝑞𝑖𝑛𝑓  The soil hydraulic literature parameters for sand and clay-loam (Table 5.1) were obtained from the Soil Catalog of the HYDRUS-1D code (Simunek and van Genuchten, 2008; Simunek et al., 2012), which were adapted from Carsel and Parrish, (1988) for the van Genuchten model (van Genuchten, 1980) . The soil parameters include 𝑆𝑟 (residual saturation of aqueous phase), 𝐾𝑠 (saturated hydraulic conductivity), soil hydraulic function parameters, 𝛼, 𝑛, and 𝑚, where 𝑚 = 1 −1𝑛 (Table 5.2). For parameters of the mass transfer terms, the average matrix block size of 2 cm (a = 1 cm), geometrical factor β = 3 and scaling factor of γw = 0.4 were considered (Gerke and van Genuchten, 1993a, 1993b).    148  Table 5.2. Hydraulic parameters used in uniform and non-uniform (preferential) flow simulations Parameter Porosity 𝑺𝒓 α 𝒏 𝑰 𝑲𝒔 Unit [-] [-] [1/m] [-] [-] [m/s] Mobile/ Preferential Flowa 0.34cX 𝑤𝑓d 0.1047 14.5 2.68 0.5 1.65×10-4 Immobile/ Matrixb 0.34c X (1-𝑤𝑓) 0.232 1.9 1.31 0.5 1.44×10-6e a Hydraulic parameters of sand were used for the entire domain in uniform flow model (single porosity) model and for the mobile/preferential flow regions in the preferential flow models  b Hydraulic parameters of clay-loam were used for immobile/matrix region c Porosity data from Javadi et al. (2012) d 𝑤𝑓 (volumetric weighting factor):  total volume of fracture pore system per volume of the medium e𝐾𝑠 : saturated hydraulic conductivity for the immobile region was set to 1×10-15 m/s  The initial condition for variably saturated flow was set consistently in all models to a hydraulic head of -10m for the whole domain relative to the bottom of the column, extending from the base to the top of the column, and representing relatively dry initial conditions. The variably saturated flow simulations started at the start of pile construction in August 2007 (907 days before tracer application). The tracer was applied on Pile 2 in the middle of the wet season 2009-2010. The wet season in 2009-2010 started mid-October 2009 and finished at the end of April 2010. As a result, there were rainfall events that occurred before the start of the tracer test and the waste rock material had already wet-up for the season. At the time of tracer release in the model, the water content in the pile and the outflow rate were representative for typical wet season conditions (Javadi et al., 2012). The initial condition for transport in all models was set to bromide concentration reflecting background concentrations in the waste rock (0.2-0.8 mg/L) (Blackmore et al., 2014).   149   The inflow boundary condition for variably saturated flow was assigned as specified flux (Neumann) boundary condition (Table 5.3). The specified flux was equal to the daily recharge estimated as a fraction of daily precipitation measured at the UBC weather station located in close proximity to Pile 2. For details of recharge estimation refer to Chapter 3. The inflow boundary condition for solute transport was assigned as specified mass flux (Cauchy) (Table 5.3). This mas flux had low bromide concentration for the entire six-year period of simulation except for 4.5 hours on day 907 (January 20th 2010) when the tracer was applied on Pile 2. The bromide tracer (1895 mg/L) was applied to the surface of the soil column, corresponding to the measured concentration in the solution applied on the pile. The outflow boundary condition was set to a free exit boundary.   The soil columns are modeled as 10m long, 1-D vertical columns discretized into 200 control volumes. The simulation period corresponds to the time from commissioning of Pile 2 to over 2200 days (over six years), using a maximum time step of one day to update the daily transient recharge.   5.2.6 Sensitivity analysis on 𝒘𝒇, 𝑲𝒔𝒂, 𝑫𝒂 and 𝒒𝒊𝒏𝒇 parameters Table 5.1 shows the parameters used for sensitivity analysis for each conceptual model. The 𝐾𝑠𝑎 and 𝐷𝑎 parameters define the water and mass transfer between the preferential flow region and matrix and are difficult to estimate or measure (Gerke and Maximilian Köhne, 2004). To evaluate and identify the appropriate range of values that may explain the observations in the field for each conceptual model, the uncertainty was estimated by a  150  sensitivity analysis on 𝑤𝑓, 𝐾𝑠𝑎 and 𝐷𝑎 parameters.  In a stepwise manner, series of simulations were conducted to investigate the bromide tracer transport in the porous medium (Table 5.1). First, the uniform-flow and solute transport modeling was performed followed by the preferential flow (non-uniform flow) and solute transport models, stepping up the complexity of the models. The preferential flow models started with the mobile-immobile approach and then progressed to dual-porosity, and dual-permeability models. For the dual-permeability approach, three scenario sets (dual-permeability 1, dual-permeability 2 and dual-permeability 3) were simulated by varying distribution of the inflow boundary condition (𝑞𝑖𝑛𝑓) applied to the preferential flow and matrix regions (Table 5.3). In the mobile-immobile model, the water transfer term was set to zero, to make diffusive transfer the only exchange process between the two pore regions. In the remaining non-uniform flow models both water and solute transfer coefficients were adjusted to evaluate their impact on the agreement between field data and simulation results.   Table 5.3. Inflow boundary condition for unsaturated flow and solute transport applied on the surface of mobile/PF and immobile/matrix pore regions. PF: Preferential Flow region, 𝒒𝒊𝒏𝒇: Transient Recharge infiltration as inflow boundary condition Model Flow  Boundary Condition Solute Transport  Boundary Condition Br-1 concentration (mg/L) Mobile/PF Immobile/Matrix Mobile/PF Immobile/Matrix Uniform flow - 𝑞𝑖𝑛𝑓 - 1895 Mobile-immobile 𝑞𝑖𝑛𝑓 - 1895 - Dual-porosity 𝑞𝑖𝑛𝑓 - 1895 -  151  Model Flow  Boundary Condition Solute Transport  Boundary Condition Br-1 concentration (mg/L) Mobile/PF Immobile/Matrix Mobile/PF Immobile/Matrix Dual-permeability 1 𝑞𝑖𝑛𝑓 - 1895 - Dual-permeability 2 - 𝑞𝑖𝑛𝑓 - 1895 Dual-permeability 3 55 % of 𝑞𝑖𝑛𝑓 45% of 𝑞𝑖𝑛𝑓 1895 1895  For each conceptual model, 𝑤𝑓 , 𝐾𝑠𝑎, and 𝐷𝑎 parameters were varied over a wide range for the purpose of sensitivity analysis: 𝑤𝑓 = 0.2, 0.3, 0.4, 0.5 and 0.6, 𝐾𝑠𝑎 = 1×10-2, 1×10-4, 1×10-6, 1×10-8 and 1×10-10 ms-1, 𝐷𝑎 = 1×10-5, 5×10-6, 1×10-6, 5×10-7 and 1×10-7 m2s-1. The  𝑤𝑓 parameter defines the ratio of volumes of the preferential flow region and the total pore system (unitless), 𝐾𝑠𝑎 is the effective saturated hydraulic conductivity (LT-1) of the interface, 𝐷𝑎 is the effective ionic or molecular diffusion coefficient (L2T-1) of the matrix block near the interface, and 𝑞𝑖𝑛𝑓 is the inflow (LT-1)  boundary condition. In total, 725 simulations were conducted.   5.3 Results and Discussion The simulations presented in this chapter serve to show the capabilities of the MIN3P-THCm-DP model for simulating various non-equilibrium flow and solute transport scenarios in a uniform flow (single-porosity), mobile-immobile, dual-porosity, and dual-permeability type waste rock medium. Drainage outflow, bromide concentration, and bromide mass flux  152  for 2200 days (over six-years) in the 10m column were simulated with MIN3P-THCm-DP. The modeling results were compared repeatedly with data collected for outflow, bromide concentration, and bromide mass flux at Pile 2 Sub-lysimeter B to determine the best match. The results demonstrate the sensitivity of each conceptual model to 𝐾𝑠𝑎 and 𝐷𝑎  parameters in the first-order mass transfer terms for water and solute transport.   In the figures depicting bromide concentration, there are four criteria that were compared with the corresponding observed data for validation of the model and estimation of the goodness-of-fit: 1) the “pre-peak” bromide concentration (the concentration of bromide between the time of tracer application and concentration peak), 2) the “peak” concentration of bromide, 3) arrival time of bromide at “peak” concentrations, and 4) shape of the “post-peak” curve (i.e. tail part or draindown part of the curve).   Uniform Flow Model Figure 5.5 presents the field-observed and modeled daily outflow hydrograph, bromide concentration and bromide mass flux for the basal Sub-lysimeter for a time period of over six years. The observed outflow hydrograph shows a strong seasonal pattern with high discharge during the wet season and much reduced discharge during the dry season. This response is also clearly visible in the observed hydrograph (Figure 5.5), which reveals a relatively rapid response of pile outflow to precipitation events.  In the wet season, maximum discharge exceeds 0.008 m3d-1 per surface area of the Sub-lysimeter B, while flows are reduced to less than 0.0005 m3d-1m-2 during the dry season. In this study, a water year is considered to be from July 1st through June 30th, which includes the outflow from that wet season in addition  153  to the draindown in the dry season. The outflow data collected from the pile, exhibits three distinct stages that include: 1) wet-up stage starting at the beginning of each wet season and lasting usually from October to December; 2) peak of the wet season, usually from January to mid-April, and 3) draindown stage, from late-April to September (Peterson, 2014). For the wet-up stage (stage 1), the uniform flow model provides a close match for the two wet seasons starting at 500 and 1200 days, respectively; however, model predictions falls behind for the following two wet seasons starting at 800 and 1900 days. The model predicts a slower draindown in all seasons, which provides evidence for the presence of fast-draining preferential flow paths in the field, which are not represented in the model.  In the field, the bromide concentration increased in the drainage 129 days after tracer application on June 3, 2010 (Peterson, 2014). The hydraulic properties of waste rock were described using the van Genuchten parameters, saturated hydraulic conductivity and residual saturation of sand (Table 5.1 and Table 5.2). The uniform-flow model predicts an earlier arrival of bromide at higher concentrations than observed (Figure 5.5), indicative for tracer uptake into the matrix in the field, a process not considered by the model.  However, the peak concentration occurs at the same time as observed.   The modeled mass loadings for the uniform flow model (Figure 5.5) closely match the observations between 1200-1500 days. These results indicate the dominant role of drainage flux on the mass loadings compared to tracer concentrations. Although the predicted concentration do not provide a good match for several criteria, the mass loadings plot shows an adequate match due to the closes fit in outflow results.  154    Figure 5.5. Uniform-flow model: outflow, bromide concentration and bromide mass flux of Pile 2 sub-lysimeter B drainage for the experimental period since August 2007 (blue line: field observations, red and green line: simulated data).  Preferential Flow (Non-Uniform Flow) Models The results of the sensitivity analysis for the preferential flow simulations are presented in this section. For each conceptual model, the effect of 𝐷𝑎, and 𝐾𝑠𝑎 on the outflow,  155  concentration, and mass flux, is explored separately for five different 𝑤𝑓 values (𝑤𝑓 = 0.2, 0.3, 0.4, 0.5 and 0.6).   5.3.1 Effect of 𝒘𝒇 and 𝑫𝒂 parameters The approach for the sensitivity analysis scenarios on 𝑤𝑓 and 𝐷𝑎 parameters is depicted in Figure 5.6. For each conceptual model, the outflow hydrograph, bromide concentrations and bromide mass flux results are presented for each 𝑤𝑓 value (0.2, 0.3, 0.4, 0.5 and 0.6) and 𝐷𝑎 value (1×10-5, 5×10-6, 1×10-6, 5×10-7 and 1×10-7 m2s-1). The 𝐾𝑠𝑎 parameter for all simulations is kept constant at 𝐾𝑠𝑎 = 1×10-2  ms-1.   Figure 5.6. Sensitivity analysis scenarios to investigate the effect of 𝑫𝒂 parameter on outflow, bromide concentration and bromide mass flux in Pile 2 Lysimeter B drainage.  5.3.1.1 Mobile-Immobile Approach The outflow hydrograph from 1 to 2200 days is simulated with MIN3P-THCm-DP model using the mobile-immobile approach (Figure 5.7). The model predicted a peak earlier than Conceptual ModelOutflow wf DaConcentration wf DaMass flux wf DaKsa 156  500 days for all 𝑤𝑓 values that does not exist in data. The reason is that that peak occurs at the time when Pile 2 was under construction and data collection had not started. In each figure, the simulation results with different 𝐷𝑎 values demonstrate the same outflow. This result shows that, as expected, the outflow does not show sensitivity to the parameter 𝐷𝑎 in the mobile-immobile model. In each figure, the model overpredicts the wet-up stage between 1000-1500 days at all of the 𝑤𝑓 values, especially 𝑤𝑓 = 0.4, 0.5 and 0.6. However, the timing of the draindown curve in the simulations show a good match with data. At 𝑤𝑓= 0.5 and 0.6 the model overpredicts the outflow in the second stage of outflow (peak of wet season stage), seemingly related to the application of the bromide tracer at 907 days. Presence of this high peak in the model results can be explained by channeling of the water applied with the tracer and piston flow through the mobile region in model. However, in the field, the water applied with the tracer may be taken up into immobile region through water transfer process which is not considered in mobile-immobile model. This discrepancy between data and simulation results points out that the mobile-immobile model is not adequate to describe the water flow in studied waste rock system for large 𝑤𝑓 values (0.5 and 0.6).  The outflow results demonstrate slight sensitivity to the 𝑤𝑓 parameter when using the mobile-immobile model especially at the wet-up stage. The closest approximation of the outflow data is obtained with 𝑤𝑓 = 0.2, 0.3 and 0.4. The recharge applied on the mobile region is shown in Figure 5.7f.   The bromide concentration from 1 to 2200 days is simulated with MIN3P-THCm-DP using the mobile-immobile approach (Figure 5.8). The results are shown for the time period of 800 to 1800 days when bromide concentration increases are seen in the drainage. The results in  157  Figure 5.8 were obtained by varying 𝑤𝑓 and 𝐷𝑎 parameters. At 𝑤𝑓 = 0.2, 0.3 and 0.4, the closest match with peak concentration is obtained when 𝐷𝑎 is equal to 1×10-5, and 5×10-6 m2s-1. For 𝑤𝑓 = 0.2, the pre-peak concentration, peak concentration and peak timing have a close match with observed concentrations for 𝐷𝑎 equal to 1×10-5 and 5×10-6 m2s-1. While the peak concentration of the breakthrough curve in simulation results matches well with observations for 𝑤𝑓 = 0.2, post-peak concentrations during the start of the dry season do not agree well with observations. The simulated post-peak tail is indicative of bromide release at high concentration during the following dry season.    158   Figure 5.7. Mobile-immobile model: outflow of Pile 2 sub-lysimeter B drainage for the experimental period since August 2007. Black curve: field data collected from Pile 2 sub-lysimeter B. Colored curves: simulation results. Sensitivity analysis is performed on 𝑫𝒂  and 𝒘𝒇 parameters.   