Applied Science, Faculty of
Mining Engineering, Keevil Institute of
DSpace
UBCV
Baidya, Durjoy
Doctor of Philosophy - PhD
University of British Columbia
Efficient carbon capture within mine tailings on an industrial scale holds the potential to make substantial strides in providing permanent solutions for carbon removal from the environment. This dissertation studies the feasibility of carbon sequestration in mine tailings by injecting flue gas. Its investigations revolve around exploring the large-scale implementation, assessing operational feasibility in cold climates, and addressing techno-economic aspects of the concept of diesel exhaust injection in mine tailings for carbon sequestration. Following the delineation of the research scope, the investigation embarks on conceptualizing a design for large-scale CO₂ sequestration within dry stack mine tailings through the utilization of embedded perforated pipes at remote mining operations. The core contribution of this dissertation involves the conception and validation of a novel (1+1)D Reduced Order Model (ROM) designed to predict the pressure phenomenon of the perforated pipes installed in the tailings. This ROM efficiently predicts injection pressures, outflow rates through the perforations, and pressure profiles with a level of precision comparable to commercial numerical solvers while demanding significantly less computational resources and time. The developed model showed the potential to be an asset in the decision-making process by furnishing a strategy for the design of energy-optimal injection scenarios. This research advances the development and validates a numerical model that assesses the feasibility of harnessing the thermal energy from flue gas to avert freezing in tailings beds, thus showcasing the possibility of year-round operation in cold climates. The study quantifies several crucial parameters, including injection rate, temperature, and other operating factors, emphasizing the flexibility of carbon sequestration approaches in frigid environments. A comprehensive array of sensitivity analyses scrutinizes the adaptability of the proposed concept across various operational and climatic conditions. Furthermore, the study develops a techno-economic cost model, accounting for factors such as piping infrastructure and energy operational expenditures. This model informs decision-making by identifying the critical balance between power costs and piping expenditures necessary for optimal operational expenses. Notably, the study emphasizes that carbon capture within mine tailings can be managed efficiently at a reasonable operating cost, reinforcing the practicality of greenhouse gas sequestration.
Study of Fluid Flow and Heat Transfer for Carbon Mineralization in Mine Wastes by Durjoy Baidya M.A.Sc. (Mining Engineering), The University of British Columbia, Vancouver, Canada, 2019 B. Sc. (Petroleum & Mining Engineering), Chittagong University of Engineering and Technology, Bangladesh, 2015 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in THE FACULTY OF GRADUATE AND POSTDOCTORAL STUDIES (Mining Engineering) THE UNIVERSITY OF BRITISH COLUMBIA (Vancouver) April 2024 © Durjoy Baidya, 2024 ii The following individuals certify that they have read, and recommend to the Faculty of Graduate and Postdoctoral Studies for acceptance, the dissertation entitled: Study of Fluid Flow and Heat Transfer for Carbon Mineralization in Mine Wastes submitted by Durjoy Baidya in partial fulfilment of the requirements for the degree of Doctor of Philosophy in Mining Engineering Examining Committee: Dr. Seyed Ali Ghoreishi-Madiseh, Assistant Professor, Mining Engineering, UBC Supervisor Dr. Gregory Dipple, Professor, Earth, Ocean and Atmospheric Sciences, UBC Co-supervisor Dr. Scott Dunbar, Professor, Mining Engineering, UBC Supervisory Committee Member Dr. Bern Klein, Professor, Mining Engineering, UBC University Examiner Dr. Susan A. Baldwin, Professor, Chemical and Biological Engineering, UBC University Examiner Additional Supervisory Committee Members: Dr. Nadja Kunz, Assistant Professor, Mining Engineering, UBC Supervisory Committee Member iii Abstract Efficient carbon capture within mine tailings on an industrial scale holds the potential to make substantial strides in providing permanent solutions for carbon removal from the environment. This dissertation studies the feasibility of carbon sequestration in mine tailings by injecting flue gas. Its investigations revolve around exploring the large-scale implementation, assessing operational feasibility in cold climates, and addressing techno-economic aspects of the concept of diesel exhaust injection in mine tailings for carbon sequestration. Following the delineation of the research scope, the investigation embarks on conceptualizing a design for large-scale CO2 sequestration within dry stack mine tailings through the utilization of embedded perforated pipes at remote mining operations. The core contribution of this dissertation involves the conception and validation of a novel (1+1)D Reduced Order Model (ROM) designed to predict the pressure phenomenon of the perforated pipes installed in the tailings. This ROM efficiently predicts injection pressures, outflow rates through the perforations, and pressure profiles with a level of precision comparable to commercial numerical solvers while demanding significantly less computational resources and time. The developed model showed the potential to be an asset in the decision-making process by furnishing a strategy for the design of energy-optimal injection scenarios. This research advances the development and validates a numerical model that assesses the feasibility of harnessing the thermal energy from flue gas to avert freezing in tailings beds, thus showcasing the possibility of year-round operation in cold climates. The study quantifies several crucial parameters, including injection rate, temperature, and other operating factors, emphasizing iv the flexibility of carbon sequestration approaches in frigid environments. A comprehensive array of sensitivity analyses scrutinizes the adaptability of the proposed concept across various operational and climatic conditions. Furthermore, the study develops a techno-economic cost model, accounting for factors such as piping infrastructure and energy operational expenditures. This model informs decision-making by identifying the critical balance between power costs and piping expenditures necessary for optimal operational expenses. Notably, the study emphasizes that carbon capture within mine tailings can be managed efficiently at a reasonable operating cost, reinforcing the practicality of greenhouse gas sequestration. v Lay Summary This dissertation investigates the viability of a large-scale solution to capture carbon in mine wastes by injecting flue gas using a series of perforated pipes. A reliable numerical tool was developed to estimate and establish control over the energy needed to run the operation. A guided pathway was developed, showing how to attain an optimum injection scenario from the perspective of energy requirement. Additionally, the research investigated using flue gas heat to prevent freezing in the tailings to continue the operation year-round. Parameters such as injection rate, temperature, and thermal conductivity were analyzed for adaptability in various conditions. A cost model was developed to assist the decision-making process in finding a cost-effective way to capture carbon in mine tailings, reducing the carbon footprint of the mining operation. vi Preface The entire research was conducted under the supervision of Dr. Seyed Ali Ghoreishi-Madiseh, and Dr. Gregory Dipple. The research presented in Chapter 3 and Chapter 5 of this dissertation were published as peer-reviewed journals, as detailed below. • D. Baidya, E. Wynands, P. Samea, S. A. Ghoreishi-Madiseh, and G. Dipple, “A Reduced-Order Fluid Flow Model for Gas Injection into Porous Media: For Application in Carbon Sequestration in Mine Tailings,” Minerals, vol. 13, no. 7, p. 855, Jun. 2023, doi: 10.3390/min13070855. o I was responsible for the conceptualization, methodology, software, investigation, validation, formal analysis, and writing—original draft, review, and editing. Mr. Eric Wynands and Dr. Parham Samea collaborated on the experimental investigation and in developing the base 3D numerical model, respectively. • D. Baidya, G. Dipple, and S. A. Ghoreishi-Madiseh, “A techno-economic analysis of diesel exhaust injection into mine tailings for carbon sequestration,” Heliyon, vol. 10, no. 6, Mar. 2024. doi:10.1016/j.heliyon.2024.e27791 o I was responsible for the conceptualization, methodology, software, investigation, validation, formal analysis, and writing—original draft, review, and editing. The research presented in Chapter 4 has been submitted to the peer-reviewed journals as following: • D. Baidya, P. Samea, G. Dipple, and S. A. Ghoreishi-Madiseh, “Thermal Behavior of Mine Tailings Subjected to Flue Gas Carbon Sequestration in Cold Climates: a Numerical Study,” (under review). vii o I was responsible for the conceptualization, methodology, software, investigation, validation, formal analysis, and writing—original draft, review, and editing. Dr. Parham Samea collaborated on the validation. viii Table of Contents Abstract ......................................................................................................................................... iii Lay Summary .................................................................................................................................v Preface ........................................................................................................................................... vi Table of Contents ....................................................................................................................... viii List of Tables .............................................................................................................................. xiii List of Figures ............................................................................................................................. xiv List of Symbols .......................................................................................................................... xxii List of Abbreviations .................................................................................................................xxv Acknowledgements ................................................................................................................. xxvii Dedication ............................................................................................................................... xxviii Chapter 1: Introduction ................................................................................................................1 1.1 The Role of Mining in Fighting Climate Change ........................................................... 1 1.2 Mining at Remote Locations ........................................................................................... 3 1.3 General Organization of the Thesis ................................................................................ 