159  For 𝑤𝑓 = 0.3 and 0.4, the lowest 𝐷𝑎 value (i.e. 1×10-7 m2s-1) results in an early high peak of bromide concentrations (earlier than 1000 days) which is indicative of macropore flow behavior. This behavior is not observed in data obtained from Pile 2 Sub-lysimeter B drainage due to its fine particle size (soil-like waste rock) (Figure 5.4a).  It is apparent from this result that the low diffusive mass transfer (i.e. 1×10-7 m2s-1) inhibits the mass transfer from mobile to immobile region and as a result, most of the mass is released through the mobile region immediately after application of tracer (in the same wet season).   For 𝑤𝑓 = 0.5, the closest match for peak concentration and post-peak tracer release is obtained when 𝐷𝑎 = 1×10-6 m2s-1; however, the pre-peak concentrations and peak-timing are not a close approximation of the data. The high pre-peak concentrations result in early release of bromide mass during the dry season prior to observed peak arrival. For 𝐷𝑎 = 1×10-5 and 5×10-6 m2s-1, the model shows close agreement with pre-peak concentrations and peak-timing, but overpredicts the peak concentration. This behavior can be attributed to tracer diffusion into the immobile region during the wet season when the tracer is applied on the pile, facilitated by high diffusion coefficients (i.e. 𝐷𝑎 = 1×10-5 and 5×10-6 m2s-1). Subsequently the tracer is retained in the immobile zone during the dry season between 1000-1200 days (Figure 5.7f). After 1200 days the tracer diffuses back into mobile region and gets released into drainage during the peak flows.   For 𝑤𝑓 = 0.4, 0.5 and 0.6, and 𝐷𝑎 = 1×10s-5 and 5×10-6 m2s-1, the post-peak tail shape shows a decreasing trend in model results, sharper than observed compared to experimental data.    160   Figure 5.8. Mobile-immobile model: concentration of bromide tracer in Pile 2 sub-lysimeter B drainage for the experimental period since August 2007. Data are shown from 800 to 1800 days for clarity. Black  161  curve: field data collected from Pile 2 sub-lysimeter B. Sensitivity analysis is performed on 𝑫𝒂  and 𝒘𝒇 parameters.  The model results show a short tail due to the fast release of all of the remainder of tracer mass during the dry season following peak arrival. Under field conditions, bromide release is characterized by a gradual trend during the dry season which can be explained by a lower diffusive mass transfer coefficient than the value considered in the model. In addition, under field conditions, the bromide concentrations in drainage can be diluted by mixing with water flowing through slower pore regions in the waste rock (i.e. the matrix region), which is not considered in the mobile-immobile approach and requires more a complex model such as the dual-permeability approach which considers flow of water in both preferential flow and matrix pore regions.    For 𝑤𝑓 = 0.6, the model overpredicts the peak concentration for all 𝐷𝑎 values. However, the timing of the peak arrival is in good-agreement between all simulation results and observed data.   The bromide mass flux from 1 to 2200 days is simulated with MIN3P-THCm-DP using the mobile-immobile approach (Figure 5.8). The results are shown for the time period from 800 to 1800 days when increased bromide concentrations are present in drainage. The mass flux results include the effect of both outflow and bromide concentrations. The simulated outflow hydrographs generally show a good match with data, therefore, the goodness-of-fit in mass flux results is mostly sensitive to the goodness-of-fit in bromide concentration (Figure 5.8).  162  The closest approximation of field data is obtained when 𝑤𝑓 = 0.2 and 0.3 and 𝐷𝑎 = 1×10-5 and 5×10-6 m2s-1. The results for 𝐷𝑎 = 1×10-6 and 5×10-7 m2s-1 also demonstrate a close match with data, but they show increased bromide mass flux in drainage at around 1000 days which is not consistent with observations. The increased bromide mass flux at 1000 days might be due to less bromide mass being transferred from mobile to immobile region because of lower diffusive mass transfer coefficients (i.e. 𝐷𝑎 = 1×10-6 and 5×10-7 m2s-1). Although the observed tailing of bromide concentrations was not well reproduced by the model, the tailing of the mass flux demonstrates similar trends than observed in the data. The reason is that the tailing of the mass flux curves is dominated by the draindown response (Figure 5.7), which showed a close match with data at around 1400 days.  These sensitivity analysis results indicate that for the mobile-immobile model to be representative for flow and transport above Sub-lysimeter B at Pile 2, the ratio of mobile to immobile domain has to be in the range of to 0.4. In addition, an effective diffusive mass transfer coefficient (𝐷𝑎) ranging from 1×10-5 to 5×10-6 m2s-1 is required to transfer part of the tracer mass into immobile region in a time frame comparable to observed data.  In summary, for the mobile-immobile conceptual model, comparison between the modeling results and observed data provides the following findings: 1) the closest approximation of bromide concentration in data is obtained when 𝑤𝑓 = 0.2, 0.3 and 0.4 and 𝐷𝑎 = 1×10-5, and 5×10-6 m2s-1; 2) With increasing 𝑤𝑓, the macropore flow behavior decreases in simulations with the lowest 𝐷𝑎 value (i.e. 1×10-7 m2s-1) and the early peak arrival of bromide concentration disappears; 3) increase in 𝐷𝑎 results in lower macropore flow behavior; 4)  163  increases in 𝑤𝑓 result in lower pre-peak concentrations and therefore better match with data; 5)  in most cases, increases in 𝐷𝑎 result in lower pre-peak concentrations; 6) increases in 𝑤𝑓 results in lower post-peak bromide concentrations; and 7) increases in 𝐷𝑎 result in overprediction of peak concentrations.    164   Figure 5.9. Mobile-immobile model: mass flux of bromide tracer in Pile 2 sub-lysimeter B drainage for the experimental period since August 2007. Data are shown from 800 to 1800 days for clarity. Sensitivity analysis is performed on 𝑫𝒂  and 𝒘𝒇 parameters.   165  5.3.1.2 Dual-porosity Approach The outflow hydrograph from 1 to 2200 days is simulated with MIN3P-THCm-DP using the dual-porosity approach (Figure 5.10). Similar to results obtained with the mobile-immobile model, the predicted outflow hydrographs for the dual-porosity model also are a close approximation of the data. In each figure, the simulation results with different 𝐷𝑎 values demonstrate the same outflow. This result shows that, as expected, the outflow does not show sensitivity to 𝐷𝑎 parameter in the dual-porosity model, similar to the mobile-immobile model. In each figure, the model shows a high outflow peak in second wet season. This high outflow rate occurs at 907 days, coinciding with the day of tracer application. Presence of this high peak in the simulation results might be indicative of channeling of water through the preferential region, not observed under the field conditions, where water can be taken up into finer-grained material.    The outflow results also show an earlier time for the onset of the wet-up stage between 1000-1500 days for all  𝑤𝑓 values. Similar to the mobile-immobile model, the simulated draindown curves agree well with the observations. Although the comparison of predicted and observed outflow data suggests that the dual-porosity approach provides close agreement with observations, the occurrence of high outflow rates at 907 days indicates that the for dual-porosity approach might not fully capture the hydraulic properties of the waste rock. Simulated outflow demonstrates slight sensitivity to the 𝑤𝑓 parameter. The predicted outflow shows an increase in outflow rates earlier than 500 days not observed in the experiment,  166  which demonstrates sensitivity to 𝑤𝑓 and appears when 𝑤𝑓 is equal to 0.5 and 0.6. The closest approximation of the outflow data is obtained with 𝑤𝑓 = 0.2 and 0.3.   167   Figure 5.10. Dual-porosity model: outflow of Pile 2 sub-lysimeter B drainage for the experimental period since August 2007. Data are shown from 800 to 1800 days for clarity. Sensitivity analysis is performed on 𝑫𝒂  and 𝒘𝒇 parameters.  168  The bromide concentrations from 1 to 2200 days are simulated with MIN3P-THCm-DP using the dual-porosity approach (Figure 5.11). The results are shown for the time period of 800 to 1800 days, when bromide concentrations are present in elevated levels in drainage. The major difference between dual-porosity and mobile-immobile approaches  is that, in the dual-porosity model, both water and solute can be transferred between the preferential flow and matrix pore regions, while the mobile-immobile approach is limited to solute transfer. In addition, the solute exchange term between preferential flow and matrix regions includes contribution of both advective and diffusive transport in the dual-porosity approach, unlike mobile-immobile model which only includes diffusive transport.   Unlike the mobile-immobile model that had the closest match for peak concentrations at 𝑤𝑓 = 0.2, 0.3 and 0.4, the dual-porosity model underpredicts the bromide concentration for 𝑤𝑓 = 0.2 and 0.3. At 𝑤𝑓 = 0.2, the bromide concentration in drainage is not sensitive to 𝐷𝑎 values and all solute mass gets transferred to the matrix and is being released after 1400 days. At 𝑤𝑓 = 0.3, depending on the diffusive mass transfer coefficient, portions of the tracer gets transferred into the matrix following its application to the preferential flow region and later is transferred back to the preferential flow region and released into drainage.    For 𝑤𝑓 = 0.4 and 𝐷𝑎 equal to 1×10-5, and 5×10-6 m2s-1, the bromide concentration shows a close match with pre-peak concentrations and peak concentrations as well as an acceptable match with the timing of peak arrival; however, the predicted post-peak tailing does not follow the same trend as seen in the observational data.   169   Figure 5.11. Dual-porosity model: concentration of bromide tracer in Pile 2 sub-lysimeter B drainage for the experimental period since August 2007. Data are shown from 800 to 1800 days for clarity. Sensitivity analysis is performed on 𝑫𝒂  and 𝒘𝒇 parameters.  170  The reason may be due to slow back-diffusion or advection of solute from the matrix to the preferential flow region during the dry season around 1400 days. The dual-porosity model ignores water flow and solute transport in the matrix region, which in reality can drain slowly during the dry season. Therefore, consideration of a more complex model such as dual-permeability that considers flow and solute transport in both pore regions, might decrease such discrepancies.   For 𝑤𝑓 = 0.5, the closest match for pre-peak concentrations, peak concentrations and post-peak tailing is obtained when 𝐷𝑎 = 1×10-5 and 5×10-6 m2s-1; however, the predicted post-peak tail shows higher concentrations compared to experimental data. Lower 𝐷𝑎 values (i.e. 1×10-6 and 5×10-7 m2s-1) result in higher pre-peak and post-peak concentrations compared to data. 𝐷𝑎 values as low as 1×10-7 m2s-1 results in macropore flow behavior. The high pre-peak concentration results in early release of bromide during the dry season, before the observed peak arrival.   For 𝑤𝑓 = 0.6, and 𝐷𝑎 = 1×10-5 and 5×10-6 m2s-1 the peak-arrival timing shows a close match with observations; however, the peak-concentration is overpredicted.   The bromide mass flux results are presented in Figure 5.12. Similar to the mobile-immobile model, the mass flux results include the effect of both outflow and bromide concentration results. The closest approximation of field data is obtained when 𝑤𝑓 = 0.5 and 𝐷𝑎 = 1×10-6 m2s-1, but the plot shows an early increase in mass flux at around 1000 days which is not observed in the experiment. In general, all simulations show an arrival of bromide mass flux  171  at 1200 days, much earlier than seen in the field, which is due to the high outflow rates in all simulations during that period of time.   172   Figure 5.12. Dual-porosity model: mass flux of bromide tracer in Pile 2 sub-lysimeter B drainage for the experimental period since August 2007. Data are shown from 800 to 1800 days for clarity. Sensitivity analysis is performed on 𝑫𝒂  and 𝒘𝒇 parameters.  173  Results of this sensitivity analysis indicate that for the dual-porosity model to be a representative of flow and solute transport through waste rock above Sub-lysimeter B at Pile 2, the ratio of mobile to immobile domain has to be 0.5. In addition, an effective diffusion coefficient (𝐷𝑎) between 1×10-5 and 5×10-6 m2s-1 (when 𝐾𝑠𝑎 is considered constant and equal to 1×10-2 m2s-1) is required to transfer part of the mass into matrix region at a timing comparable than seen in the observed data.  In summary, for the dual-porosity approach, the comparison between simulations and experimental data indicate the following findings: 1) the closest approximation of observed bromide concentrations is obtained when 𝑤𝑓 = 0.5 and for 𝐷𝑎 values of 1×10-5 and 5×10-6 m2s-1; 2) contrary to the mobile-immobile model, with increasing 𝑤𝑓, the macropore flow behavior increases in simulations with lower 𝐷𝑎 values (i.e. 1×10-6, 5×10-7 and 1×10-7 m2s-1) and the premature arrival of bromide peak concentrations appears in simulation results; 3) similar to the mobile-immobile model, increase in 𝐷𝑎 result in lower macropore flow behavior; 4) contrary to the mobile-immobile model, an increase in 𝑤𝑓 results in higher pre-peak concentrations; 5)  similar to mobile-immobile model, in most cases, an increase in 𝐷𝑎 results in lower pre-peak concentrations; 6) similar to the mobile-immobile model, an increase in 𝑤𝑓 results in lower post-peak bromide concentration; 7) similar to the mobile-immobile conceptual model, an increase in 𝐷𝑎 results in higher peak concentration and overprediction of peak concentrations.    174  5.3.1.3 Dual-permeability 1 Approach The outflow hydrograph from 1 to 2200 days is simulated with MIN3P-THCm-DP using dual-permeability mode l (Figure 5.13). The dual-permeability 1 approach implies that all recharge is applied to the preferential flow region. Similar to outflow from mobile-immobile and dual-porosity models, the predicted outflow hydrographs for the dual-permeability 1 model closely approximate experimental data. In each figure, the simulation results with different 𝐷𝑎 values show the same outflow. This result demonstrates that, as expected, the outflow does not show sensitivity to 𝐷𝑎 parameter in dual-permeability 1 model similar to mobile-immobile and dual-porosity models. Unlike the mobile-immobile and dual-porosity models, in each figure, the model does not show a high outflow peak in second wet season (i.e. after 907 days, corresponding to the day of tracer application). The absence of this outflow peak in simulation results indicates that water is being transferred into the matrix, slowing its downward percolation. This result is consistent with experimental data and shows that the dual-permeability approach better captures the flow behavior in Sub-lysimeter B of Pile 2 than the approaches introduced above.  