5 Chapter 2: Literature Review and Research Objectives ............................................................7 2.1 Carbon Mineralization: Background and Rationale ....................................................... 7 2.2 Carbon Sequestration in Mine Tailings ........................................................................ 10 ix 2.3 Diesel Exhaust Flue Gas ............................................................................................... 13 2.4 Dry Stack Tailings ........................................................................................................ 17 2.5 Injection in Porous Media ............................................................................................. 19 2.5.1 Fluid flow in porous media ................................................................................... 20 2.5.2 Heat transfer in porous media ............................................................................... 24 2.6 Carbon Market .............................................................................................................. 26 2.7 Research Objectives ...................................................................................................... 29 Chapter 3: Fluid Flow Investigation for Flue Gas Injection into Mine Tailings ...................31 3.1 Introduction ................................................................................................................... 31 3.2 Methodology ................................................................................................................. 34 3.2.1 Conceptual design ................................................................................................. 34 3.2.2 Experimental setup of injection through a perforated pipe ................................... 36 3.2.2.1 Permeability measurement ................................................................................ 38 3.2.3 3D Model development......................................................................................... 39 3.2.4 (1+1)D Model development .................................................................................. 42 3.3 Results and Discussion ................................................................................................. 49 3.3.1 Validation of the numerical models ...................................................................... 49 3.3.1.1 Experimental results.......................................................................................... 49 x 3.3.1.2 Comparison of the experimental and numerical results .................................... 51 3.3.2 Progression of the (1+1)D reduced-order model .................................................. 52 3.3.2.1 Impact of design parameters on the 𝑚-factor ................................................... 53 3.3.2.2 Establishing correlations between Design Parameters and 𝑚-factor ................ 56 3.3.3 Performance evaluation of the (1+1)D ROM ....................................................... 59 3.3.3.1 Inlet pressure ..................................................................................................... 59 3.3.3.2 Pressure profile throughout the injection pipe .................................................. 61 3.3.3.3 Outflow distribution .......................................................................................... 63 3.3.4 Application of the (1+1)D ROM to an optimal design ......................................... 65 3.4 Summary ....................................................................................................................... 68 Chapter 4: Cold Climate Impact on Flue Gas Injection into Mine Tailings ..........................70 4.1 Introduction ................................................................................................................... 70 4.2 Methodology ................................................................................................................. 71 4.2.1 Boundary conditions ............................................................................................. 72 4.2.2 Governing equations ............................................................................................. 74 4.2.3 Grid and domain independence ............................................................................ 78 4.2.4 Model validation ................................................................................................... 79 4.3 Results and Discussions ................................................................................................ 81 xi 4.3.1 Base case scenario................................................................................................. 81 4.3.2 Parametric studies ................................................................................................. 86 4.3.2.1 Injection flow rate ............................................................................................. 86 4.3.2.2 Injection temperature ........................................................................................ 88 4.3.2.3 Properties of tailings ......................................................................................... 89 Air volume fraction ....................................................................................................... 90 Water mass content ....................................................................................................... 91 Thermal conductivity .................................................................................................... 93 4.3.2.4 Operating conditions ......................................................................................... 94 Initial soil temperature .................................................................................................. 95 Starting time of the operation ....................................................................................... 96 Locations ....................................................................................................................... 99 4.3.3 Approaches toward minimizing the impact of harsh weather ............................ 103 4.4 Summary ..................................................................................................................... 107 Chapter 5: Techno-Economics of Flue Gas Injection into Mine Tailings for Carbon Sequestration ..............................................................................................................................109 5.1 Introduction ................................................................................................................. 109 5.2 Methodology ............................................................................................................... 110 xii 5.2.1 Extension of (1+1)D reduced-order model ......................................................... 111 5.2.1.1 3D Numerical model development for rectangular block............................... 111 5.2.1.2 (1+1) ROM development for tailings block.................................................... 113 5.2.2 Financial analysis ................................................................................................ 116 5.3 Results and Discussion ............................................................................................... 121 5.3.1 Establishment of energy-optimum scenario ........................................................ 121 5.3.2 Financial analysis ................................................................................................ 126 5.3.2.1 Fixed re-piping period approach ..................................................................... 128 5.3.2.2 Variable re-piping period approach ................................................................ 138 5.4 Summary ..................................................................................................................... 147 Chapter 6: Contributions and Recommendations ..................................................................149 6.1 Core contribution ........................................................................................................ 149 6.2 Future work recommendations ................................................................................... 151 Bibliography ...............................................................................................................................153 Appendices ..................................................................................................................................170 Appendix A Material Characterization for experimental setup ............................................. 170 Appendix B Sand Permeability Variability Testing .............................................................. 172 Appendix C Additional Publications ..................................................................................... 174 xiii List of Tables Table 1-1. Gradual demand estimates for different metals in kilotonnes under different energy transition scenarios to achieve net-zero emission by 2050 . .......................................................... 2 Table 2-1. Fundamental carbon mineralization reactions .….. ..................................................... 10 Table 2-2. CO2 absorption and storage capacity for different reactant minerals.. ........................ 11 Table 2-3. Amount of CO2 available in different sources under study for carbon mineralization .......................................................................................................................................................... 12 Table 2-4. Typical composition of diesel exhaust gas. ................................................................. 14 Table 2-5. Values for the constants employed in Ergun correlations across varying porosities and particle sizes stated in different literature as mentioned in ........................................................... 22 Table 4-1. Key parameters used in numerical investigations. ...................................................... 82 Table 5-1. Key parameters used in constructing the (1+1)D ROM and 3D FE models for results comparison. ................................................................................................................................. 122 Table 5-2. Base parameters used in the financial aspects analysis. ............................................ 127 xiv List of Figures Figure 1-1. (a) Approximate locations of remote mines (development and production phase) in Canada and (b) power generation streams in remote mines. .......................................................... 4 Figure 2-1. Analysis of Waste Heat from Diesel Generators with Varied Power Outputs; the left axis represents bar values, while the right axis corresponds to the values of lines or markers. ... 15 Figure 2-2. Illustration depicting an exhaust heat recovery system utilized for heating mine intake air (case A) in underground operation and providing heating for spaces along with a domestic hot water system (case B) for surface operation ................................................................................. 16 Figure 2-3. Global carbon capture costs (US$/tonne of CO2) by approach or technology as of September 2020. ........................................................................................................................... 