For 𝑤𝑓 = 0.2 and 0.3, the onset of the wet-up stage occurs a few days later seen in the than experimental data, especially in the second, fourth and fifth wet seasons (i.e. they occur at 750, 1600, 2000 days, respectively). Predicted draindown curves produce a slower drainage process than observed in the experiment implying that the contribution of water draining through the fine particle-size material (i.e. the matrix) is overpredicted by the model.   175   Figure 5.13. Dual-permeability 1 model: outflow of Pile 2 sub-lysimeter B drainage for the experimental period since August 2007. Data are shown from 800 to 1800 days for clarity. Sensitivity analysis is performed on 𝑫𝒂  and 𝒘𝒇 parameters.   176  For 𝑤𝑓 = 0.4, 0.5 and 0.6, all three stages of the wet-up, peak of wet season and draindown are well-represented by the model, except for 𝑤𝑓 = 0.6, in which case the model predicts an earlier onset of wet season drainage between 1000 and 1500 days.  The comparison of predicted and observed outflow demonstrates that the dual-permeability 1 approach can produce a close match with observational data. Contrary to mobile-immobile and dual-porosity models, an unrealistically a high outflow rate at 907 days, was not produced by the dual-permeability 1 model. These results imply that the dual-permeability 1 approach provides a more suitable approximation of the hydraulic properties of the waste rock. The outflow results demonstrate slight sensitivity to 𝑤𝑓 parameter. However, the predicted outflow shows slower draindown rates at the end of each wet season than observed in the experiments, which demonstrates sensitivity to 𝑤𝑓 and appears when 𝑤𝑓 is equal to 0.2 and 0.3. The closest approximation of the outflow data is obtained with 𝑤𝑓 = 0.5 and 0.6.   The bromide concentration from 1 to 2200 days is simulated with MIN3P-THCm-DP using the dual-permeability 1 approach (Figure 5.14). The results are shown for the time period of 800 to 1800 days when elevated bromide concentration are present in drainage.    177   Figure 5.14. Dual-permeability 1 model: concentration of bromide tracer in Pile 2 sub-lysimeter B drainage for the experimental period since August 2007. Data are shown from 800 to 1800 days for clarity. Sensitivity analysis is performed on 𝑫𝒂  and 𝒘𝒇 parameters.  178  Similar to the dual-porosity approach, in the dual-permeability 1 model both water and solute can be transferred between the preferential flow and matrix pore regions, and the solute exchange term between preferential flow and matrix regions also includes contributions from both advective and diffusive transport.   Unlike the dual-porosity model that showed the closest match to peak concentrations for 𝑤𝑓 = 0.5 and a high diffusive mass transfer coefficient (i.e. 𝐷𝑎 = 1×10-5, and 5×10-6 m2s-1), the dual-permeability 1 model overpredicts the peak bromide concentration when using the parameters. This response may be due to fast transfer of all bromide mass stored in the matrix through advective and diffusive transport to the preferential flow region during the wet season. In the experiment, at the end of data collection time only 55% of the initial mass of bromide applied on the surface of waste rock pile above Sub-lysimeter 2 had been released into drainage. Therefore, 45% of the bromide mass still remained within the pile. For 𝑤𝑓 = 0.5 and high diffusive mass transfer coefficients (i.e. 𝐷𝑎 = 1×10-5, and 5×10-6 m2s-1), all tracer applied is released with basal drainage in a single wet season and there is not any bromide stored in the matrix region, which is not consistent with data.    179   Figure 5.15. Dual-permeability 1 model: mass flux of bromide tracer in Pile 2 sub-lysimeter B drainage for the experimental period since August 2007. Data are shown from 800 to 1800 days for clarity. Sensitivity analysis is performed on 𝑫𝒂  and 𝒘𝒇 parameters.   180  For 𝑤𝑓 = 0.2 and 0.3, at all 𝐷𝑎 values, the simulated bromide peak arrives around 400 days later than observed in the experiment. The late peak arrival is indicative of bromide transport along slow flow paths within the matrix. In the model, bromide was taken up by the matrix following its application on top of the pile. All simulated results do not show any sensitivity to changes in 𝐷𝑎, except for 𝑤𝑓 = 0.3 and 𝐷𝑎 = 1×10-7 m2s-1, which indicates macropore flow behavior at around 1000 days.  For 𝑤𝑓 = 0.4 and 𝐷𝑎 = 5×10-7 m2s-1, the closest approximation of the experimental data is obtained; however, the simulations overestimate the pre-peak concentrations, the peak concentrations and trends during tailing. For 𝑤𝑓 = 0.4, the bromide concentrations show sensitivity to changes in the 𝐷𝑎 value. The bromide concentrations in drainage are not sensitive to 𝐷𝑎 values and all the mass gets transferred to the matrix and is released after 1400 days. For 𝑤𝑓 = 0.3, depending on the diffusive mass transfer coefficient, a fraction of the mass gets transferred into matrix, when the tracer is applied to the preferential flow region and later is transferred back to the preferential flow region and released into drainage.    For 𝑤𝑓 = 0.6, the pre-peak bromide concentrations are overpredicted for all 𝐷𝑎 values. Therefore, a large fraction of the bromide mass gets released prior to reaching peak concentrations and there is no mass left in either the preferential flow or matrix regions.  The bromide mass flux results are presented in Figure 5.15. The closest approximation of field observations is obtained for 𝑤𝑓 = 0.4 and 𝐷𝑎 ranging from 1×10-7 to 5×10-7 m2s-1.  181  However, the results show a slight overprediction of the mass flux mid-wet season (i.e. between 1200 and 1400 days) especially for 𝐷𝑎 = 5×10-7 m2s-1 and also a premature increase in mass flux at around 1000 days, which is not observed for 𝐷𝑎 = 1×10-7 m2s-1. Contrary to the dual-porosity model, for which all simulations produced an early arrival of bromide mass flux at 1200 days, the dual-permeability 1 model, produced only two simulations for each 𝑤𝑓 value with an early arrival of bromide mass flux at around 1200 days (i.e. at 𝑤𝑓 = 0.3, 𝐷𝑎 = 1×10-7 m2s-1 and for 𝑤𝑓 =  0.4 and 0.6, 𝐷𝑎 = 5×10-7 and 1×10-7 m2s-1), which is likely due to a combination of outflow rate and concentration being high at the same time.   This sensitivity analysis results indicate that for dual-permeability 1 model to be representative for water flow and solute transport above Sub-lysimeter B in Pile 2, the ratio of preferential flow to matrix region has to be 0.4. In addition, an effective mass transfer coefficient (𝐷𝑎) as low as 1×10-7 m2s-1 (when 𝐾𝑠𝑎 is considered constant and equal to 1×10-2 m2s-1) is required to transfer part of the mass into the matrix region in order to produce tracer release comparable to observations.  In summary, for the dual-permeability 1 model, the comparison between the modeling results and data produce the following findings: 1) the closest approximation of simulated bromide concentrations to observations is obtained when 𝑤𝑓 = 0.4 and 𝐷𝑎 = 5×10-7 m2s-1; 2) contrary to the mobile-immobile and dual-porosity models, there is no macropore flow effect observed for bromide using the dual-permeability 1 model, except for 𝑤𝑓 = 0.3 and 𝐷𝑎 = 1×10-7 m2s-1. This is consistent with soil-like behavior that Pile 2 waste rock has consistently  182  demonstrated over the years; 3) contrary to the mobile-immobile model and similar to the dual-porosity model, an increase in 𝑤𝑓 results in higher pre-peak concentrations; 4)  contrary to mobile-immobile and dual-porosity models, the pre-peak concentrations are not sensitive to changes in 𝐷𝑎 except for simulations with 𝑤𝑓 = 0.4. For 𝑤𝑓 = 0.4, an increase in 𝐷𝑎 results in higher pre-peak concentrations; 5) similar to the mobile-immobile model, an increase in 𝑤𝑓 results in lower post-peak bromide concentrations; 6) contrary to mobile-immobile and dual-porosity models, for which an increase in 𝐷𝑎 results in higher peak concentrations and overprediction of peak concentrations, for the dual-permeability 1 model, the peak concentrations do not show sensitivity towards 𝐷𝑎 except for 𝑤𝑓 = 0.4 and  0.6; 7) the post-peak concentrations do not show sensitivity to 𝐷𝑎 except for 𝑤𝑓 = 0.4.     183  5.3.1.4 Dual-permeability 2 Approach The outflow hydrograph from 1 to 2200 days is simulated with MIN3P-THCm-DP using the dual-permeability 2 model (Figure 5.16). The only difference between the dual-permeability 1 and 2 models is that in the dual-permeability 2 model, all recharge (𝑞𝑖𝑛𝑓) is applied to the matrix region. Similar to outflow from mobile-immobile, dual-porosity and dual-permeability 1 models, the predicted outflow hydrographs for the dual-permeability 2 model also provide a close approximation to observations. The presented outflow hydrographs in Figure 5.16 are quite similar to dual-permeability 1 results (Figure 5.13), which is due to the high interfacial hydraulic conductivity 𝐾𝑠𝑎 = 1×10-2 ms-1 that is considered for all the presented simulations in this section. The effect of 𝐾𝑠𝑎 on outflow, bromide concentration and bromide mass flux are presented in the appendix of this chapter.   Comparison of predicted and observed outflow shows that the dual-permeability 2 model provides a close match with observations, similar to the dual-permeability 1 model. Contrary to mobile-immobile and dual-porosity models, which produced a high outflow rate at 907 days, the dual-permeability 2 model provided a closer representation of the hydraulic properties of the waste rock. The outflow results demonstrate slight sensitivity to 𝑤𝑓 parameter. The predicted outflow shows slower draindown rates at the end of each wet season, which is not observed in the experimental data. The closest approximation of the observed outflow is obtained with 𝑤𝑓 = 0.5 and 0.6.     184   Figure 5.16. Dual-permeability 2 model: outflow of Pile 2 sub-lysimeter B drainage for the experimental period since August 2007. Data are shown from 800 to 1800 days for clarity. Sensitivity analysis is performed on 𝑫𝒂  and 𝒘𝒇 parameters.  185  The bromide concentration from 1 to 2200 days is simulated with MIN3P-THCm-DP using the dual-permeability 2 model (Figure 5.17). The results are shown for the time period of 800 to 1800 days, when bromide concentrations are elevated in drainage. The presented results for predicted bromide concentrations in Figure 5.17 are quite similar to bromide concentrations using the dual-permeability 1 model (Figure 5.14), except for 𝑤𝑓 = 0.4, showing a lower peak concentration in the dual-permeability 2 model than in the dual-permeability 1 model. This similarity between the bromide concentration results of the two approaches demonstrates that when the 𝐾𝑠𝑎 parameter (i.e. the interfacial hydraulic conductivity) is set to a high value (i.e. 1×10-2 ms-1), hydraulic equilibrium is reached quickly between the preferential flow and matrix regions. Therefore, for high 𝐾𝑠𝑎 value (i.e. 1×10-2 ms-1), the bromide concentrations do not show sensitivity to where recharge is applied and both dual-permeability 1 (i.e. recharge applied exclusively on preferential flow region) and dual-permeability 2 (i.e. 𝑞𝑖𝑛𝑓 applied exclusively on matrix region) show similar bromide concentration trends. Similar to the dual-permeability 1 model, the closest approximation of the experimental data is achieved for 𝑤𝑓 = 0.4 and 𝐷𝑎 = 5×10-7 m2s-1.    186   Figure 5.17. Dual-permeability 2 model: concentration of bromide tracer in Pile 2 sub-lysimeter B drainage for the experimental period since August 2007. Data are shown from 800 to 1800 days for clarity. Sensitivity analysis is performed on 𝑫𝒂  and 𝒘𝒇 parameters.  187  The bromide mass flux results are presented in Figure 5.18. Similar to the dual-permeability 1 model, the closest approximation of field data is obtained when 𝑤𝑓 = 0.4 and 𝐷𝑎 ranges from 1×10-7 to 5×10-7 m2s-1; however, the plot shows overprediction of the mass flux in the middle of wet season (i.e. between 1200 and 1400 days) especially for 𝐷𝑎 = 5×10-7 m2s-1 and also an early increase in mass flux at around 1000 days which is not observed in data for 𝐷𝑎 = 1×10-7 m2s-1. The similarity between the bromide mass flux for dual-permeability 1 and 2 models show that, for high a 𝐾𝑠𝑎 value (i.e. 1×10-2 ms-1), the mass flux is not sensitive to recharge being applied on either preferential flow or matrix pore regions.   In summary, these sensitivity analysis results indicate that for the dual-permeability 2 model to be representative for flow and solute transport processes in waste rock above Sub-lysimeter B in Pile 2, similar to the dual-permeability 1 model, the ratio of preferential flow to matrix region has to be 0.4. In addition, an effective diffusive mass transfer coefficient (𝐷𝑎) as low as 1×10-7 m2s-1 (when 𝐾𝑠𝑎 is considered constant and equal to 1×10-2 m2s-1) is required to transfer part of the mass into the matrix region in comparable timing to observed data. In addition, the results show that when a high value is assumed for 𝐾𝑠𝑎 (1×10-2 ms-1), the predicted outflow hydrograph, bromide concentration and bromide mass flux are not sensitive to recharge being applied on either the preferential flow or matrix regions.    188   Figure 5.18. Dual-permeability 2 model: mass flux of bromide tracer in Pile 2 sub-lysimeter B drainage for the experimental period since August 2007. Data are shown from 800 to 1800 days for clarity. Sensitivity analysis is performed on 𝑫𝒂 and 𝒘𝒇 parameters.    189  5.3.1.5 Dual-permeability 3 Approach The outflow hydrograph from 1 to 2200 days is simulated with MIN3P-THCm-DP using the dual-permeability 3 model (Figure 5.19). The only difference between the dual-permeability 1, 2 and 3 models is that in the dual-permeability 3 model 55% of the recharge (𝑞𝑖𝑛𝑓−𝑃𝐹) is applied as on the preferential flow region and 45% is applied on the matrix region (𝑞𝑖𝑛𝑓−𝑀). Similar to the outflow from mobile-immobile, dual-porosity and dual-permeability 1 and 2 models, the predicted outflow hydrographs for the dual-permeability 2 model provide a close approximation of the observed data. The presented outflow hydrographs in Figure 5.19 are quite similar to dual-permeability 1 and 2 results (Figure 5.13 and Figure 5.16), which is due to the high interfacial hydraulic conductivity 𝐾𝑠𝑎 = 1×10-2 ms-1 that is considered for all the simulations presented in this section. The effect of 𝐾𝑠𝑎 on outflow, bromide concentration and bromide mass flux are presented in the appendix of this chapter.   The bromide concentration from 1 to 2200 days is simulated with MIN3P-THCm-DP using the dual-permeability 3 model (Figure 5.20). The results are shown for the time period of 800 to 1800 days when that bromide concentrations are elevated in drainage. The results for predicted bromide concentration are presented in Figure 5.20 and are quite similar to bromide concentrations produced by dual-permeability 1 and 2 models (Figure 5.14 and Figure 5.17), except for 𝑤𝑓 = 0.4, which shows a higher peak concentration in the dual-permeability 1 model than in the dual-permeability 2 and 3 models. This similarity between the bromide concentration results of the three models, demonstrates that when 𝐾𝑠𝑎 (i.e. the interfacial hydraulic conductivity) is set to a high value (i.e. 1×10-2 ms-1), the hydraulic equilibrium is reached quickly between the preferential flow and matrix regions.   190   Figure 5.19. Dual-permeability 3 model: outflow of Pile 2 sub-lysimeter B drainage for the experimental period since August 2007. Data are shown from 800 to 1800 days for clarity. Sensitivity analysis is performed on 𝑫𝒂  and 𝒘𝒇 parameters.  191  Therefore, for a high 𝐾𝑠𝑎 value (i.e. 1×10-2 ms-1) the bromide concentrations do not show sensitivity to where the recharge is applied and dual-permeability 1 (i.e. recharge applied exclusively on the preferential flow region), dual-permeability 2 (i.e. recharge applied exclusively on the matrix region) and dual-permeability 3 (i.e. 55% of recharge applied on the preferential flow region and 45% applied on matrix region) show similar bromide concentration trends. Similar to dual-permeability 1 and 2 models, the closest approximation of the experimental data is achieved at 𝑤𝑓 = 0.4 and 𝐷𝑎 = 5×10-7 m2s-1.   The bromide mass flux results are presented in Figure 5.21. Similar to dual-permeability 1 and 2 models, the closest approximation of field data is obtained when 𝑤𝑓 = 0.4 and 𝐷𝑎 ranges between  1×10-7 and 5×10-7 m2s-1; however, the plot shows overprediction of the mass flux in the middle  of the wet season (i.e. between 1200 and 1400 days) especially for 𝐷𝑎 = 5×10-7 m2s-1 and also an early increase in mass flux at around 1000 days which is not observed in data for 𝐷𝑎 = 1×10-7 m2s-1. The similarity between the bromide mass flux for dual-permeability 1, 2 and 3 models show that, for high 𝐾𝑠𝑎 value (i.e. 1×10-2 ms-1), the mass flux is not sensitive to the recharge being applied on either preferential flow or matrix pore regions or in this case both of those regions.      192   Figure 5.20. Dual-permeability 3 model: concentration of bromide tracer in Pile 2 sub-lysimeter B drainage for the experimental period since August 2007. Data are shown from 800 to 1800 days for clarity. Sensitivity analysis is performed on 𝑫𝒂  and 𝒘𝒇 parameters.  193  In summary, these sensitivity analysis results indicate that for the dual-permeability 3 model to be representative for flow and solute transport processes in waste rock of the pore system above Sub-lysimeter B at Pile 2, similar to dual-permeability 1 and 2 models, the ratio of preferential flow to matrix region has to be 0.4. In addition, an effective diffusion coefficient (𝐷𝑎) as low as 1×10-7 m2s-1 (when 𝐾𝑠𝑎 is considered constant and equal to 1×10-2 ms-1) is required to transfer part of the mass into the matrix region in comparable timing to observed data. In addition, the results show that when 𝐾𝑠𝑎 is assumed at a high value (1×10-2 ms-1), the predicted outflow hydrograph, bromide concentration and bromide mass flux are not sensitive to recharge being applied on either the preferential flow or matrix or both regions. Dual-permeability 2 and 3 models produced similar bromide concentration and mass flux results due to high saturated hydraulic conductivity value (𝐾𝑠𝑎 = 1×10-2 ms-1) between the preferential flow and matrix regions. The high 𝐾𝑠𝑎 resulted in achieving hydraulic head equilibrium between the two regions quickly. As a result, it might be considered redundant to present both dual-permeability 2 and 3 scenarios. However, it is important to note that each of these two conceptual models present a different condition in the field: while dual-permeability 2 is representative of 100% of  the inflow precipitation entering through the matrix region and later transferring to the preferential flow region within the pile below the berm, the dual-permeability 3 model is representative of the real-world condition. In the dual-permeability 3 model the inflow precipitation can enter through either preferential flow region or matrix into the pile.   194   Figure 5.21. Dual-permeability 3 model: mass flux of bromide tracer in Pile 2 sub-lysimeter B drainage for the experimental period since August 2007. Data are shown from 800 to 1800 days for clarity. Sensitivity analysis is performed on 𝑫𝒂  and 𝒘𝒇 parameters.   195  5.4 Summary and Conclusions This chapter presents a comparative study of flow and solute transport behavior using uniform flow, and mobile-immobile, dual-porosity and dual-permeability models in a one-dimensional domain that is part of an experimental mine waste rock pile the at Antamina Mine, Peru. The waste rock pile was initially hypothesized as a pile with soil-like behavior that dominantly demonstrates matrix flow behavior (Peterson, 2014).  The numerical modeling of flow and solute transport using a uniform flow model revealed that the model was able to closely match cumulative discharge and the response of the hydrograph to wet and dry seasons using bulk soil hydraulic parameters. However, the uniform flow and transport model failed to adequately reproduce the response to a tracer test, providing a strong indication for the occurrence of preferential flow in this waste rock pile, despite its soil-like nature (see details in Chapter 3). In this chapter, the non-uniform flow and solute transport models that were developed and verified in Chapter 4 were used to evaluate water and solute mass transfer parameters that determine the distribution of the solute between the preferential flow and matrix pore regions. The error in estimation of these parameters was evaluated by an extensive sensitivity analysis. The estimated parameters included the (1) the ratio of the volume of the preferential pore region and the total pore system (𝑤𝑓), (2) hydraulic conductivity between the two pore regions (𝐾𝑠𝑎) (shown in appendix), (3) the effective diffusive mass transfer coefficient (𝐷𝑎) between the two pore regions, and (4) the distribution of recharge at the inflow boundary (𝑞𝑖𝑛𝑓). The model results were compared to observed tracer test data collected from a transient Sub-lysimeter B located at the back of the waste rock pile including: (1) daily outflow, (2) tracer concentration, and (3) tracer mass loading.  196   The limitation of using more complex non-uniform models lies in the difficulty of defining their parameters. The number of required parameters increase from mobile-immobile to dual-permeability models and some of the parameters are difficult, if not impossible to measure. In addition, we recognize that the underlying limitations of such models results in a non-unique set of parameters and other parameter sets may also be able to reproduce the experimental observations. The analysis of simulation results and data demonstrate the following findings:   The outflow results from mobile-immobile and dual-porosity simulations show a large peak at the time of tracer application which is not observed in the field data. This is due to flow of water in the mobile region and lack of infiltration into the immobile pore region in the mobile-immobile model and retention of water in the matrix in the dual-porosity model. In dual-permeability models, simulations with higher 𝑤𝑓 and 𝐾𝑠𝑎  do not produce this peak due to lateral transfer of recharge from the preferential flow region to the matrix. The outflow results are indicative of an improved in representation of water flow using these more complex dual-permeability models.  In terms of tracer concentrations, the timing of the peak arrival and peak concentrations has improved with an increase in model complexity; reproduction of the tailing behavior was also improved. The mass flux is dominated by the water flux, but also affected to a lesser degree by solute concentrations.    197  The main parameters that have been explored include 𝑤𝑓  (volumetric weighting factor), interfacial diffusive mass transfer coefficient (𝐷𝑎), and the effective saturated hydraulic conductivity of the interface (𝐾𝑠𝑎) (see appendix). The sensitivity analysis performed for  𝐷𝑎 demonstrates that a higher mass transfer rate results in a faster diffusion of solutes from preferential flow (mobile) to matrix (immobile) regions and a closer match in the first part of the concentration curve; however, the tailing of the breakthrough curve does not show a good match for high mass transfer coefficients.  Improvement of outflow, concentration peak arrival, as well as tailing trend was obtained using the dual-permeability model, indicating that an increase in model complexity allows an improved representation of water flow and solute transport in waste rock. However, the bromide concentration peak and post-peak trend did not improve, suggesting bromide is possibly retained in fine-grained material, leading to entrapment of mass for a very long time and very slow release.   The data analysis for the P2B tracer shows that at 1477 days, which is the last day of bromide tracer data collection (August 17, 2011), 55% of the tracer which was applied on top if the sub-lysimeter B was recovered. The remaining 45% of the bromide mass was entrapped within the fine-grained soil and was not released until the final day of data collection. However, the simulation produced usually 80-100% of tracer recovery by the same date. The presented models did not have a region to retain the stagnant (immobile) mass except for the mobile-immobile model, which demonstrated the closest agreement between simulated tailing trends and concentrations to the observed bromide concentrations between 1400 to  198  1600 days. This result might be indicative of the presence of more than two pore regions within the waste rock which could include an immobile region in addition to matrix and preferential flow regions that could entrap and retain the remaining 45% of the bromide mass.  The models developed in this study can be used for drainage volume and quality predictions from full-scale waste rock dumps at the Antamina mine and can also be used as an example for other mines with similar waste rock and atmospheric conditions as the Antamina mine. The findings of this study have implications for water and solute transport in mine waste rock, structured soils, agricultural soils, mine tailings and petroleum engineering that have partitioning of solute species or contaminant mass between preferential flow and matrix pore regions and require management strategies for drainage quality and quantity. Further study is required to investigate the sensitivity of the tracer mass distribution in preferential and matrix pore region to different soil hydraulic parameters.        199  Chapter  6: Application of non-uniform flow and transport models for the simulation of reactive transport in mine waste rock   6.1 Introduction This chapter aims to demonstrate the application of MIN3P-THCm-DP code to investigate acid rock drainage production and acid neutralization in an experimental waste rock pile that is affected by preferential flow. The MIN3P-THCm-DP model developed for this study is an extension to the existing reactive transport code MIN3P (Mayer et al., 2002), and can be used to simulate reactive transport in macroporous soil media such as mine waste rock. The details of the model development, verification and application for conservative solute transport can be found in Chapters 4 and 5, respectively. In this chapter, two sets of simulations are presented to demonstrate the capabilities of the model. The main reactions considered are oxidation-reduction, mineral dissolution-precipitation, aqueous complexation, hydrolysis, in combination with reactive solute transport. The preferential flow approach used for this study is dual-permeability.   Several studies have focused on the water flow and tracer transport in the soil (Brusseau et al., 1994; Dusek et al., 2010; Gerke and Maximilian Köhne, 2004; Gerke et al., 2007; Kätterer et al., 2001). However, fewer studies consider chemical reactions occurring in each pore region and their effect on the quality of drainage. The number of studies are even more limited, when considering interactions between preferential flow and matrix pore regions.    200  There are three main objectives of this study. (1) To demonstrate the capabilities of the enhanced model for simulating reactive transport in preferential flow and matrix pore regions, including  water and mass transfer between the two pore regions (2) Evaluate the chemical reactions using the enhanced dual-domain model on the scale of an experimental waste rock pile.(3) Investigate the effect of reactivity distribution in preferential flow and matrix regions in the dual-domain porous medium in relation to data form an experimental waste rock pile at the Antamina mine site.   6.2 Materials and Methods 6.2.1 Conceptual model All conceptual models described here consist of various sub-types of Class A intrusive waste rock material according to Antamina’s waste rock type classification system. The first conceptual model consists of a one-dimensional column containing reactive Class A intrusive material, UBC2-1A. The porous medium consists of two sub-domains, describing preferential flow and matrix regions. The second conceptual model is similar to the first conceptual model, since it is a one-dimensional column, with the difference that it includes a more reactive sub-type of waste rock  material A, named UBC2-1B. The details of the solid phase elemental analysis of these rock types are summarized in Table 6.2. In all the above-mentioned conceptual models, the soil column is assumed to be located under the crown and at the back of the experimental waste rock pile. Therefore, the soil column does not get affected by physical and chemical processes occurring in the pile’s berms such as higher evaporation, shorter flow paths and faster transport of contaminants towards the basal lysimeter.   201  6.2.2 Model parametrization and discretization For defining the soil hydraulic parameters for the different waste rock types, the van Genuchten parameters and saturated hydraulic conductivities were adapted from parameters used in Chapter 5 (Table 6.1). In Chapter 5, the soil water retention parameters of sand and clay-loam were adapted for preferential flow and matrix regions, respectively. The same soil water characteristic curves are considered for the preferential flow and matrix regions in all simulations. The difference between the materials in the various simulations is in their initial mineralogy. The mineralogy data used to constrain the initial conditions for reactive transport is derived from XRD analyses and Rietveld refinement as reported in Peterson (2014).  Table 6.1. Hydraulic parameters used in the non-uniform reactive transport simulations Parameter Porosity 𝑺𝒓 α 𝒏 𝑰 𝑲𝒔 Unit [-] [-] [1/m] [-] [-] [m/s] Preferential Flow Region a 0.34c × 𝑤𝑓d 0.1047 14.5 2.68 0.5 1.65×10-4 Matrix Region b 1-𝑤𝑓 0.232 1.9 1.31 0.5 1.44×10-6  a Hydraulic parameters of sand were used for the preferential flow region  b Hydraulic parameters of clay-loam were used for the matrix region c Porosity data from Javadi et al. (2012) d 𝑤𝑓 (volumetric weighting factor):  volume of preferential flow region relative to total volume of the medium. 