28 Figure 3-1. Schematic of the proposed carbon sequestration method implemented at remote mines........................................................................................................................................................ 35 Figure 3-2. Experimental setup for studying the outflow from a perforated pipe into a porous medium: (a) entire experimental setup; and (b) perforated pipe. .................................................. 37 Figure 3-3. Permeameter setup ..................................................................................................... 39 Figure 3-4. The geometry and the boundary conditions implemented in the 3D FE simulations. 42 Figure 3-5. The (1+1)D model development for perforated injection pipes embedded in a porous medium. ........................................................................................................................................ 43 xv Figure 3-6. Visual representation of the transition and smooth zone for gas flow into the porous medium. ........................................................................................................................................ 47 Figure 3-7. Comparison between the gauge pressure profiles in the injection pipe from the experimental and numerical results. ............................................................................................ 49 Figure 3-8. Comparison between the measured permeability range of the sand samples and the predicted permeability range from the (1+1)D model results. ...................................................... 50 Figure 3-9. Visual representation of the cases studied: (a) variation in the perforation arrangement for a constant perforation ratio; (b) variation in the perforation ratio for a fixed perforation arrangement; and (c) cross-section of the system and the definition of 𝑟𝑟. .................................. 54 Figure 3-10. Effect on the m-factor from changes in the: (a) permeability, (b) inlet flow rate, (c) perforation arrangement, (d) injection pipe perforated area, and (e) thickness of the porous domain........................................................................................................................................................ 56 Figure 3-11. Range of m-factor for different porous domain thicknesses and injection pipe perforation schemes. ..................................................................................................................... 58 Figure 3-12. Comparison of inlet pressures obtained from the 3D FE and the (1+1)D numerical model at different operating variables: (a) permeability; (b) inlet flow rate; (c) perforation arrangement; (d) perforation ratio; and (e) size of the porous domain. ........................................ 60 Figure 3-13. Comparison of the pressure profile along the injection pipe obtained from the 3D FE and (1+1)D numerical models at different operating variables: (a) permeability, (b) inlet flow rate, (c) perforation arrangement, (d) perforation ratio, and (e) size of the porous domain. ................ 62 xvi Figure 3-14. Comparison of the outflow distribution obtained from the 3D FE and (1+1)D numerical models under different operating parameters: (a) permeability, (b) inlet flowrate, (c) perforation arrangement, (d) perforation ratio, and (e) size of the porous domain. ..................... 64 Figure 3-15. Heat maps: inlet pressure (in Pa) variation for different perforation arrangements and porous domain sizes. ..................................................................................................................... 66 Figure 3-16. Heat maps: difference in the inlet pressure calculations with and without considering the effect of the perforation arrangement. ..................................................................................... 67 Figure 4-1. Diagrammatic representation of the computational area of the dry stack tailings for carbon sequestration, along with the associated boundary conditions. ........................................ 72 Figure 4-2. Validation of the developed FEA-based numerical model with the experimental results; (a) temperature distribution at different time intervals; and (b) pressure drop at different operating hours. ............................................................................................................................................. 80 Figure 4-3. The climatic condition of the base off-grid location of the remote mine; (a) daily average temperature and wind speed of the location; and (b) ambient air convective heat transfer coefficient at the surface. .............................................................................................................. 83 Figure 4-4. Temperature contours of the tailings body throughout the year for base conditions. 85 Figure 4-5. Impact of injection flow rate variance on (a) the amount of frozen tailings body throughout the year, and (b) the annualized average of the frozen and unfrozen amount of tailings body............................................................................................................................................... 87 xvii Figure 4-6. Impact of injection temperature variance on (a) the amount of frozen tailings body throughout the year, and (b) the annualized average of the frozen and unfrozen amount of tailings body............................................................................................................................................... 89 Figure 4-7. Impact of air volume fraction of tailings on (a) the amount of frozen tailings body throughout the year, and (b) the annualized average of the frozen and unfrozen amount of tailings body............................................................................................................................................... 91 Figure 4-8. Impact of the variance of water mass content in tailings on (a) the amount of frozen tailings body throughout the year, and (b) the annualized average of the frozen and unfrozen amount of tailings body. ............................................................................................................... 92 Figure 4-9. Impact of different thermal conductivities of tailings on (a) the amount of frozen tailings body throughout the year, and (b) the annualized average of the frozen and unfrozen amount of tailings body. ............................................................................................................... 94 Figure 4-10. Impact of different soil initialization temperatures on (a) the amount of frozen tailings body throughout the year, and (b) the annualized average of the frozen and unfrozen amount of tailings body. ................................................................................................................................. 96 Figure 4-11. Impact of different starting times on the carbon sequestration operation: (a) daily average temperature and wind speed of the location accompanied by the starting points; the amount of frozen tailings body throughout the year for starting the operation on month (b) 1 to 4, (c) 5 to 8, (d) 9 to 12, and (e) the annualized average for the frozen and the amount of tailings body for different starting points. ................................................................................................................ 98 xviii Figure 4-12. Geographical locations of the selected places for investigating the impact of different weather conditions on the carbon sequestration in mine tailings through diesel exhaust injection...................................................................................................................................................... 100 Figure 4-13. The climatic condition of different remote locations; (a) daily average temperature, (b) average daily wind speed, and (c) calculated ambient air convective heat transfer coefficient applied on the top surface. .......................................................................................................... 101 Figure 4-14. Impact of different climatic conditions on (a) the amount of frozen tailings body throughout the year, and (b) the annualized average frozen and unfrozen amount of tailings body...................................................................................................................................................... 102 Figure 4-15. Temperature contours of the tailings body throughout the year for different ambient air convective heat transfer coefficients at the surface. .............................................................. 104 Figure 4-16. Impact of the reduced ambient air heat transfer coefficient because of reduced wind speed on (a) the amount of frozen tailings body throughout the year, and (b) the annualized average frozen and unfrozen amount of tailings body. ............................................................................ 105 Figure 4-17. Impact of insulation layers on (a) the amount of frozen tailings body throughout the year and (b) the annualized average frozen and unfrozen amount of tailings body. .................. 107 Figure 5-1. Diagram illustrating the computational domain of the rectangular tailings block for carbon sequestration, accompanied by the pertinent boundary conditions for the numerical modeling. .................................................................................................................................... 112 Figure 5-2. Variability in 𝑚-factor across distinct heights of tailings blocks and various patterns of perforations in the injection pipe. ........................................................................................... 114 xix Figure 5-3. Comparison of the inlet pressures obtained from the 3D FE models and (1+1)D ROM for rectangular tailings block (𝑅′ = 5) for different perforation configurations, based on the number of the perforations around the circumference of the pipe: (a) 𝑛𝑐 = 4, (a) 𝑛𝑐 = 6, (a) 𝑛𝑐 =8, and (a) 𝑛𝑐 = 10. ..................................................................................................................... 123 Figure 5-4. Comparison of the inlet pressures obtained from the 3F FE models and (1+1)D ROM for rectangular tailings block (𝑅′ = 12) for different perforation configurations based on the number of the perforations around the circumference of the pipe: (a) 𝑛𝑐 = 4, (a) 𝑛𝑐 = 6, (a) 𝑛𝑐 =8, and (a) 𝑛𝑐 = 10. ..................................................................................................................... 124 Figure 5-5. Heat maps illustrating variations in inlet pressure for tailings blocks of different dimensions and various perforation arrangements. .................................................................... 126 Figure 5-6. Relationship between the reactivity indexes of the tailings and the ratio of the mass of the tailings to the mass of the exhaust injection. ........................................................................ 129 Figure 5-7. Total operating expenditure and the associated energy ratios per tonne of CO2 captured targeting 1 MW power sequestered in the reactivity-index driven amount of mine tailings for different permeabilities at fixed re-piping period scenarios: (a) 𝐾𝑡 = 10−10 m2, (b) 𝐾𝑡 =10−11 m2, (c) 𝐾𝑡 = 10−12 m2, (d) 𝐾𝑡 = 10−13 m2, and (e) 𝐾𝑡 = 10−14 m2. ........................... 