𝑤𝑓 equals to 0.5 for the simulation in this chapter   202  6.2.3 Reaction network 6.2.3.1 Pyrite oxidation and sulfide mineral weathering reactions, acid neutralization and secondary mineral formation The reactions in this chapter include acid rock generation due to pyrite oxidation and acid neutralization and pH-buffering due to dissolution of carbonate and silicate minerals and formation of secondary mineral phases. Pyrite oxidation in the preferential flow or matrix pore regions results in acidity and release of sulfate into the pore water. This reaction tends to occur more rapidly within the matrix due to the smaller grain size and higher reactive surface area compared to the preferential flow region. The reaction rates for sulfide minerals (i.e. pyrite, chalcopyrite and sphalerite) are set to be one order of magnitude higher in matrix compared to the preferential flow region, due to finer particle size and higher reactive surface area in matrix. Pyrite and chalcopyrite were identified in the both UBC2-1A and UBC2-1B waste rock types using XRD analysis (Peterson, 2014) (Table 6.4). The identified phases were quantitatively analyzed using Rietveld refinement (Peterson, 2014). These minerals were included in the simulations based on measured concentrations (Table 6.4).  Table 6.2. Summary of unmodified Sobek ABA test, solid phase elemental analysis results and water:rock ratio of material UBC2-1A and UBC2-1B for intrusive waste rock type (Modified from Peterson, 2014)  Unit UBC2-1A UBC2-1B Rock Type - Intrusive Intrusive Total S % 0.20 4.26 Total C % 0.15 0.09 Total Ca % 0.8 5.5 Bulk NP tCaCO3/1000t 12.0 8.0 AP tCaCO3/1000t 6.3 133.1 NP/AP* - 1.90 0.06 water:rock** kg/kg 0.14 0.14 *NP represents unmodified Sobek (Sobek et al., 1978) neutralization potential.  203  **water:rock: average water to rock ratio in wet season. The average moisture content is adapted from Pile 2 average moisture content observed in the wet season. Data from Peterson (2014).  Sphalerite was not detected in XRD-analyses; however, Mineral Liberation Analyzer (MLA) studies revealed the presence of < 1% sphalerite in UBC2-1B waste rock (St. Arnault, personal communication, 2018). Sphalerite was not observed in UBC2-1A; however, sphalerite was considered in both simulations as a primary mineral phase due to presence of zinc in the effluent from Sub-lysimeter B. Molybdenite was identified in UBC2-1A and UBC2-1B in trace amounts, but was not included in the present simulations, because Mo-concentrations in the drainage were insignificant. The evaluation of Mo release and attenuation processes as beyond the scope of this study. The reaction stoichiometries of the sulfide weathering reactions considered in the simulations are summarized in Table 6.5.  Table 6.3. Results of quantitative XRD analyses for UBC2-1A and UBC2-1B waste materials (Modified from Peterson, 2014, ND = Not Detected) Mineral Abundance [wt%] UBC2-1A UBC2-1B Actinolite ND 1.4 Albite 2.8 1.5 Albite low ND ND Andradite ND 22.1 Biotite 1M 2.8 2.1 Chalcopyrite 0.8 4.1 Diopside 1.9 ND Ferrihydrite 0.2 ND Kaolinite 1.0 ND Magnetite ND 3.4 Melanterite ND ND Molybdenite 2H 0.09 <0.05 Muscovite 2M1 2.2 ND Oligoclase 6.4 6.1 Orthoclase 42.3 22.4  204  Mineral Abundance [wt%] UBC2-1A UBC2-1B Pyrite 0.5 5.0 Pyrrhotite ND ND Quartz 38.8 31.9 Siderite 0.2 ND Wollastonite ND ND  The dissolution of carbonate minerals neutralizes the acidity. Calcite was not detected in XRD analysis in the studied material, similar to the waste rock material studied in Chapter 2 (i.e. UBC2-3A material). However, the circum-neutral pH of drainage from field barrels containing materials UBC2-1A and UBC2-1B for several years after commissioning of the field barrels provides evidence for presence of acid-neutralizing carbonate minerals, likely calcite, in these waste rock materials. Based on these observations, calcite was included in the simulations as a primary mineral at low abundances. The initial volume fraction of calcite for the simulations was estimated by calibration of the model to match measured pH in field barrel drainage during the initial phase of the experiment for each waste material type (i.e. UBC2-1A and UBC2-1B). The results for the field barrel scale simulations of materials UBC2-1A and UBC2-1B are not presented here.         205  Table 6.4. Initial volume fractions, effective rate coefficients, and calibrated surface areas for primary and secondary minerals in UBC2-1A material. The mineral content in wt (%) is from XRD analysis. Mineral content expressed as volume fractions represent model-calibrated values (PF: preferential flow region, M: matrix, ND= not detected)  Mineral Mineral Content  Kim, Kim,eff Si   calibrated Primary Minerals Volume Fraction (-) mol L-1 s-1 m2L-3 bulk 1) pyrite 1.76 × 10-3 10-12 (PF), 10-11 (M) - 2) chalcopyrite 3.21 × 10-3 10-11 - 3) sphalerite 1.00 × 10-3 10-13 - 4) calcite 8.39 × 10-4 10-7 - 5) biotite-ph 1.68 × 10-2 10-10.97 10 6) orthoclase 2.94 × 10-1 10-9.93 100 7) albite 6.2 × 10-2 10-9.69 0.5 8) muscovite 1.39 × 10-2 10-12.60 10 Secondary Minerals    9) gibbsite - 10-6 - 10) gypsum - 10-7 - 11) ferrihydrite - 10-8 - 12) malachite - 10-7 - 13) brochantite  - 10-7 - 14) antlerite - 10-7 - 15) smithsonite - 10-7 - 16) K-jarosite - 10-9 - 17) silica-am - 10-6 -  The computed saturation indices for secondary minerals are indicative of formation of gypsum, malachite, antlerite, and smithsonite in both preferential flow and matrix regions.  206  The simulated volume fractions of secondary minerals are generally higher in the matrix than in the preferential flow region due to higher sulfide oxidation rates and lower pH in matrix pore water. The volume fractions of secondary minerals are only presented for gypsum in this chapter.  Table 6.5. Mineral dissolution-precipitation, aqueous oxidation and gas dissolution-exsolution reactions  Mineral Reaction    Primary Minerals log Kim  1) pyrite* FeS2 (s) + H2O + 7/2O2 (aq) → Fe2+ + 2SO42- + 2H+ - 61.488 2) chalcopyrite CuFeS2  (s) +  4O2  (aq) → Cu2+ + Fe2+ + 2SO42-  -35.27 3) sphalerite ZnS (s) + 2O2 (aq) → Zn2+ + SO42-  -11.618 4) magnetite Fe2+Fe23+O4(s) + 8H+ → 2Fe3+ + Fe2+ + 4H2O 3.7370 5) calcite CaCO3 (s) ↔ Ca2+  + CO32-  -8.475 6) biotite-ph  K (Mg2Fe) (AlSi3O10) (OH)2 (s) + 10H+ → K+ + 2Mg2++ Fe2++ Al3++ 3H4SiO4(aq)  - 7) orthoclase  KAl3Si3O8 (s) + 4H+  +4H2O → K+ + Al3++ 3H4SiO4(aq)  - 8) albite NaAl3Si3O8 (s) + 4H+  +4H2O → Na+ + Al3++ 3H4SiO4(aq)  - 9) muscovite-ph KAl3Si3O10(OH)2 (s) + 10H+ → K++ 3Al3+ + 3H4SiO4(aq)  -   Secondary Minerals   10) gibbsite Al(OH)3 + 3H+ ↔ Al3+ + 3H2O  8.110 11) gypsum CaSO4 .2H2O ↔  Ca2+ + SO42- + 2H2O  -4.580 12) ferrihydrite Fe(OH)3 (am) + 3H+ ↔  Fe3+ + 3H2O  4.891 13) Malachite Cu2 CO3 (OH)3 + 2H+ ↔ 2Cu2++ 2H2O + CO32-  -5.18 14) brochantite  Cu4(SO4) (OH)6 + 6H+ ↔  4Cu2+ + 6H2O + SO42-  15.34 15) antlerite Cu3(SO4) (OH)4 + 4H+ ↔  3Cu2+ + 4H2O + SO42-  8.29 16) smithsonite  ZnCO3  ↔ Zn2+ + CO32-  -10.0 17) k-jarosite  K Fe3(SO4)2 (OH)6 + 6H+ ↔ K+ + 3Fe3+ + 2SO42- + 6H2O -9.210  18) silica-am  SiO2 (am) + 2H2O ↔ H4SiO4 (aq)  -2.710  Aqueous Oxidation Reduction   207   Mineral Reaction   19) Fe(II)/Fe(III) Fe2+ + 14O2  (aq)  + H+ ↔  Fe3+ + 1/2H2O 8.50 20) SO42-/HS- HS- + 2O2  (aq)  ↔ SO42- + H+ 138.51  Gas Dissolution Exsolution  21) O2 (g)/O2(aq)  O2  (g) ↔ O2  (aq) -2.898 22) CO2(g) /CO2(aq)  CO2  (g) + H2O  ↔  CO32-+ 2H+ -18.149  6.2.4 Boundary and initial conditions The inflow boundary condition for variably saturated flow was assigned as a specified flux (Neumann) boundary condition. The specified flux was equal to the daily recharge estimated as a fraction of daily precipitation measured at the weather station located in close proximity to Pile 2. The recharge is calculated using the following equation: Recharge (R) = Rainfall precipitation (P) – Evaporation (E). Evaporation is estimated by calibration of the model to match a multi-year daily and cumulative outflow data set for the largest lysimeter that covers the base of the Pile 2 (Lysimeter D) (Javadi et al., 2012). Lysimeter D collects 97% of the drainage from the pile. It is assumed that the evaporation calibrated for Lysimeter D also applies to the smaller size sub-lysimeters, including sub-lysimeter B, which is the focus of this study. For details of recharge estimation, the reader is referred to Chapter 3. The inflow boundary condition for solute transport was assigned as specified mass flux (Cauchy). This mass flux contained low concentrations for the major ions during the whole six-year period of simulation (Table 6.6). The outflow boundary condition for solute transport was set to a free exit boundary. The initial concentrations of major ions in both preferential flow and matrix regions are summarized in Table 6.6.    208   Table 6.6. Chemical composition of recharge water and initial waste rock pore water in the model Component Concentration (mol L-1) Recharge Water Waste Rock pCO2 3.17 X 10-4 3.17 X 10-4 SO42- 1.0 X 10-10 1.0 X 10-10 H4SiO4 1.0 X 10-10 1.0 X 10-10 K+ 1.0 X 10-10 1.0 X 10-10 Mg2+ 1.0 X 10-10 1.0 X 10-10 Ca2+ 1.0 X 10-10 1.0 X 10-10 Zn2+ 1.0 X 10-10 1.0 X 10-10 Pb2+ 1.0 X 10-10 1.0 X 10-10 Cu2+ 1.0 X 10-10 1.0 X 10-10 Mn2+ 1.0 X 10-10 1.0 X 10-10 Na+ 1.0 X 10-10 1.0 X 10-10 Al3+ 1.0 X 10-10 1.0 X 10-10 Cl- 1.0 X 10-10 1.0 X 10-10 pH 5.5 6.0 pO2 (atm) 0.21 0.21 Fe3+ 1.0 X 10-10 1.0 X 10-10 Fe2+ 1.0 X 10-10 1.0 X 10-10 HS- 1.0 X 10-10 1.0 X 10-10  6.2.5 Water and Solute Mass Transfer Terms The water and solute mass transfer parameters for the dual-permeability model are adapted from the parameters that were used to calibrate conservative tracer transport in Chapter 5 (Table 6.7). The 𝑤𝑓 parameter defines the ratio of the volume of the preferential flow region and the total volume (unitless) and is set to 0.5 in the simulations in this chapter. 𝐾𝑠𝑎 is the effective saturated hydraulic conductivity (ms-1) for mass transfer between the preferential flow region and the matrix, 𝐷𝑎 is the effective molecular diffusion coefficient (m2s-1) for mass transfer between the two pore regions. The values for saturated hydraulic conductivity and effective diffusion coefficient parameters selected for this chapter are the values that  209  demonstrated the closest match with the observed bromide concentration and mass flux in the simulations from Chapter 5 (presented in Figures B14 and B15 in Appendix B). The average matrix block size is 2 (cm) (a = 1 cm). A geometrical factor β = 3 and scaling factor of γw = 0.4 were considered (Gerke and van Genuchten, 1993a, 1993b).   Table 6.7. Dual-permeability mass transfer parameters for the sand and clay-loam soil profiles used for the simulations of Antamina Mine waste rock Parameter 𝒘𝒇 𝜸𝒘 𝜷 a 𝑫𝒂 𝑲𝒔𝒂 Unit [-] [-] [-] [cm] [m2/s] [m/s] Exchange term 0.5 0.4 3.0 1.0 1.0×10-6 1.0×10-10  6.3 Results and discussion 6.3.1 UBC2-1A waste rock The simulations presented in this chapter serve to show the capabilities of the MIN3P-THCm-DP model for simulating non-equilibrium flow and reactive transport in a dual-permeability type porous medium. For the simulated 1D vertical column with 10m depth containing UBC2-1A waste rock, the results for pH and concentration of selected aqueous species over the simulation period of 2196 days (Figure 6.1), reflect near equilibrium conditions between preferential flow region and matrix region. These aqueous species include sulphate, calcium, copper, and zinc in the drainage.   The results in Figure 6.1 are best explained by considering the spatial variations in the key parameters. There parameters include water saturation, hydraulic head (Figure 6.2), mineral  210  volume fractions, pH (Figure 6.3), water and mass transfer rates (Figure 6.4). Simulated water saturation and hydraulic head over the depth of column are shown in Figure 6.2. The distribution of moisture is characterized by a complex distribution that follows the initial water saturation in each pore region with fully saturated initial conditions in the matrix region and lower saturation in the preferential flow region. Results at later times show a decreasing trend in water saturations in both pore regions due to changes in recharge values over annual wet and dry seasons. The decrease in saturation is more pronounced in the preferential flow region due to its soil hydraulic properties that are representative of a coarser porous medium (sand), compared to the more fine-grained matrix (clay-loam). The water saturation plots indicate that the infiltration front has moved downward to the bottom of the column at all output times.  The only exception is after 150 days, which coincides with the onset of the first wet season after commissioning of Pile 2, corresponding to the initial wetting up of this pile.  Simulated calcite volume fractions and pH over the depth are shown in Figure 6.3. In the calcite volume fraction plot, the matrix is distinguishable from the preferential flow pore region with lower values for the matrix. Although both regions have the same initial volume fraction of calcite, the matrix ends up with lower volume fraction of this mineral. This occurs due to higher reaction rates for pyrite in the matrix region, resulting in more substantial dissolution of calcite.  Over time, the preferential flow region demonstrates a decreasing trend in calcite volume fractions as well, which is indicative of acid neutralization occurring in the preferential flow pore region as well as in the matrix region.    211  The pH values demonstrate similar numbers in both pore regions over depth and are shown at 150, 750, 1250 and 2196 days after commissioning of the experimental Pile 2. The initial value of pH is 6. At 150 days, pH is slightly different in the preferential flow region and the matrix region in the lower 4 meters of the solution domain. This difference can be explained by water saturation at 150 days (Figure 6.2). The water saturation indicates that the infiltration front has not reached the bottom of pile at 150 days. This is due to the fact that the start of the simulations coincides with the time of construction of the pile. At 150 days, Pile 2 is exposed to the onset of the first wet season after its commissioning, starting at 100 days and ending at 265 days, at which point the pile is wetting up.   Figure 6.4 shows the water flux between the subdomains in addition to advective and diffusive mass transfer fluxes of sulfate between the two pore regions. Sulfate was selected as a key component to demonstrate mass transfer processes. The water transfer term (Γ𝑤) is assumed to be proportional to the difference in hydraulic heads between the preferential flow region and the matrix region. This formulation is based on the approach taken by Gerke and Genuchten (1993a, 1993b) and the details of related equations and concepts are described in Chapter 4. The formulation considers dynamic interactions between the two pore regions with separate hydraulic properties. The solute mass-transfer term (Γ𝑠) includes two mass transfer terms: advective and diffusive.  Water transfer fluxes in Figure 6.4 are small values (10-7-10-8 md-1) at all output times except at 150 days. At 150 days, the infiltration front has reached a depth of 2.4 m, but the saturation of the matrix in the rest of the domain is still the same as its initial water saturation before  212  wet up. The same behavior is noted in hydraulic heads of the preferential flow region and the matrix region at 150 days. Therefore, a large water flux at 150 days is likely due to the difference in hydraulic heads between the two pore regions. The advective mass transfer is a direct function of the water flux term and consequently hydraulic head differences between the two pore regions.   213    214  Figure 6.1. pH and concentration of key components sulfate, calcium, copper and zinc, and recharge applied on preferential flow and matrix pore regions over the simulation period in the column containing waste rock material UBC2-1A     Figure 6.2. Water saturation and hydraulic head calcite volume fraction over depth of the column for preferential flow region and matrix. Note the vertical axis is depth (m) for both plots. PF = Preferential flow and M = Matrix  At 1250 days there is also a notable water transfer between the sub-domains and advective mass transfer, which is also due to the pronounced differences in hydraulic head between the preferential flow pore region and the matrix. The diffusive mass transfer is a function of matrix water content and the concentration gradient between the preferential flow region and the matrix. The advective mas transfer is from the matrix towards the preferential flow region at 150 and 1250 days, due to higher hydraulic head in the matrix region. Both output times at 150 and 1250 days coincide with mid-wet season high recharge events. At 150 days the pile is wetting up. resulting in a high hydraulic gradient between the preferential flow region and  215  the matrix. At 1250 days, the pile has already wet up. At 750 days and 2196 days, there are low hydraulic head differences between the two pore regions, which results in near zero advective mass transfer in most of the column. Both of these output times are in the dry season, coinciding with minimal recharge on both pore regions. In general, diffusive mass transfer is larger than advective mass transfer both in the wet and dry seasons with larger difference in the wet season when preferential flow is active in the pile.    216     Figure 6.3. From top left to bottom right: pH, sulfate concentration, calcite and gypsum volume fraction, and gypsum saturation indices over the depth of the column for preferential flow region and matrix at five output times. Note the vertical axis is depth (m) for sulfate concentration plot and elevation (Z (m)) for calcite volume fraction and pH. PF = Preferential flow and M = Matrix  The UBC2-1A waste rock is characterized by a low reactivity and has maintained average pH values of 7.5 in drainage both at the field barrel (1m high material barrel) and experimental pile scale (10m high pile) in over six years of studies (data not presented here). The volume  217  fraction and saturation indices of gypsum (Figure 6.3) indicate that gypsum precipitation does not occur in the time of study. Brochantite, antlerite, jarosite that can retain sulfate in this waste rock column (data not presented here) show low volume fractions. Therefore, sulfate’s behavior is representative of a conservative component in this waste material.   Figure 6.4. Water transfer and advective and diffusive mass transfer for sulfate between the preferential flow pore region and the matrix over depth.   6.3.2 UBC2-1B waste rock For the simulated 1D vertical column with 10m depth containing UBC2-1B waste rock, the simulated pH and aqueous concentration of sulphate, calcium, copper, and zinc in drainage over the simulation period of 2196 days are presented in Figure 6.5 and Table 6.6. Figure 6.6 shows simulated pH, sulfate concentrations, calcite and gypsum volume fractions and gypsum saturation indices versus depth. Figure 6.5 shows pH values gradually decreasing over time in both preferential flow and matrix regions, especially in the matrix, due to oxidation of pyrite. In the matrix, pH values decrease from 6 to around 5.7 at 500 days,  218  which demonstrates that calcite becomes depleted in the matrix region after 500 days (Figure 6.5). Meanwhile, in the preferential flow region pH stayed around 6.0 beyond 500 days, indicating continued dissolution of calcite. At later times, pH decreases to around 4.7 at 1200 days when calcite is depleted. Figure 6.6 depicts that at 150 days calcite is present in both preferential flow and matrix regions. At 750 days calcite is depleted in the matrix region while the preferential flow regions still contain calcite. At 1250 days, calcite has been depleted in both regions. The simulations indicate that depletion of calcite occurs more slowly in the preferential flow region due to a slower pyrite oxidation rates in this pore region.  Dissolved calcium and sulfate concentrations (Figure 6.5) are controlled by equilibrium with gypsum. Early time results (150 days) are characterized by similar volume fractions of gypsum both in the matrix region and preferential flow region. However, the gypsum volume fraction increases more rapidly in the matrix region compared to the preferential flow region (Figure 6.6). Dissolved calcium concentrations are also higher in the preferential flow region between 500 and 1200 days. This is due to lower calcite dissolution rates in the preferential flow region compared to the matrix region at that time. However, after 1200 days, dissolved calcium concentrations approach equilibrium conditions between the preferential flow region and matrix.  219    220  Figure 6.5. pH and concentrations of key components sulfate, calcium, copper and zinc, and recharge applied to preferential flow and matrix pore regions over the simulation period for waste rock material UBC2-1B  Simulated water saturations and hydraulic heads over the depth are similar to values shown for material UBC2-1A (Figure 6.2), with fully saturated initial conditions in the matrix and lower saturations in the preferential flow region. Similarly, in material UBC2-1B the infiltration front has reached the bottom of the column at all output times, except for 150 days which coincides with the onset of the first wet season after commissioning of Pile 2 and wetting up of this pile.  Dissolved sulfate concentrations are similar in the preferential flow and matrix regions for the initial 500 days of the simulation (Figure 6.5). However, from 500 days to the end of the simulation period, the concentrations of sulfate are slightly higher in the matrix than in the preferential flow region. Sulfate concentrations are limited by precipitation of gypsum after 500 days in both regions, especially in the matrix region (Figure 6.6).   221   Figure 6.6. pH, sulfate concentrations, calcite and gypsum volume fractions, and gypsum saturation indices over the depth in the preferential flow and matrix regions at five output times. Note the vertical axis is depth (m) for the sulfate concentration plot and elevation (Z (m)) for calcite volume fractions and pH. PF = Preferential flow and M = Matrix  Diffusive mass transfer is a function of the matrix water content and concentration gradient between the preferential flow region and the matrix region. Figure 6.7 depicts the water transfer flux, as well as advective and diffusive mass transfer fluxes of sulfate between the preferential flow and matrix pore regions. The water transfer term (Γ𝑤) demonstrates the  222  same behavior as the water transfer term for UBC2-1A material due to having the same soil hydraulic parameters for the preferential flow region and matrix in both simulations. In addition, both simulations assume the same effective saturated hydraulic conductivity (𝐾𝑠𝑎) for mass transfer between the two regions. On the other hand, the solute mass-transfer term between the regions (Γ𝑠) is near zero during the simulation period except for early times (e.g. 150 days is shown in Figure 6.7). At 150 days, the mass-transfer term is very small as well (i.e. in the range of 10-14 m/d). Mosr substantial mass transfer at 150 days can be attributed to the difference in hydraulic head between the two pore regions.    Figure 6.7. Water transfer, advective and diffusive mass transfer fluxes for sulfate between preferential flow and matrix regions over depth.  6.4 Summary and conclusions This chapter investigates the application of the dual-permeability extension developed for the multi-component reactive transport code MIN3P for simulating acid and neutral rock  223  drainage behavior in an experimental waste rock pile (Pile 2) at the Antamina mine, Peru. The results demonstrate the capabilities of the enhanced version of the MIN3P code for dual-permeability simulations. The focus of this study is specifically on sub-lysimeter B at the back of Pile 2 and. The conceptual model for flow and solute transport is based on results from Chapter 5. The model is applied to two one-dimensional 10m high columns containing a less reactive waste rock type (UBC2-1A) and a more reactive waste rock type (UBC2-1B) from the Antamina mine. The reactive transport model was able to investigate the complex processes in waste rock in variably saturated porous media. The modeling contains the following processes : (1) sulfide oxidation, acid neutralization and pH-buffering through carbonate and silicate mineral dissolution, (2) precipitation of secondary minerals such as gypsum, brochantite, antlerite, jarosite, siderite in both pore regions, (3) advection of solutes through both pore regions, water transfer and advective and diffusive mass transfer from the matrix and to preferential flow region, mostly during the wet season.    The MIN3P model has the ability of considering kinetic and equilibrium rate expressions for minerals and this ability also exists in developed preferential flow extension. Therefore, kinetic rate expressions were assumed for sulfide and silicate minerals and geochemical equilibrium was considered for secondary minerals, respectively. This model is a process-based representation of transport in waste rock, which consists of fast and slow flow and solute transport paths due to its physically heterogeneous nature. Furthermore, the experimental data from the Antamina mine demonstrate that drainage is collected from the piles continuously throughout the year and even during the dry seasons, which is indicative of the flow and solute transport occurring in the matrix pore region. In other words, the dual- 224  permeability model provides a closer representation of the processes in a waste rock pile compared to mobile-immobile and dual-porosity models that assume no water flow and solute transport in the matrix region. The developed code and results of this study have implications for practical field problems in macroporous media such as acid rock drainage formation in mine waste rock, transport of herbicides and fertilizers in agricultural soils, and the transport of industrial chemicals and pathogens to groundwater.  The main limitations of this study and many other non-equilibrium models is the estimation of hydraulic and transport parameters for both pore regions and the mass transfer parameters between the pore regions, especially for porous media similar to mine waste rock with a wide range of particle sizes. Measurement of these parameters is not possible at the field scale and instead requires parameter calibration by fitting simulation results to experimental data. The simulations in this chapter were run using a constant set of parameters for 𝐾𝑠𝑎, 𝐷𝑎, 𝑤𝑓, which were selected from the sensitivity analysis performed in Chapter 5. To improve the understanding of reactive transport along fast and slow flow and transport pathways, a sensitivity analysis study is required to investigate the effect of 𝐾𝑠𝑎, 𝐷𝑎 , 𝑤𝑓 on the transfer of solute between the pore regions affected by sulfide mineral oxidation and pH-neutralization reactions.     225  Chapter  7: Conclusions and Recommendations The main objective of this research was to develop a reactive transport model that includes a flexible formulation for dual-domain flow and solute transport and apply the model to simulate acid rock drainage generation and attenuation in highly heterogeneous waste rock at various scales. The simulations investigated the interactions between flow and mass transport processes and the dominant mineralogical controls and geochemical processes in each waste rock type. For that purpose, hydrologic and geochemical data from 1-m tall field barrels and a 10-m tall experimental waste rock pile were compiled for multiple years and subsequently analyzed. The results of this work were presented in five chapters that discussed geochemical and hydrogeological processes controlling ARD at the field barrel scale (Chapter 2), analysis of variably-saturated flow and conservative solute transport in an experimental waste rock pile based on a uniform flow and transport model (Chapter 3), development and verification of a dual-domain flow and solute transport model with formulations for mobile-immobile, dual porosity and dual permeability domains (Chapter 4), analysis of variably-saturated flow and conservative solute transport in an experimental waste rock pile based on mobile-immobile, dual-porosity and dual-permeability model formulations  (Chapter 5) and demonstration of simulation capabilities for multicomponent reactive transport in waste rock under consideration of preferential flow (dual permeability conditions) (Chapter 6).   7.1 Multicomponent Reactive Transport in Waste Rock: Field Barrel Scale The purpose of the chapter 2 was to evaluate conceptual models that adequately describe transition of pH from neutral to acidic conditions and how secondary minerals and silicate minerals buffer acidity in a low carbonate waste rock environment at the field barrel scale.  226  This work was performed using a uniform approach to describe flow and transport processes. The results of a separate mineralogical study (Peterson, 2014) provided constraints on the minerals and their abundances for inclusion in the model. The six-year evolution of drainage quality from the field barrel is complex and is affected by precipitation and dissolution of various secondary minerals and the enhancement of sulfide weathering rates with declining pH. A representative conceptual model that adequately approximates the field-observed pH and the concentrations of sulfate, calcium, copper and zinc required consideration of both calcite and wollastonite dissolution and precipitation/dissolution of the secondary minerals gibbsite, malachite, ferrihydrite, smithsonite, antlerite, brochantite and gypsum. The simulation results indicate that secondary mineral precipitation and dissolution provide important controls for the release of components such as sulfate, copper, zinc and calcium to the effluent solution and demonstrate that the estimation of weathering rates cannot be directly derived from drainage chemistry, even on this relatively small scale.  