131 Figure 5-8. Correlation analysis elucidating the interdependence of reactivity indexes of the tailings and the mass ratio between tailings and exhaust injection in (a) the minimum OPEX for each reactivity cases displayed in Figure 5-7, (b) the associated width to height ratio of the block size for the minimum OPEX cases, and (c) the associated energy ratio for each of the minimum OPEX cases. ................................................................................................................................ 133 xx Figure 5-9. Total operating expenditure per tonne of CO2 captured and the associated energy ratio for sequestrating (a) 0.5 MW, (b) 2.7 MW, and (c) 8.05 MW of power in 4.5 MT of tailings with reactivity index of 0.1%, 0.5%, and 1.5%, respectively, in a fixed re-piping period scenario. ..................................................................................................................................................... 137 Figure 5-10. Comparison of the total operating expenditure per tonne of CO2 captured and the corresponding energy ratio for the sequestration of 1 MW power in 4.5 MT of tailings, considering distinct permeabilities under a variable re-piping period scenario: (a) 𝐾𝑡 = 10−9 m2, (b) 𝐾𝑡 =10−10 m2, (c) 𝐾𝑡 = 10−11 m2, (d) 𝐾𝑡 = 10−12 m2, (e) 𝐾𝑡 = 10−13 m2, and (f) 𝐾𝑡 = 10−14 m2..................................................................................................................................................... 140 Figure 5-11. Comparison of the total operating expenditure per tonne of CO2 captured and the corresponding energy ratio for the sequestration of 3 MW power in 4.5 MT of tailings, considering distinct permeabilities under a variable re-piping period scenario: (a) 𝐾𝑡 = 10−9 m2, (b) 𝐾𝑡 =10−10 m2, (c) 𝐾𝑡 = 10−11 m2, (d) 𝐾𝑡 = 10−12 m2, (e) 𝐾𝑡 = 10−13 m2, and (f) 𝐾𝑡 = 10−14 m2..................................................................................................................................................... 142 Figure 5-12. Comparison of the total operating expenditure per tonne of CO2 captured and the corresponding energy ratio for the sequestration of 8.05 MW power in 4.5 MT of tailings, considering distinct permeabilities under a variable re-piping period scenario: (a) 𝐾𝑡 = 10−9 m2, (b) 𝐾𝑡 = 10−10 m2, (c) 𝐾𝑡 = 10−11 m2, (d) 𝐾𝑡 = 10−12 m2, (e) 𝐾𝑡 = 10−13 m2, and (f) 𝐾𝑡 =10−14 m2 ..................................................................................................................................... 144 Figure 5-13. (a) Contour plot showing tailings quantity required for sequestering specific power levels, considering tailings reactivity, and dashed lines representing the re-piping period with an xxi annual availability of 4.5 MT of tailings. (b) Re-piping periods for the carbon sequestration cases targeting to capture 1, 3, and 8.05 MW power for cases considering 4.5 MT of tailings available yearly........................................................................................................................................... 146 xxii List of Symbols 𝐴𝑖𝑛 Surface area of the pipe inlet (m2) 𝐴𝑝 The total perforated surface area of the pipe 𝐴𝑟 The perforated surface area ratio of the injection pipe 𝑐𝐹 Forchheimer coefficient 𝐶𝑃 Specific heat capacity (J/(kgK)) 𝑑ℎ Hydraulic diameter (m) 𝑑𝑝 Particle diameter (m) 𝑓𝑢𝑖 Flow uniformity index 𝑔 Gravitational acceleration (m/s2) ℎ Convective heat transfer coefficient (W/m2K) ℎ∗ Ancillary convection coefficient (W/mK) 𝑰 Identity matrix 𝑖 Index 𝑘 Thermal conductivity (W/(mK)) 𝐾𝑡 Permeability of the tailings (m2) 𝐿 Length of the injection pipe and the tailings block (m) 𝐿𝑤 Latent heat of the water (J/kg) 𝑀𝐶𝑂2 Amount of CO2 sequestrated (tonnes) 𝑀𝑡𝑎𝑖𝑙𝑖𝑛𝑔𝑠 Quantity of tailings used in the operation in certain operating period (tonnes) 𝑚𝑤 Water mass or the moisture content of the tailings (%) xxiii 𝑁𝑢 Nusselt number 𝑛𝑐 The number of perforations around the circumference of injection pipe 𝑜𝑥𝑒𝑙𝑒𝑐 Piping cost to capture 1 tonne of CO2 in every operating year (C$) 𝑜𝑥𝑝𝑖𝑝𝑖𝑛𝑔 Electricity cost to capture 1 tonne of CO2 in every operating year (C$) 𝑜𝑥𝑡 Total operating expenditure to capture 1 tonne of CO2 in every operating year (C$) 𝑃 Pressure (Pa) 𝑃𝑟 Prandtl number 𝑝′ Mid-perforation pressure (Pa) 𝑝𝑎𝑡𝑚 Atmospheric pressure (Pa) 𝑄 Volumetric flow rate (m3/s) 𝑅𝐼 Reactivity index 𝑅𝑒𝐿 Reynolds number 𝑅𝑤ℎ The width to height ratio of the tailings block 𝑅𝛦 Energy ratio 𝑟𝑖𝑛 Inner radius of the injection pipe (m) 𝑟𝑝 Perforation radius (m) 𝑠 Center-to-center distance of the perforations (m) 𝑆𝑏 Specific surface area (1/m) 𝑡𝑝𝑖𝑝𝑖𝑛𝑔 Re-piping period (years) 𝑡𝑠𝑜𝑖𝑙 Initial temperature of the soil below tailings (°C) 𝑢𝑐𝑒𝑙𝑒𝑐 Cost of electricity (C$/kWhr) xxiv 𝑢𝑐𝑝𝑖𝑝𝑖𝑛𝑔 Unit cost of piping ($/m) 𝑣𝑎𝑖𝑟 Daily average wind speed of the location (m/s) 𝑊𝑐𝑜𝑚𝑝 Energy consumer by the compressor operating (W) 𝑊𝑓𝑎𝑛 Energy consumer by the fan operating (W) 𝑧 Distance from the pipe inlet (m) Δ𝑄 Outflow (m3/s) 𝛾 Adiabatic index 𝛿 Pipe roughness (m) 𝜀𝑡 Air volume fraction of the tailings (%) 𝜂𝑐𝑜𝑚𝑝 Efficiency of the compressor (%) 𝜂𝑓𝑎𝑛 Efficiency of the fan (%) 𝜃 Temperature-dependent phase transition function 𝜆 Darcy-Weisbach friction coefficient 𝜇 Dynamic viscosity (Pa ∙ s) 𝜌 Density (kg/m3) xxv List of Abbreviations Ca Calcium CCS Carbon capture and storage CDR Carbon dioxide removal from the air CFD Computational fluid dynamics CS Coarse sand C$ Canadian dollar D Dimensional DACSS Direct air capture with synthetic sorbents EHRS Exhaust heat recovery system FEA Finite element analysis FS Fine sand GHG Greenhouse gas IC Internal combustion IPCC International Panel for Climate Change IPL Injection pressure loss LTE Local thermal equilibrium LTNE Local Thermal Non-Equilibrium Mg Magnesium OPEX Operating expenditure PSD Particle size distribution xxvi RANS Reynolds Averaged Navier-Stokes ROM Reduced-order model S Sensor TPL Transportation pressure loss TSF Tailings storage facility US$ United States dollar xxvii Acknowledgements I am profoundly grateful to my supervisors, Dr. Seyed Ali Ghoreishi-Madiseh and Dr. Gregory Dipple, for their unwavering dedication, expert guidance, and insightful feedback throughout this journey. Their mentorship has been pivotal in refining my research and enhancing my academic skills. Sincere acknowledgment is owed to my supervisory committee members, Dr. Scott Dunbar and Dr. Nadja Kunz, for their valuable contributions to enhance the quality of this thesis. Special gratitude is extended to Dr. Leyla Amiri for her invaluable guidance during the initial phase of this research. I am indebted to my friends and colleagues at The CarbMin Lab for their camaraderie, thought-provoking discussions, and intellectual exchange. I extend my gratitude to my friends, Dr. Vinoth Kumar, Mr. Eric Wynands, and Dr. Sally Innis, for their stimulating conversations and unwavering encouragement during the highs and lows of this research journey. Gratitude also goes to The Norman B. Keevil Institute of Mining Engineering staff and faculty for their administrative support, which facilitated the smooth progression of this research. Special acknowledgment is extended to De Beers Canada and Natural Resources Canada for their generous support of this research. In conclusion, I am profoundly thankful to all those who have contributed to this journey. Each person, whether mentioned or not, has played a significant role in this achievement. While words may fall short of expressing my true gratitude, please accept my heartfelt thanks for your invaluable contributions. xxviii Dedication To my partner, Sangita Mitra. Your unconditional love, unwavering belief in me, and endless patience have been my anchor throughout this process. Your constant support, whether through a listening ear or a comforting presence, has given me the strength to overcome challenges and persevere. This thesis bears not only my name but also the indelible imprint of your influence. 1 Chapter 1: Introduction 1.1 The Role of Mining in Fighting Climate Change The extraction of metals and other minerals has consistently played a vital role in global economic growth, population expansion, enhancement of consumer lifestyles, and the formulation of global energy and growth policies. [1, 2]. Technological advancement has also positively influenced the usage of various mining commodities. This continuous increase in demand for metals and other mining commodities has caused the mining industry to augment the scale of its operations. Ensuring the provision of minerals essential for affordable and clean energy in the future, as well as for maintaining global atmospheric temperature increases within 1.5-2°C above pre-industrial levels, will result in even greater demands for minerals [3]. To achieve these goals, the dependence on fossil fuels for power generation must be shifted to renewable energies, such as, wind, solar, and so forth [4-6]. These green-tech systems (e.g., wind turbines, solar panels, electric vehicles, batteries, etc.) require a significant number of metals and minerals. Table 1-1 illustrates the gradual increase in production required for four key metals to achieve net-zero emission through successful energy transition by 2050 under various scenario analyses [7]. It is evident that the production of battery minerals such as lithium, graphite, and cobalt must increase exponentially to meet all the net-zero targets. The nickel production in 2050 must be twofold in comparison to the production rate achieved in 2018 to limit the average global temperature rise to 2°C by 2100 with a 50% likelihood, as detailed in [8]. The demand for these minerals will further escalate if the goal of limiting temperature rise to below 2°C is to be achieved. 2 Table 1-1. Gradual demand estimates for different metals in kilotonnes under different energy transition scenarios to achieve net-zero emission by 2050 (adapted from [7]). Copper Sector 2025 2030 2035 2040 2045 2050 Solar PV 1,259 1,990 2,063 2,026 1,674 1,880 Wind 705 1,630 1,543 1,328 881 1,303 Other low emissions power generation 93 225 228 180 148 142 Electric vehicles 1,152 2,704 3,799 3,884 3,897 3,583 Grid battery storage 77 258 441 685 734 665 Electricity networks 5,024 8,924 11,445 12,574 11,757 9,778 Other uses 19,563 19,881 19,215 20,218 21,269 22,382 Cobalt Sector 2025 2030 2035 2040 2045 2050 Electric vehicles 130 188 231 244 278 291 Grid battery storage 6 17 18 14 7 0 Other uses 144 163 179 196 213 229 Lithium Sector 2025 2030 2035 2040 2045 2050 Electric vehicles 243 592 985 1,106 1,173 1,104 Grid battery storage 11 37 58 82 85 74 Other uses 82 93 103 113 124 135 Nickel Sector 2025 2030 2035 2040 2045 2050 Wind 66 138 129 102 71 104 Other low emissions power generation 382 724 595 634 346 283 Electric vehicles 1,157 2,414 3,392 3,451 3,444 3,289 Grid battery storage 18 60 74 65 40 0 Hydrogen technologies 36 115 118 93 64 87 Other uses 2,375 2,363 2,349 2,357 2,388 2,432 In parallel with the adoption of different renewable energy sources, there exists a global urge to champion diverse carbon dioxide removal (CDR) initiatives [9]. This directive stems from the recommendation from the International Panel for Climate Change (IPCC) to attain a total reduction of 100-1000 Gt of CO2 over the current century for keeping global warming below 1.5-2°C [10]. 3 Climate change has been recognized as one of the major challenges for the modern mining industry worldwide. To achieve and maintain sustainability, the mining industry is incessantly looking for ways to mitigate carbon emissions while increasing the number of operations. To make that possible, the mineralization of carbon should go hand in hand with the development of mining operations. Carbon mineralization is the formation of solid carbonate minerals through the reaction of CO2 with ultramafic rocks rich in Mg and Ca [11, 12]. Though this carbon mineralization holds the potential to be an inexpensive and viable solution for achieving net zero emission by storing carbon permanently, it has remained untested, especially at a large-scale [13]. 1.2 Mining at Remote Locations Mining operations are responsible for the annual emission of 1.9-5.1 gigatonnes (Gt) of CO2 equivalent (CO2e) greenhouse gas (GHG) globally, with the predominant source being the fugitive methane released primarily in underground coal mine operations. Power generation to run these mining operations directly contributes around 0.4 gigatonnes [14]. For simple contextualization of these numbers, it is worth noting the emissions of two major North American regions: British Columbia emitted 61.4, while California emitted 369.2 Mt of CO2e in 2020 [15, 16]. As an energy-intensive industry, mining has its own target to transition towards decarbonized operations [17]. Nonetheless, achieving a full-scale shift to renewable energy sources for power generation presents considerable challenges for the mining sector, particularly for new operations in off-grid areas [18, 19]. The detachment from the grid or natural gas pipelines defines a location as 'remote' [20]. The mining industry needs to develop operations in different remote locations to satisfy the increasing demands of the metal market and because of the depletion of resources [21]. 4 Building upon prior research work [19], a map showing the approximate locations of remote mines (both in the production and development phase) in Canada was formulated and is shown in Figure 1-1(a). Figure 1-1. (a) Approximate locations of remote mines (development and production phase) in Canada and (b) power generation streams in remote mines (based on [19]). Due to their cold climatic locations, mines operating in remote areas depend heavily on fossil fuels, particularly diesel, for essential functions such as power generation and heating [19]. Though a positive trend of transitioning toward clean energy is being observed, when it comes to providing electric power for remote mining operations, fossil fuel-based generators still emerge as the most reliable option [22]. Being off-grid and operating in remote locations, on average, 98% of the power demand of these mines is sourced from fossil fuel generators (60% from diesel and the rest DieselDual fuel (Diesel / LNG)LNGHybrid (Diesel + Wind)60%4%34%2%DieselLNGDual fuelWind(a) (b)5 from natural gas, Liquefied Petroleum Gas (LPG), or other fossil fuels) as shown in Figure 1-1(b) [19]. This reliance on fossil fuels results in the inevitable direct emissions of CO2 in the form of exhaust from the generators employed in these off-grid mines. Also, it is essential to mention that most of these remote locations have limited road access throughout the year. Therefore, this enormous amount of diesel required to power these mines needs to be transported in a very short span of the year along with all the other necessary equipment [23]. Therefore, this heavy dependance on fossil fuels also contributes significantly to the indirect emissions associated with these mines. Since the mafic and ultra-mafic minerals in tailings exhibit the potential for carbon sequestration, and emissions associated with power generation and heating remain an unavoidable challenge in the off-grid mine. The injection of diesel flue gas from the power-generating units into mine tailings to capture and store CO2 holds the potential to significantly reduce the carbon footprint of these operations [24]. Ensuring the large-scale feasibility of carbon mineralization in ultramafic mine tailings can yield two positive impacts on greener mining: the reduction of GHG emissions from these mining operations and the utilization of tailings for financial and environmental benefits [12]. It is also worth mentioning that the management of tailings and controlling GHG emissions are on the top of the list of mining industry issues. In the future, pending stringent environmental regulations will make the situation even more challenging. 1.3 General Organization of the Thesis Chapter 1 of this dissertation provides the necessary background to establish the importance of the present research. It also contains an outline for the individual chapter. 6 Chapter 2 contains the relevant literature review on carbon sequestration in mine tailings, exhaust flue gas of the diesel generator, dry stack tailings management, injection in porous media, and carbon market basics. This chapter also establishes the core objective of the dissertation along with the list of sub-objectives that were defined to accomplish the primary target of the present research. Chapter 3 identifies the critical components of the research target and proposes a concept for large-scale carbon sequestration in mine tailings through diesel exhaust injection. It establishes a detailed methodology for developing a reduced-order model that can be applied to predict the fluid flow and pressure profile for a perforated pipe embedded in a dry stack tailings bed to inject diesel exhaust to capture carbon within the tailings. This chapter also contains the experimental investigation that was carried out to validate the reduced-order model. Chapter 4 discusses the impact of the cold climatic conditions of the off-grid locations on the carbon sequestration operation in mine tailings using flue gas injection. It contains the details of the numerical investigations and the accompanying parametric studies conducted to examine the viability of operating the proposed system year-round in remote mine sites. Chapter 5 shows the application of the reduced-order model developed in Chapter 3 in conducting a financial analysis of the proposed concept. Major cost components were identified, and the variance in the operating cost at different operating conditions was measured. Chapter 6 contains a summary of the entire study, providing recommendations for future work. 7 Chapter 2: Literature Review and Research Objectives 2.1 Carbon Mineralization: Background and Rationale Being the largest anthropogenic GHG emission, carbon dioxide has contributed significantly to global warming [25]. The natural buffering system and the earth's elementary carbon pool lacks the capability to absorb CO2, resulting in its gradual accumulation in the atmosphere. [26]. This critical situation has resulted in urgent and global demands for large-scale solutions to capture the anthropogenic carbon and store it in different potential ways [27-29]. The idea of carbon mineralization for removing carbon from the atmosphere by depositing it in permanent safe storage was proposed about three decades ago [30, 31]. Being a part of the greater carbon cycle, carbon mineralization occurs naturally [32]. This process involves mineral weathering in which divalent cations are released from the minerals and react with aqueous CO2, leading to the formation of carbonate minerals. The rate of this process hinges on mineral-specific dissolution rates, which vary markedly [33]. Identifying suitable minerals and accelerating this natural process is crucial for the success of carbon mineralization. Engineered carbon mineralization systems offer stable storage with almost no leakage by forming solid carbonate minerals [34]. This solution can mitigate environmental and health hazards in particular cases [35]. In a broader aspect, these strategies could be distinguished by the storage location. Depleted gas or oil reservoirs [36], igneous rocks abundant with mafic minerals (abundant in magnesium and iron) [37], saline aquifers, or sedimentary formations [38, 39] are the prospective candidates when the physiochemical process of carbonation is governed by either the high pressures or temperatures in underground formations [40]. Conversely, in above-ground 8 conditions, ultramafic mine wastes (specifically tailings) are considered as potential candidates for carbon sequestration in contact with atmospheric CO2 and water [41-43]. Lately, the likelihood of carbon mineralization in commercial alkaline waste and waste debris has also been evaluated [11, 44, 45]. According to a relevant research [46], intensifying the sequestration capacities of mine tailings will add lucrative options to the existing portfolio of carbon capture and storage (CCS). At present, most of the technologies available for carbon mineralization focus on carbon dioxide removal from the air (CDR). Brief descriptions of these methods are given below. In ex-situ CDR, the carbon mineralization candidate or the source of alkalinity is transported to a carbon sequestration site. Due to its relative abundance and appropriate reactivity, olivine has been studied mainly as a suitable mineral for ex-situ carbon mineralization. Mine tailings, which are rich in serpentine, are also a compelling alternative [47]. This process generally requires high temperature (for olivine ~185°C) and pressure reaction vessels [44]. This method is generally more expensive than the other available options, almost 10 times more expensive than CO2 injection in a subsurface reservoir for sequestration purposes [48]. In the case of in-situ CDR, supercritical CO2 or CO2-bearing fluid (e.g., surface water) is circulated into geologic formations (e.g., saline aquifers, depleted gas or oil reservoirs, hydraulically fractured shale formation, and so forth) [48, 49]. Although this method potentially holds a scope of an extreme amount of carbon mineralization with a comparatively lower area footprint requirement, impacts of several key parameters (e.g., injectivity, permeability, geomechanics, and so forth) are yet to be explored [13]. Furthermore, the process is notably governed by pH 9 fluctuations, with elevated pH promoting carbon precipitation and lowered pH intensifying mineral dissolution. [50, 51]. In surficial CDR, the reaction of dilute or concentrated gaseous CO2 occurs at the surface with the on-site crushed and or ground tailings, commercial alkaline wastes, or sedimentary formation, which are rich in reactive rock fragments [13, 47]. This method potentially holds the maximum opportunity to reduce the on-site CO2 emissions for a mine with mafic and ultramafic tailings [52, 53]. The other method is the combination of direct air capture with synthetic sorbents (DACSS) with surficial or in-situ carbon mineralization for partial enrichment of CO2. The most recent cost estimations show that these methods should be less expensive for CDR. However, these methods still require more in-depth investigation and hold significant room for optimization [13, 48, 54]. The reaction rate between the minerals and CO2 plays a vital role in the economic feasibility of any carbon mineralization project. The highly reactive rocks, which are rich in