In field barrel UBC2-3A, the observed pH evolution and relatively high solute concentrations demonstrated that the effective reaction rates of acid generating minerals, especially pyrite, did not decrease due to passivation throughout the six years of study. In fact, obtaining improved fits with observational data required to include sulfide oxidation rates that increased under acidic pH-conditions, suggesting acceleration of oxidation by microbial mediation. Reactive transport modeling results indicate the occurrence of seasonal formation and dissolution of gypsum in the field barrel, explaining seasonal variations in concentrations of calcium and sulfate. In the dry season, gypsum precipitates within the field barrel. In the wet season, abundant supply of low-salinity recharge results in dissolution of gypsum.   227  The results illustrate the role of calcite dissolution for acid neutralization at pH-values around 6.3 and the role of wollastonite in pH-buffering at pH 4. The simulation results based on calcite content estimated from bulk NP yielded neutral-pH conditions for the entire duration of the field experiment, which was inconsistent with field observations. This finding indicates that bulk NP determined from ABA is not always a good representation for the effective neutralization potential in this rock type and can substantially overestimate the available NP under field conditions. Similar simulation results were obtained by estimating the calcite content based on calcium and carbon from solid phase elemental analysis. Better simulation results for evolution of pH and elemental release could be obtained by attributing NP to both calcite and wollastonite.  If all NP was assigned to wollastonite, dissolution of wollastonite was able to neutralize acidity; however, its rate of dissolution and capacity for acid neutralization was too slow compared to carbonate minerals in this rock type and observed early time behavior could not be simulated. These results imply that despite the fact that calcite was not detected in XRD, its presence is required to maintain pH above 6.3 at early time.   It is also important to point out that some of the high concentrations in drainage at the start of the annual wet season, are represented by data from a single sampling event. Increasing sampling frequency throughout the wet season, especially at the onset of wet season, would benefit the development of an improved understanding of metal accumulation and release in such experiments.     228  7.2 Variably Saturated Hydrology-Experimental Waste Rock Pile Scale In chapter 3, a simple 1D-composite model based on uniform flow and solute transport with only two spatially uniform calibration parameters (recharge and saturated hydraulic conductivity) was used to simulate discharge from a 10 m tall experimental waste rock pile for a time period of four years, including the response to a tracer test.  The model was able to closely match cumulative discharge and the response of the hydrograph to wet and dry seasons. The model also allowed to distinguish the response to distinct infiltration events in the wet and dry seasons. However, the uniform flow and transport model failed to adequately reproduce the response to a tracer test, providing strong evidence for the occurrence of preferential flow in this waste rock pile, despite its generally soil-like nature. The key information gained from these simulations is that matching the outflow hydrograph and cumulative discharge alone is insufficient to fully characterize residence times in this waste rock pile. This result is in accord with results from other hydrological studies, which have shown that tracer data provide complementary information not present in flow data (Harvey and Gorelick, 1995). This finding has implications for prediction of metal release and attenuation processes within waste rock and provides the motivation for the development of a model that accounts for matrix and preferential flow, as well as solute transport.      7.3 Development of a Generalized Dual Domain Formulation for Flow and Solute Transport  Motivated by the findings of chapter 3, a flexible formulation for non-uniform flow and solute transport was implemented into the multicomponent reactive transport code MIN3P-THCm, resulting in MIN3P-THCm-DP. This new model includes a formulation that allows  229  simulating mobile-immobile, dual-porosity and dual-permeability systems for up to two spatial dimensions. This model has the capability of simulating variably-saturated flow conditions under either steady-state or transient conditions and multi-component reactive transport in dual-domain systems. The mass transfer between the two pore regions is set as a first-order mass transfer term. The accuracy of the code was successfully verified against an established code, HYDRUS-1D, for a variety of flow and conservative solute transport problems. The advantage of the current approach is that a consistent formulation for mobile-immobile, dual-porosity and dual-permeability systems is provided.  7.4 Variably-saturated Flow and Conservative Solute Transport in Macroporous Waste Rock at the Experimental Waste Rock Pile Scale Chapter 5 presents the results of a comparative study of flow and solute transport behavior using uniform flow, mobile-immobile, dual-porosity and dual-permeability models in a soil column that is part of an experimental mine waste rock pile. The studied waste rock pile was initially hypothesized as a pile with soil-like behavior that dominantly demonstrates matrix flow behavior (Peterson, 2014).  However, the numerical modeling of flow and solute transport using the uniform model revealed that this formulation is not able to adequately reproduce the response to a tracer test, providing a strong indication for the occurrence of preferential flow in this waste rock pile, despite its soil-like nature. In this chapter, the non-uniform flow and solute transport models developed and verified in Chapter 4 were used to evaluate the water and solute mass transfer parameters that best capture the outflow hydrograph and solute release at the base of the waste rock pile and in this way provide additional insights into the distribution of flow and solute transport within the preferential  230  flow and matrix pore regions. The misfit between observations and simulated results was evaluated by an extensive sensitivity analysis to determine the parameter set that best describes field observations. Parameters considered in the sensitivity analyses included (1) the ratio between the volume of the preferential pore region and the total volume (𝑤𝑓), (2) the hydraulic conductivity controlling water transfer between the two pore regions (𝐾𝑠𝑎), (3) the effective diffusion coefficient (𝐷𝑎) controlling diffusive solute mass transfer between the two pore regions, and (4) the distribution of inflow into the subdomains (𝑞𝑖𝑛𝑓). The model results were compared to observed tracer test data collected from a Sub-lysimeter B located at the back of the waste rock pile providing transient data for: (1) daily outflow, (2) tracer concentrations, and (3) tracer mass loading.  Comparative analyses of observational data and simulation results led to the following findings:   The outflow results from mobile-immobile and dual-porosity simulations show a large peak at the time of tracer application which is not observed in field data. This is due to flow of water in the mobile region and zero infiltration into immobile pore region in the mobile-immobile model and limited retention of water in the matrix in the dual-porosity model. In dual-permeability models, the presented simulations with higher 𝑤𝑓 and 𝐾𝑠𝑎  do not show this peak due to water transfer from the preferential flow region into the matrix. These results suggest that mobile-immobile and dual-porosity formulations may be insufficient to adequately describe flow behavior in waste rock and that more complex models, such as dual-permeability models, may be warranted.  231  In terms of tracer release, the timing and peak concentration of tracer in the basal discharge improved with increased model complexity. In addition, more complex models were also able to provide a better reproduction of the observed tailing. All dual-domain formulations provided an improved match with observational data compared to the uniform flow and solute transport approach.   Results of the sensitivity analysis demonstrate that a higher mass transfer coefficient 𝐷𝑎 leads to faster diffusion of solutes from the mobile (preferential flow) region to the immobile (matrix) region resulting in closer match for the first part of the concentration release; however, the same parameters do not provide a very good match for the second part of the breakthrough curve, implying that flow and transport processes in the waste rock pile are more complex than captured by the current model formulation.  An improved representation of the outflow hydrograph, peak tracer concentrations and tailing, when using the dual-permeability model, demonstrates the capability of this more sophisticated approach to more adequately represent water flow and solute transport in waste rock. However, although peak concentrations and post-peak concentrations trends were improved, substantial differences to observations remained. These differences are indicative of tracer retention in fine-grained material; leading to entrapment of mass for a very long time and very slow release. This process is not captured by a dual permeability formulation. Analysis of the tracer test shows that at the end of the monitoring period (1477 days), less than 55% of the tracer on top of sub-lysimeter B was recovered. However, most simulation results reported that 80-100% of tracer was released within the same time frame. This result  232  provides further evidence for the presence of more than two pore regions within the waste rock, likely including an immobile region in addition to matrix and preferential flow regions.  This study has implications for flow and solute transport in mine waste rock, structured soils and agricultural soils and in general materials that are affected by partitioning of solutes or contaminants between preferential flow and matrix pore regions and require management strategies for drainage quality and quantity.   The limitation of using these more complex non-uniform models lies in the difficulty of defining the mass transfer parameters. The number of required parameters increases from uniform to mobile-immobile, dual porosity and dual-permeability models and some of the parameters cannot be measured. These limitations tend to lead to non-unique parameters when calibrating a model, putting into question the representativeness of the calibrated model.  7.5 Demonstration of Multicomponent Reactive Transport in Macroporous Waste Rock at the Experimental Pile Scale Chapter 6 demonstrated the applicability of the dual-permeability extension developed for the multi-component reactive transport code MIN3P for simulating acid and neutral rock drainage behavior in an experimental waste rock pile (Pile 2) at the Antamina mine, Peru. The focus of this study is specifically on sub-lysimeter B at the back of Pile 2. The conceptual model for flow and solute transport is based on results from Chapter 5, while the geochemical system and reaction network is derived from the results presented in Chapter 2.  233  The model is applied to a one-dimensional 10m-tall column containing a less reactive waste rock type (UBC2-1A) and a more reactive waste rock type (UBC2-1B) from the Antamina mine. The reactive transport model was able to investigate complex processes in waste rock under variably saturated conditions, accounting for multicomponent solute transport and geochemical reactions in both pore regions, as well as water transfer and advective and diffusive mass transfer between the matrix and the preferential flow regions.    The MIN3P model has the ability of considering kinetic and equilibrium rate expressions for minerals and this ability also exists in the preferential flow extension. Therefore, kinetic rate expressions were assumed for sulfide and silicate minerals and geochemical equilibrium was considered for secondary minerals, respectively. This model provides a process-based representation of solute transport in waste rock, which consists of fast and slow flow and solute transport pathways due to its physically heterogeneous nature. The developed code and results of this study have implications for practical field problems in macroporous media such as acid rock drainage formation in mine waste rock, transport of herbicides and fertilizers in agricultural soils, and the transport of industrial chemicals and pathogens to groundwater.  As for conservative transport (Chapter 5), the main limitations of this study and many other non-equilibrium models are the estimation of hydraulic and transport parameters for both pore regions and the mass transfer parameters between the pore regions, especially for porous media similar to mine waste rock with a wide range of particle sizes. Measurement of these parameters is not possible at the field scale and instead requires parameter calibration by  234  fitting simulation results to experimental data. The simulations in this chapter were run using a constant set of parameters for 𝐾𝑠𝑎, 𝐷𝑎, 𝑤𝑓, which were selected from the sensitivity analysis performed in Chapter 5. To improve the understanding of reactive transport along fast and slow flow and transport pathways, a sensitivity analysis study is required to investigate the effect of 𝐾𝑠𝑎, 𝐷𝑎 , 𝑤𝑓 on the transfer of solute between the pore regions affected by sulfide mineral oxidation and pH-neutralization reactions.  7.6 Recommendations The main recommendations of this thesis are: 1. Develop the capability of gas transport in dual domain systems and gaseous mass-transfer between the pore regions, accounting for exchange of gases between the pore regions. 2. Develop a multi-domain model that includes an immobile region in addition to matrix and preferential flow regions to better account for retention of mass and long-term tailing. 3. Perform an additional modeling study to investigate the role of the coating and skin formation on the parameters controlling advective (𝐾𝑠𝑎) and diffusive (𝐷𝑎) solute transfer between the preferential flow and matrix regions. 4. 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Soil water characteristic curve for mine waste rock containing coarse material. In Proc. of the CSCE Annual Conf., London, ON, Canada, pp. 198–202.    