Mg and Ca, generally incorporate mantle peridotite along with ultramafic intrusions. These rocks provide a crucial source of alkalinity due to the presence of olivine and pyroxene. In the case of altered ultramafic rocks, the mineral brucite (0-10% of altered peridotite by weight), along with some fibrous polytypes of serpentine (frequently, chrysotile), are the best candidates for surficial CDR (in mine tailings) [13]. The rates of reaction of wollastonite, olivine, and brucite are comparable, and are rapid. Though wollastonite reacts faster than olivine and pyroxene, the smaller global reserve [54] limits its candidacy in large-scale carbonation projects. Fibrous serpentines also offer the same reaction rate 10 when the surface area to volume ratio is higher. Mg and Ca in commercial or industrial waste provide almost the same reaction rate when not combined with aluminosilicate compounds [13]. Some fundamental reactions of carbon mineralization (mentioned in [13]) are given in Table 2-1. Table 2-1. Fundamental carbon mineralization reactions [13]. Name of the reactant mineral Fundamental reaction Equation No. Wollastonite 𝐶𝑎𝑆𝑖𝑂3 + 𝐶𝑂2 ↔ 𝐶𝑎𝐶𝑂3 + 𝑆𝑖𝑂2 (2.1) Olivine 𝑀𝑔2𝑆𝑖𝑂4 + 2𝐶𝑂2 ↔ 2𝑀𝑔𝐶𝑂3 + 𝑆𝑖𝑂2 (2.2) Pyroxene 𝐶𝑎𝑀𝑔𝑆𝑖2𝑂6 + 2𝐶𝑂2 ↔ 𝐶𝑎𝑀𝑔(𝐶𝑂3)2 + 2𝑆𝑖𝑂2 (2.3) Serpentine polytypes 𝑀𝑔3𝑆𝑖2𝑂5(𝑂𝐻)4 + 3𝐶𝑂2 ↔ 3𝑀𝑔𝐶𝑂3 + 2𝑆𝑖𝑂2 + 2𝐻2𝑂 (2.4) Brucite 𝑀𝑔(𝑂𝐻)2 + 𝐶𝑂2 ↔ 𝑀𝑔𝐶𝑂3 + 𝐻2𝑂 (2.5) 2.2 Carbon Sequestration in Mine Tailings The focus now shifts towards the intricacies of carbon sequestration in mine tailings. It explores the potential opportunities and addresses the challenges associated with this concept, all of which are the subjects of ongoing research. Ultramafic rocks, with their rich Mg and Ca contents, can capture and store carbon in solid form through mineral carbonation. There are mine tailings available in vast stacks containing up to 20 wt% Mg (primarily in the form of silicates and hydroxides of Mg; e.g., serpentines, olivine, forsterite, brucite, and so on [12]). These tailings can form solid storage of carbonates through mineral sequestration chemical reactions mentioned in Table 2-1 [31, 55, 56]. To extract valuable 11 minerals (such as diamond or nickel), the ore is crushed to a fine particle size range, significantly increasing the reactive exchange surface by orders of magnitude. Hence, mines producing nickel, diamond, or platinum group metals [12] have the potential to provide vast amounts of "cost-free" feedstock for surficial carbon sequestration [13]. This means that using tailings as a candidate for mineral carbonation saves the operating cost of crushing the rocks to prepare them for sequestration. The CO2 absorption and storage capacity for accomplished carbonation of these minerals are given in Table 2-2. Table 2-2. 𝐂𝐎𝟐 absorption and storage capacity for different reactant minerals [13]. Name of the reactant mineral Tonnes of CO2 storage capacity per tonne of reactant mineral Olivine ~0.62 Brucite ~0.76 Pyroxene, Serpentine, Wollastonite ~0.4-0.5 According to informal estimates mentioned in [13], there are at present less than 10 billion tonnes of ultramafic tailings available, and an unknown amount of it has already naturally sequestered CO2. On the other hand, ~420 million tonnes of ultramafic tailings become available every year [57]. Therefore, it is imperative to develop efficient solutions to make the best use of these tailings to capture and store the maximum amount of CO2 possible. Another challenge is that most of the mafic or ultramafic minerals (excluding brucite and fibrous serpentine containing labile Mg) tend to react slowly at surface conditions of ~10-30 °C and ~405 Pa [41, 52, 58]. Various strategies are currently under study to overcome these issues, 12 especially the slowness of the reaction. Several studies suggest the local modification of the tailings by stirring to ensure the reactive surfaces of the tailings are always in contact with air [13]. Studies have shown that adding microorganisms to the disposal pond also accelerates the rate of carbonation process [59, 60]. Though the high surface area of tailings attained through the processing facilitates the carbonation process, the reaction rate can often be constrained due to the limitation in the availability of CO2 [42, 61]. A strategy to improve this situation could be the injection of CO2-rich gas into the tailings, sparging air, or water-saturated by air [46, 62, 63]. Lab-scale studies have shown that this strategy holds the potential to speed up the reaction process significantly [46, 52]. The possible approximate amounts of CO2 in different sources have been tabulated in Table 2-3. Table 2-3. Amount of 𝐂𝐎𝟐 available in different sources under study for carbon mineralization [47]. Source Amount of CO2 (Volumetric %) Ambient air ~0.04 Flue gas from power generation sector ~5-12 Air-saturated Mg-rich peridotite groundwater ~0.01 CO2-saturated fluid / high purity CO2 gas or fluid ~99.5 All these studies indicate a great potential of reducing the carbon footprint of the off-grid mines that have fossil fuel-based power generation plants by injecting flue gas in the available ultramafic mine tailings. 13 2.3 Diesel Exhaust Flue Gas As stated above, diesel generators continue to serve as the dependable primary power source for mining operations in remote areas. The flue gas emitted from these generators holds the potential for injection into mine waste to facilitate carbon sequestration. Therefore, gathering essential details of diesel exhaust pertaining to the current study at this stage is necessary. A diesel generator is an assembly of an Internal Combustion (IC) engine (i.e., diesel thermal cycle) and an electric generator followed by several supporting systems (e.g., control systems, sound attenuation, canopy, circuit breakers, and so forth). The diesel engine converts the chemical energy of the fuel into mechanical power through diesel fuel combustion, producing exhaust (flue) gas. Being a mixture of hydrocarbons, in ideal thermodynamic equilibrium, the complete combustion of diesel will result in exhaust containing only H2O and CO2 in the combustion chamber [64]. Nevertheless, the air-fuel ratio, ignition timing, turbulence inside the combustion chamber, temperature, and so many other factors make this ideal state unattainable [65]. The composition of the diesel exhaust gas from the diesel generator depends on the design of the engine, operating circumstances, and mostly on the type of diesel being used as fuel [66]. The requirement to use diesel fuel with lower sulfur content is becoming more prevalent globally [67]. However, even the exhaust from a diesel generator with ultra-low sulfur diesel fuel has higher carbon content than all the possible sources of CO2 for carbon mineralization in mine tailings mentioned in Table 2-3. This provides off-grid mines a unique opportunity to cut down their unavoidable carbon emissions for power generation purposes by large-scale injection of diesel exhaust in mine tailings. 14 The typical composition of the diesel exhaust gas is shown in Table 2-4. Table 2-4. Typical composition of diesel exhaust gas (based on [68]). Name Amount (volumetric %) N2 67 CO2 12 H2O 11 O2 9 Pollutants (CO, HC, NOx, SOx, PM) 1 Due to a series of thermo-mechanical deficiencies, even with the best technology available, a typical generator converts only ~33% of its fuel input into electricity [69]. The rest is discarded as heat (accompanied by noise and vibration) through its aftercooler, water-jacket, oil cooler, radiation to the atmosphere, and exhaust stream [70]. According to a detailed study [71] on a series of industrial-scale diesel generators, ~31-41% of the energy in the consumed diesel fuel is discarded through the exhaust of the generator while operating. The same study [71] also shows that while generating 1 kW of electricity with a typical diesel generator (running at 100% load factor), approximately 1 kW of heat is discarded through the exhaust. Figure 2-1 demonstrates the overall fuel consumption and the extent of heat wasted particularly through the exhaust, in the process of generating 1 kW of electricity using diesel generators of different power ratings. 15 Figure 2-1. Analysis of Waste Heat from Diesel Generators with Varied Power Outputs; the left axis represents bar values, while the right axis corresponds to the values of lines or markers. (adapted from [71, 72]) Harnessing the available thermal energy of the diesel exhaust has been shown to yield both economic and environmental benefits at remote mining operations. Several noteworthy studies [22, 71-73] are available that demonstrate the effective utilization of thermal energy from diesel exhaust in various mining-related applications. These studies show that the development of certain sustainable practices of handling the diesel exhaust in off-grid mines can establish Combined Heat and Power (CHP) solutions in remote mines sites. An example of a diesel exhaust heat recovery system (DEHRS) operating in an off-grid mine is illustrated in Figure 2-2. In the case of underground operations, the DEHRS recovers the heat from the diesel exhaust and supplies it to preheat the mine intake air to the set-point temperature. In the case of surface operations, this 0.000.200.400.600.801.001.201.401.601.802.002.202.402.602.803.003.203.400.000.501.001.502.002.503.003.504.004.505.005.506.006.507.007.508.008.50364 500 648 800 1,000 1,360 1,500 1,750 1,825 2,000 2,250 2,500 2,725 2,825 3,100Energy consumed or rejected per kWgenerator power output (kW)Quantity of heat (MW)Generator power output (ekW)Heat rejected through the exhaust Heat available in fuelTotal heat rejected from generator Fuel consumed per ekW outputTotal heat rejected per ekW output Heat rejected through exhaust per ekW outputAverage ~ 2.74 kW Average ~ 1.81 kW Average ~ 1 kW 16 recovered heat can be used to provide necessary heating to facilities. Available studies [22, 71-74] showed establishing a control over the temperature up to which the exhaust was cooled down (shown as warm exhaust in Figure 2-2) and it was kept above 80°C. Figure 2-2. Illustration depicting an exhaust heat recovery system utilized for heating mine intake air (case A) in underground operation and providing heating for spaces along with a domestic hot water system (case B) for surface operation (adapted from [71, 72]). The effective utilization of thermal energy within the diesel exhaust flue gas in various applications establishes a foundation to investigate the potential viability of capitalizing on exhaust heat for carbon sequestration operation in the harsh cold climates of remote locations. Cold working fluidHot working fluidCold ambient air To mine intake shaft at set-point temperatureE-1Exhaust heat recovery unitWarm exhaustDiesel burner (air pre-heater)Intake air heating unitE-1E-1Hydronic heating and domestic hot water systemSystem case A (intake air heating)System case B (space heating and domestic hot water)Diesel gen-setE-517 2.4 Dry Stack Tailings To attain the required unsaturated tailings conditions for a uniform injection process, it is essential to filter the mine tailings and store them in a dry stack configuration. [75, 76]. The focus was placed on understanding the relevant details of tailings management through dry stacking. Mining activities generate substantial amounts of waste material, known as tailings, which pose significant environmental and safety challenges because of their conventional slurry-based tailings management facility (tailings impoundment) [77, 78]. Over the past five decades, there has been a concerning upward trend in high-consequence Tailings Storage Facility (TSF) failures [79, 80]. In response to this concern, the mining industry has been actively exploring alternative methods for tailings disposal that prioritize safety and efficiency. In dry stack tailings, alternatively referred to as stacked or filtered tailings, the tailings are dewatered and systematically stacked [81]. This method has garnered considerable interest in recent times owing to challenges encountered with conventional slurry-deposited tailings facilities and the consequential risk of catastrophic failures [82]. It is important to note that each site that has used the dry stack technology has formulated its unique approach, resulting in a need for more standardization and industry-wide communication [81]. Nevertheless, the fundamental methodology remains largely consistent across all mine sites where this system is in operation. Tailings are first dewatered through thickening, filtration, or centrifugation to increase solids concentration by removing excess water [83]. Different flocculants and polymers are added to the water to facilitate the separation of particles from it, thus improving the water removal process [84, 85]. Subsequently, the dewatered tailings are conveyed to the designated stacking area, which can be accomplished through two distinct approaches. The 18 initial approach employs a combination of loaders and trucks, while the second method integrates a series of conveyor belts [86]. The latter method offers the additional advantage of enhanced tailings dewatering and is particularly advantageous when the operation adheres to a predetermined mine plan from the outset. Despite incurring higher initial capital expenditure, the second method is a superior choice in such cases [81]. The designated area for dry stacking in the mine site must be prepared before receiving the filtered tailings. A proper drainage system along with the other infrastructure support (e.g., liners if required) is ensured [87, 88]. The tailings are then placed in thin layers in the stacking area. Each layer is carefully spread and leveled to ensure even distribution and prevent excessive settling. The thickness of each layer can vary depending on factors, such as, tailings properties and equipment used [89, 90]. Compaction is a critical step to promote stability within the stack [91]. Specialized equipment, such as bulldozers or compactors, may be used to compact the layer of tailings [92]. Compaction helps eliminate void spaces within the layer, reducing the risk of settling and increasing the overall density [93]. In some cases, a final cover, such as geosynthetic materials or a layer of granular soil, might be placed on top of the stacked tailings to prevent erosion, dust generation, and water infiltration. This cover provides additional protection to the stack and surrounding environment [87, 92, 94]. Dry stack tailings stand out as the safest option for modern mining industry tailings management due to several compelling factors. These include the elimination of tailings supernatant ponds, minimal seepage, heightened structural stability, gradual reclamation processes, enhanced tailings water recovery, diminished environmental impact, and improved standing within regulatory bodies and local communities [77, 81, 92-94]. Nonetheless, it is worth noting that the initial capital 19 investment required for implementing a dry stack tailings system is comparatively higher when contrasted with traditional tailings dams [81]. Furthermore, the presence of wet or arid climatic conditions can introduce complexities in maintaining the operational efficiency of a dry stack tailings facility, potentially leading to escalated operating costs under such circumstances [95]. However, the incorporation of carbon sequestration into dry stack tailings through flue gas injection introduces an appealing dimension. This strategy addresses environmental concerns and offers supplementary incentives, further underscoring the attractiveness of dry stack tailings as a financially viable choice for mine waste management. 2.5 Injection in Porous Media Considering that the focus of this research is the efficient injection of diesel exhaust into mine tailings, which constitute a porous medium, the pertinent aspects of injection within porous media are reviewed in the following. A porous medium, also known as a porous material, signifies a substance or material with interconnected pores (void spaces), permitting the flow of fluids or gases through them [96]. Porous materials are encountered in various contexts, in natural formations (rocks, soil, gravel, sand) and as intentionally engineered substances, including membranes and foams [97]. The solid structural component is often described as the ‘frame’ or ‘matrix’[98]. The study of fluid flow patterns, transport characteristics, and heat transfer within different porous materials holds significant importance across numerous scientific and engineering fields, including hydrology, civil, and mining engineering [99-101]. Two fundamental attributes, namely porosity and permeability, play pivotal roles in characterizing porous media [98]. Porosity denotes the 20 proportion of void spaces or pores within a material, representing a volume fraction [102]. In contrast, permeability is the capacity of the material to permit the passage of fluids [103]. 2.5.1 Fluid flow in porous media The complexity of fluid flow within porous media arises from the inherently random structure of such materials, characterized by substantial spatial variation in internal geometric attributes such as porosity, permeability, and tortuosity [104]. In the context of injection scenarios within porous media, it is imperative to understand the fluid flow behavior through the pores. Within porous media, fluid flows can exhibit various regimes, including laminar and nonlinear laminar flow where there is a transition from a viscous-dominant regime (known as the Darcy regime) to an inertial-dominant regime (referred to as the Forchheimer or non-Darcy regime), as well as turbulent flow [105]. This understanding, along with consideration of viscous and inertia terms, becomes essential for the accurate prediction of pressure gradients, which in turn influences the requisite fan power. Darcy's law is a constitutive equation derived from empirical observations describing fluid flow within porous media. This law stemmed from experimentation with water flowing through a sand bed [106]. It is widely applied in describing the flow of oil, water, and gas through various porous domains [107]. Darcy’s law establishes a linear relationship [106] between the fluid velocity field 𝒖 (in m/s) and the associated pressure loss per unit length ∇𝑝 (in Pa). 𝒖 = − 𝐾𝜇∇𝑝 (2.6) 21 where, 𝐾 (in m2) is the permeability of the porous medium, and 𝜇 (in Pa ∙ s)is the dynamic viscosity of the fluid flowing through the porous domain. Equation (2.6) is applicable when the fluid flow velocity in the porous media is low enough to maintain a laminar flow regime. The flow regime in porous media can be determined by using the following equation [97] that estimates the Reynolds number (𝑅𝑒𝐾) where the length scale is √𝐾. 𝑅𝑒𝐾 = 𝑢𝜈√𝐾 (2.7) where, 𝑢 (in m/s) is the fluid physical velocity, and 𝜈 (in m2/s) represents the kinematic viscosity of the fluid. Based on the Reynolds number, the fluid flow regimes within the porous media can be categorized as follows: laminar flow (𝑅𝑒𝑘 < 1), transitional flow (1 < 𝑅𝑒𝑘 < 10), and turbulent flow (𝑅𝑒𝑘 > 10) [97]. For Darcian flow through granular soils and packed beds, the Kozeny–Carman equation establishes a relationship between 𝐾, porous domain porosity (𝜀), and the average particle diameter, 𝑑𝑝 (in m) through the following equation [108]. 𝐾 = 𝑑𝑝2180 𝜀3(1 − 𝜀)2 (2.8) The Ergun equation ([109]) represents an expansion of the Kozeny-Carman equation, specifically designed to accommodate moderately higher Reynolds numbers. In scenarios where Darcy's linear relationship between pressure drop and velocity loses its applicability, the Ergun equation introduces an additional quadratic term to correctly model the pressure drop within a packed bed or columns of spherical particles. 22 −∇𝑝 = 𝐴𝑑𝑝2 (1 − 𝜀)2𝜀3 𝜇𝒖 + 𝐵𝑑𝑝 (1 − 𝜀)𝜀3𝜚𝒖2 (2.9) where, 𝜚 (in kg/m3) is the fluid density. 𝐴 and 𝐵 are the Ergun coefficients and variance in their values can be seen observed throughout the literature. Amiri et al. [110] compiled a comprehensive list, presented in Table 2-5, of Ergun coefficients extracted from various sources in the literature. Table 2-5. Values for the constants employed in Ergun correlations across varying porosities and particle sizes stated in different literature as mentioned in [110]. Model/Study 𝐴 𝐵 𝜀 𝑑𝑝 (× 10−3 m) Dudgeon [111] 326 − 287 1.24 − 1.58 0.37 − 0.38 15.97 − 21.33 du Plessis and Woudberg [112] 170 − 200 1.35 − 2 0.2 − 0.8 − England and Gunn [113] 180 2 0.35 − Ergun and Orning [114] 150 1.75 0.35 − 0.55 − Happel [115] 165 − 0.2 − 0.78 − Kyan, Wasan et al. [116] 236 − 184 14.1 − 12.1 0.68 − 0.83 0.42 − 0.03 23 Macdonald, El-Sayed et al. [117] 124 − 162 1.09 − 1.49 0.37 − 0.64 0.68 Reichelt [118] 200 2 0.36 9.71 − 24.5 The presence of significant inertial effects and turbulent friction forces can be observed in a porous domain with 𝑅𝑒𝐾 > 10 where the fluid transmits through the pore with a high velocity. In such cases, a term called Forchheimer drag is added to Darcy’s law to predict the pressure drop using the following equation [119]. −∇𝑝 = 𝜇𝐾𝒖 + 𝑐𝐹√𝐾 𝒖2 (2.10) where, 𝑐𝐹 indicates the Forchheimer coefficient that accounts for the resistance to flow due to the inertial effects within the porous materials. The value of the Forchheimer coefficient depends on various factors, such as the nature of the porous media or packed bed, the porosity of the porous medium, the pore size distribution, and the flow conditions. It is often estimated through experimental investigations [120, 121]. Nonetheless, considering the scope of the present study, which is to inject flue gas into mine tailings for carbon sequestration from diesel exhaust, it will be necessary to maintain laminar fluid flow velocities in the tailings. This control is necessary to facilitate the reaction between the tailings and CO2 for effective carbon sequestration. 