247  Appendices Appendix A   A.1 Numerical methods in MIN3P and MIN3P-THCm codes MIN3P and MIN3P-THCm codes use the global implicit method (GIM) for temporal discretization of the multicomponent advection-dispersion equations and the geochemical reactions. GIM method considers reaction and transport to happen simultaneously. Spatial discretization of governing equations is performed using the finite volume method to solve the Richards equation governing 3D unsaturated/saturated subsurface flows. Spatial and temporal discretization of the variably-saturated flow is as the following:   [𝑆𝑎,𝑘𝑁+1𝑆𝑠ℎ𝑘𝑁+1 − ℎ𝑘𝑁Δ𝑡+ 𝜙𝑆𝑎,𝑘𝑁+1 − 𝑆𝑎,𝑘𝑁Δ𝑡] 𝑉𝑘 − ∑ 𝑘𝑟𝑎,𝑘𝑙𝛾𝑘𝑙[ℎ𝑙𝑁+1 − ℎ𝑘𝑁+1]𝑙𝜖𝜂𝑘− 𝑄𝑎,𝑘𝑁+1 = 0    𝑘 = 1, 𝑁𝑣 Equation A.1-1  In the above equation, subscript k is the kth control volume, 𝜂𝑘 is the number of adjacent control volumes. l is the adjacent control volume. Δ𝑡 is the time increment. N+1 represemts the new time level and N shows the old time level. 𝑉𝑘 is the volume of the kth control volume. Nv defines the number of control volumes in solution domain. 𝑘𝑟𝑎,𝑘𝑙 is the representative relative permeability between control volumes k and l.   The mass conservation equation for the component can be discretized in space and time using finite volume and GIM methods, respectively. This discretized equation can be shown as:    248  𝜙𝑉𝑘Δ𝑡[𝑆𝑎,𝑘𝑁+1𝑇𝑗,𝑘𝑎,𝑁+1 − 𝑆𝑘𝑎,𝑁𝑇𝑗,𝑘𝑎,𝑁] +𝜙𝑉𝑘Δ𝑡[𝑆𝑔,𝑘𝑁+1𝑇𝑗,𝑘𝑔,𝑁+1 − 𝑆𝑘𝑔,𝑁𝑇𝑗,𝑘𝑔,𝑁]+ ∑ 𝑣𝑎,𝑘𝑙𝑇𝑗,𝑘𝑎,𝑁+1𝑙𝜖𝜂𝑘− ∑ 𝛾𝑎,𝑘𝑙𝑑 [𝑇𝑗,𝑙𝑎,𝑁+1 − 𝑇𝑗,𝑘𝑎,𝑁+1]𝑙𝜖𝜂𝑘− ∑ 𝛾𝑔,𝑘𝑙𝑑 [𝑇𝑗,𝑙𝑔,𝑁+1 − 𝑇𝑗,𝑘𝑔,𝑁+1] −𝑉𝑘Δ𝑡𝑙𝜖𝜂𝑘[𝑇𝑗,𝑙𝑠,𝑁+1 − 𝑇𝑗,𝑘𝑠,𝑁+1]− 𝑄𝑗,𝑘𝑎,𝑎,𝑁+1𝑉𝑘 − 𝑄𝑗,𝑘𝑎,𝑚,𝑀𝑉𝑘 = 0                              𝑗 = 1, 𝑁𝑐 Equation A.1-2  Where 𝑣𝑎,𝑘𝑙 is the aqeous phase flux between control volumes k and l, and 𝛾𝑎,𝑘𝑙𝑑  and 𝛾𝑔,𝑘𝑙𝑑  are the influence coefficients for the dispersive flux in aqueous and gas phases, respectively. 𝑇𝑗,𝑘𝑎,𝑁+1 is the total aqueous component. The interfacial flux 𝑣𝑎,𝑘𝑙 is calculated from the solution of flow equation:  𝑣𝑎,𝑘𝑙 = 𝑘𝑟𝑎,𝑘𝑙𝛾𝑘𝑙[ℎ𝑙𝑁+1 − ℎ𝑘𝑁+1] Equation A.1-3  The Newton linearization for algebraic nonlinear equations of variably-saturated flow is implemented using standard techniques. The system of algebraic non-linear equations for reactive transport is linearized using the Newton-Raphson method. The set of algebraic relationships leads to a large Jacobian matrix that is solved using the sparse iterative solver package WATSOLV (VanderKwaak et al., 1997). A compressed data structure is applied for both the Jacobian matrices. This data structure stores only non-zero entries that are the result  249  of discretization of the variably-saturated flow and reactive-transport and local geochemical reactions matrices (Mayer, 1999).  A.2 Input file in MIN3P-THCm-DP code The structure of input file for MIN3P-THCm-DP is similar to MIN3P-THCm code. To incorporate the mobile-immobile, dual-porosity and dual-permeability approaches, one data block is added which is named ‘Section 11B: physical parameters - dual-permeability’. To set up a simulation for MIN3P-THCm-DP code, the following data blocks require modification:  'Section 1: global control parameters':   To switch the preferential-flow option on in the code, the keyword ‘dual-permeability’ is required in the first data block, ‘global control parameters’. The 'dual-permeability' keyword is used for all dual-permeability, dual-porosity and mobile-immobile simulations.  ' Section 3: spatial discretization':  To set the domain for a dual-domain approach, the ‘number of discretization intervals in y’ is required to be equal to 2 and for each discretization interval ymin and ymax are set. For the first interval, the ymax is the location of preferential-flow region and the matrix interface in the y-direction (this number is equal to 'fracture proportion' and 'interface of matrix and fracture in y-direction' parameters that are defined in ‘Section 11B: physical parameters - dual-permeability’, discussed more in the following sections). To calculate the ymax (and the 'fracture proportion' and 'interface of matrix and fracture in y-direction'), divide the porosity  250  of fracture by total porosity (porosities are defined in Section 9, e.g. in this case ymax = 0.13/0.335 = 0.388). Table A8 shows an example of spatial discretization data block for a MIN3P-THCm-DP input file.  Table A8. Example of data block 3: spatial discretization for MIN3P-THCm-DP input file ! Section 3: spatial discretization                                          ! -------------------------------------------------------------------------- !       'spatial discretization'                                                     1                             ;number of discretization intervals in x   1                             ;number of control volumes in x    0.0  1.0                   ;xmin,xmax"    2                             ;number of discretization intervals in y       1                             ;number of control volumes in y                0.0  0.388               ;ymin,ymax   1                             ;number of control volumes in y                0.388  1.00             ;ymin,ymax  1                    ;number of discretization intervals in z 201                         ;number of control volumes in z    0.0 10.0                  ;zmin,zmax  'done'       ‘Section 9: physical parameters - porous medium’: In this section, the porosities for the fracture and matrix are defined. The way they are currently set up in MIN3P-THCm is that they are entered by the user as input parameters. The total porosity is a summation of porosity of the preferential-flow region and porosity of the matrix (in this example, the total porosity is calculated by: 0.13 + 0.205 = 0.335).   251  Table A9. Example of data block 9: physical parameters-porous medium for MIN3P-THCm-DP input file ! Section 9: physical parameters - porous medium                                ! --------------------------------------------------------------------------      'physical parameters - porous medium'                                           2                             ;number of property zones                           ! --------------------------------------------------------------------------    'number and name of zone'                                                       1    'fracture'                                                                       0.1306368              ;porosity           'extent of zone'                                                                0.0 1.0  0.0 0.388  0.0 10.0        'end of zone'                                                                      ! --------------------------------------------------------------------------    'number and name of zone'    2    'matrix'    0.205                 ;porosity           'extent of zone'    0.0 1.0  0.388 1.0  0.0 10.0        'end of zone' 'done'         ‘Section 10: physical parameters - variably saturated flow’: The variably saturated flow parameters are defined in this section. For dual-porosity and mobile-immobile models, the 'hydraulic conductivity in z-direction' in the matrix is required  252  to be set to a very small value (e.g. 1×10-15 m/s), therefore, the water and solute do not move within the immobile pore region.  Although the simulation is set as a 2D simulation with two control volumes in y-direction, it is actually a 1D domain with two co-existing porous media, so the 'hydraulic conductivity in the y-direction' does not need to be defined in this case and the code does not use the number defined here for the water and solute transfer between fracture and matrix.  ‘Section 11: physical parameters - reactive transport’: In this section, 'longitudinal dispersivity' is defined for preferential-flow region and matrix in dual-permeability case.  ‘Section 11B: physical parameters - dual-permeability’: This section is the main data block for the problem-specific input parameters and the parameters that are defined in this data block are the coefficients that are required for transfer rate calculation (Error! Reference source not found.). 'Geometry shape factor' (β) is a factor that depends on the geometry of aggregates [-]. Most studies have derived values for β which range from 3 for rectangular slabs to 15 for spherical aggregates (Gerke and van Genuchten, 1993b). 'Scaling factor' (γw)  is an empirical factor and was found to be 0.4, more or less independent of the aggregate geometry and the applied initial pressure head conditions (Gerke and van Genuchten, 1993a). 'Effective diffusion path length' (a) represents the distance [L] from the center of a fictitious matrix block to the fracture boundary. For the  253  methods used for derivation of these parameters and a detailed discussion and evaluation of the water transfer term, refer to Gerke and Genuchten, (1993b).  'Effective hydraulic conductivity' is the effective saturated hydraulic conductivity of preferential flow and matrix interface [LT-1] and can be used as a calibration parameter. This parameter is an input parameter to MIN3P-THCm-DP. In mobile-immobile and dual-porosity simulations, this parameter must be set to a very small value (e.g. 1×10-15 m/s).  'Effective diffusion coefficient':  Da [L2T-1] is the effective molecular diffusion coefficient of the matrix block near the interface (Gerke and van Genuchten, 1993a).  'Fracture proportion': wf [-] parameter is the ratio of the volumes of the fracture (inter-aggregate) and the total pore systems. This parameter is the weighting factor for the two overlapping pore regions used for weighting of porosity values, saturated hydraulic conductivity in each pore domain in z-direction, and the variably-saturated flow boundary condition.  'Interface of matrix and fracture in y-direction': this parameter defines the y-coordinate of the preferential-flow region and matrix interface.  Table A10. Example of data block 11B: physical parameters-porous dual-permeability for MIN3P-THCm-DP input file ! Section 11B: physical parameters - dual-permeability                          254  ! --------------------------------------------------------------------------   ! 'physical parameters - dual-permeability'  'geometry shape factor' 3.0d0  'scaling factor' 0.4d0      'effective diffusion path length' 0.01d0  'effective hydraulic conductivity' 1.0d-15         'effective diffusion coefficient'   1.0d-7    'fracture proportion' 0.388d0  'interface of matrix and fracture in y-direction' 0.388d0      'done'     255  Appendix B    B.1 Effect of 𝐊𝐬𝐚  Conceptual ModelOutflow wf Da KsaConcentration wf Da KsaMass flux wf Da Ksa 256  B.2 Mobile-Immobile  Figure 7B1. Mobile-immobile model: outflow of Pile 2 sub-lysimeter B drainage for the experimental period since August 2007. Data are shown from 800 to 1800 days for clarity. Sensitivity analysis is performed on 𝐊𝐬𝐚  and 𝐰𝐟 parameters.   257    Figure B2. Mobile-immobile model: concentration of bromide tracer in Pile 2 sub-lysimeter B drainage for the experimental period since August 2007. Data are shown from 800 to 1800 days for clarity. Sensitivity analysis is performed on 𝐊𝐬𝐚  and 𝐰𝐟 parameters.  258   Figure B3. Mobile-immobile model: mass flux of bromide tracer in Pile 2 sub-lysimeter B drainage for the experimental period since August 2007. Data are shown from 800 to 1800 days for clarity. Sensitivity analysis is performed on 𝐊𝐬𝐚  and 𝐰𝐟 parameters.    259  B.3 Dual-porosity  Figure B4. Dual-porosity model: outflow of Pile 2 sub-lysimeter B drainage for the experimental period since August 2007. Data are shown from 800 to 1800 days for clarity. Sensitivity analysis is performed on 𝐊𝐬𝐚  and 𝐰𝐟 parameters.  260   Figure B5. Dual-porosity model: concentration of bromide tracer in Pile 2 sub-lysimeter B drainage for the experimental period since August 2007. Data are shown from 800 to 1800 days for clarity. Sensitivity analysis is performed on 𝐊𝐬𝐚  and 𝐰𝐟 parameters.  261   Figure B6. Dual-porosity model: mass flux of bromide tracer in Pile 2 sub-lysimeter B drainage for the experimental period since August 2007. Data are shown from 800 to 1800 days for clarity. Sensitivity analysis is performed on 𝐊𝐬𝐚  and 𝐰𝐟 parameters.    262   B.4 Dual-permeability 1  Figure B7. Dual-permeability 1 model: outflow of Pile 2 sub-lysimeter B drainage for the experimental period since August 2007. Data are shown from 800 to 1800 days for clarity. Sensitivity analysis is performed on Ksa  and wf parameters.  263   Figure B8. Dual-permeability 1 model: concentration of bromide tracer in Pile 2 sub-lysimeter B drainage for the experimental period since August 2007. Data are shown from 800 to 1800 days for clarity. Sensitivity analysis is performed on Ksa  and wf parameters.  264   Figure B9. Dual-permeability 1 model: mass flux of bromide tracer in Pile 2 sub-lysimeter B drainage for the experimental period since August 2007. Data are shown from 800 to 1800 days for clarity. Sensitivity analysis is performed on Ksa  and wf parameters.   265  B.5 Dual-permeability 2  Figure B10. Dual-permeability 2 model: outflow of Pile 2 sub-lysimeter B drainage for the experimental period since August 2007. Data are shown from 800 to 1800 days for clarity. Sensitivity analysis is performed on Ksa  and wf parameters.  266   Figure B11. Dual-permeability 2 model: concentration of bromide tracer in Pile 2 sub-lysimeter B drainage for the experimental period since August 2007. Data are shown from 800 to 1800 days for clarity. Sensitivity analysis is performed on Ksa  and wf parameters.    267   Figure B12. Dual-permeability 2 model: mass flux of bromide tracer in Pile 2 sub-lysimeter B drainage for the experimental period since August 2007. Data are shown from 800 to 1800 days for clarity. Sensitivity analysis is performed on Ksa  and wf parameters.  268  B.6 Dual-permeability 3  Figure B13. Dual-permeability 3 model: outflow of Pile 2 sub-lysimeter B drainage for the experimental period since August 2007. Data are shown from 800 to 1800 days for clarity. Sensitivity analysis is performed on Ksa  and wf parameters.  269   Figure B14. Dual-permeability 3 model: concentration of bromide tracer in Pile 2 sub-lysimeter B drainage for the experimental period since August 2007. Data are shown from 800 to 1800 days for clarity. Sensitivity analysis is performed on Ksa  and wf parameters.  270   Figure B15. Dual-permeability 3 model: mass flux of bromide tracer in Pile 2 sub-lysimeter B drainage for the experimental period since August 2007. Data are shown from 800 to 1800 days for clarity. Sensitivity analysis is performed on Ksa  and wf parameters.    271  Appendix C    C.1 Concentration of selected species versus time for field barrels:   Figure C1. Drainage chemistry of field barrel UBC 1-A2. Black dots represent pH    272    Figure C2. Drainage chemistry of field barrel UBC 1-4A. Black dots represent pH    273   Figure C3. Drainage chemistry of field barrel UBC 2-3A. Black dots represent pH.    274   Figure C4. Drainage chemistry of field barrel UBC 2-0A. Black dots represent pH.    275   Figure C5. Drainage chemistry of field barrel UBC 2-2A. Black dots represent pH.    276   Figure C6. Drainage chemistry of field barrel UBC 3-1A. Black dots represent pH.     277   Figure C7. Drainage chemistry of field barrel UBC 5-0A. Black dots represent pH    278   Figure C8. Drainage chemistry of field barrel UBC 5-2A. Black dots represent pH.   

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