24 2.5.2 Heat transfer in porous media The utilization of numerical modeling has witnessed a growing adoption in predicting transport phenomena within porous media across a diverse spectrum of conditions. This approach offers a comprehensive insight into the fundamental transport mechanisms at play [122, 123]. Several studies are available investigating fluid flow and heat transfer in porous media, mostly looking into storing the heat in a porous domain for thermal energy storage [124]. The heat transfer between the solid and fluid in the porous media depends on multiple factors, e.g., thermal properties of the solid particles, porosity or the air volume fraction of the porous domain, and so on [125]. Computational fluid dynamics (CFD) simulations allowed investigation of heat transfer scenarios in porous media with a more comprehensive approach [126, 127]. Numerical studies can be categorized broadly as pore-scale or as volume-averaging based on how the heat transfer mechanisms are investigated [128]. The pore-scale method is a specialized technique employed to investigate heat transfer within porous media at the microscopic level. It aims to offer a direct solution to the transport processes within a representative porous domain, thereby fostering a more realistic understanding of the phenomena [129-132]. In this approach, an explicit solution algorithm used within the microscopic structure that enables a direct connection between the complex fluid transportation process and the porous structure itself. Hence, the understanding of any phenomenological parameters, such as, predefined constants or empirical values is not required [129]. The primary challenges inherent in this approach revolve around the intricate development of the accurate geometry of the porous structure [133, 134] and the subsequent mesh generation process to ensure the robustness and 25 efficiency of the numerical model [135, 136]. Additionally, a pore-scale model demands a considerable amount of time and incurs higher computational costs [128]. Conversely, the volume averaging method operates by averaging the governing equations for heat transfer across the representative elementary volume (REV), allowing for a more straightforward adaptation of the boundary value problem. It achieves this by focusing solely on the large-scale flow behavior [137]. Accurate identification of the REV is pivotal, as it ensures that the outcomes remain unaffected even with the incorporation of extra surrounding volume [97]. Following the selection of the REV, the next step involves the introduction of the appropriate empirical or semi-empirical terms into the momentum and energy equations [128]. There are two approaches available to explore the heat transfer phenomena in porous media using the volume averaging method. One is a more straightforward approach that considers thermal equilibrium between the solid and the fluid phase in the microscopic (pore) scale [18]. This approach is denoted Local Thermal Equilibrium (LTE), and excluding natural convection, it uses a one-phase transient energy equation or considers a simplified radial uniform temperature pattern [74]. However, this approach fails to provide accuracy in highly transient instances, where one of the phases exhibits a dominating trend in the interphase heat exchange [138]. In such scenarios, the Local Thermal Non-Equilibrium (LTNE) approach must be applied to achieve the required accuracy [139]. This approach occupies two energy equations for a two-phase energy balance which is closer to reality for complex heat transfer systems in porous media [140]. 26 2.6 Carbon Market The impact of the increasing anthropogenic greenhouse gas emissions was concerning enough to declare climate action as one of the goals for sustainable development set by the United Nations [141]. A multi-faceted measure that incorporates creating public awareness, stringent regulations, reducing greenhouse gas emissions, and so forth must be implemented to fight climate emergencies. Of these, a decrease of fossil fuel emissions has been underscored as the foremost objective to avert further detrimental impacts on the climate [142]. In response to these imperatives, the emergence of the carbon market, often referred to as an emission trading system, has arisen [143]. With access to vast quantities of mafic and ultra-mafic tailings that possess substantial CO2 capture and storage potential, the mining industry stands poised to play a pivotal role in the global carbon market, spearheading efforts to combat climate change [12, 47, 144]. The relevant concepts related to the carbon market and trading are reviewed here. The two most globally adapted carbon-control or emission reduction policies are the cap-and-trade and carbon tax [145]. In a cap-and-trade arrangement, government bodies define emission thresholds for enterprises and oversee the exchange of emission allowances among these businesses [146]. A carbon restriction or cap (also known as allowance) system enforces a stringent ceiling on emissions, which companies are obliged to stay below. On the other hand, the carbon tax is a direct financial levy on carbon emissions or the carbon content of the fossil fuel [147]. This tax is derived from the amount of CO2 (or its equivalent) released in the environment while burning a certain amount of fossil fuel and priced per tonne CO2 equivalent emissions. The current carbon tax rate in British Columbia, Canada is C$65 per tonne of CO2e emission [148]. 27 Carbon markets function as trade frameworks where carbon credits are vended and acquired [149]. Organizations or individuals have the option to employ carbon markets to offset their emissions of greenhouse gases. This is achieved through the acquisition of carbon credits from entities dedicated to either the mitigation or elimination of greenhouse gas emissions [150]. There exist two main classifications of carbon markets: compliance markets and voluntary markets. Compliance markets emerge due to national, regional, or international policy or regulatory obligations [151]. In contrast, voluntary carbon markets, operating on both national and international scales, involve the issuance, procurement, and exchange of carbon credits on a non-mandatory basis [152]. Carbon offsets denote a mechanism or practice enabling an entity to counterbalance a specific quantity of its emissions by endorsing verified initiatives or projects that effectively reduce or eliminate a corresponding measure of emissions [153]. Examples of such projects include the installation of renewable energy systems, initiatives focused on afforestation and reforestation, the capture of methane emissions from landfills, and the deployment of carbon capture technologies [154]. Generally, On the other hand, carbon credit designates a tradable unit corresponding to specific GHG emissions. When an entity emits a quantity of greenhouse gases (GHGs) that is lower than their allocated limit (set by the governments or the regulatory body) for a given year, they have the option to sell their surplus credits to other entities that have surpassed their designated emission threshold [155]. This system creates financial incentives for companies to curtail their emissions below the approved threshold and subsequently trade any excess credits for a profit [156]. A single carbon credit or offset commonly corresponds to a tonne of carbon emissions [157]. 28 Offset trading functions as a mechanism for transferring a net climate benefit from one entity to another, rather than directly removing carbon from the atmosphere. Recognizing the magnitude of carbon emissions and the inherent trading prospects within the carbon market, a notable focus is being seen on the advancement of numerous innovative and sustainable carbon removal technologies. These approaches are direct air capture (DAC), enhanced weathering, afforestation, and bioenergy combined with carbon capture and storage [158-160]. The expense associated with carbon removal is contingent upon the technology employed for the extraction process. The typical cost ranges for various carbon removal technologies are shown in Figure 2-3. This representation is generalized and the cost varies depending on the chosen technology, utilization of low-carbon energy sources, and the extent of deployment [161]. Figure 2-3. Global carbon capture costs (𝐔𝐒$/𝐭𝐨𝐧𝐧𝐞 of 𝐂𝐎𝟐) by approach or technology as of September 2020. (based on [162]) 50034520012085501355030150 100 200 300 400 500 600Afforestation / reforestationDirect air capture and storageEnhanced weathering of mineralsLand management and biochar productionBioenergy with CCSUS$/ tonne of CO2Min Max29 These costs in Figure 2-3 were long-term projections to attain in the future without factoring in inflation adjustments for the present time. On the other hand, in 2021, the voluntary carbon market experienced unprecedented growth, surging to US$ 2 billion—four times its value in 2020. Projections indicate that this market is anticipated to expand to US$ 10 − 40 billion by 2030 [163]. Currently, there are contracts worth of US$ 170 million aimed 0.36 Mt of carbon (averaging US$ 476/t) using various early-stage technologies, such as, direct air capture, enhanced weathering, direct ocean removal, and carbon mineralization [164]. These insights lay the foundation for conducting a comprehensive financial analysis of large-scale carbon sequestration in dry stack mine tailings using flue gas injection. 2.7 Research Objectives The background discussed in Chapter 1, and the relevant literature review presented so far in this chapter established the necessity for large-scale implementation of carbon sequestration operations in mine tailings. This research was directed towards identifying and resolving critical questions essential for successfully engineering the large-scale carbon sequestration within mine tailings. Accordingly, the present research followed a set of systematic, sequential investigative approaches toward the large-scale development of sustainable carbon storage facilities by injecting the flue gas from the power generation units into mine tailings for off-grid mines. With this overarching motive, the following specific objectives have been delineated. • To conceptualize a design for injecting diesel exhaust flue gas into mine tailings using perforated pipes for carbon sequestration, and to identify the pivotal components integral to the proposed concept. 30 • To develop viable numerical methodologies enabling accurate estimation of the energy requirement for the transportation and injection of flue gas within tailings storage facilities. • To verify the robustness and applicability of the developed numerical models for real-life scenarios through experimental validation at a laboratory scale. • To examine the possibility of utilizing the thermal energy of the diesel exhaust to overcome the impact of the harsh weather of remote locations for the large-scale application of carbon sequestration in mine tailings. • To execute a series of sensitivity analyses to demonstrate the flexibility and applicability of the proposed concept across diverse operating scenarios. • To construct a robust cost model, providing a reliable strategy to evaluate the economic feasibility of implementing the proposed model within real-world applications. 31 Chapter 3: Fluid Flow Investigation for Flue Gas Injection into Mine Tailings 3.1 Introduction As described in the literature review, one method to accelerate carbon sequestration within mine tailings at remote mines involves the injection of diesel generator exhaust into dry stack tailings. The techno-economic feasibility of this approach heavily depends on understanding the flow characteristics inside the perforated injection pipes embedded within the tailings. To the best knowledge of the author, no study has undertaken the design of a large-scale carbon sequestration system by injecting diesel flue gas into mine tailings. Addressing the knowledge gap, a research program was established targeting injection of diesel exhaust into mine waste using perforated pipes. Wynands [165] discussed the concept of using a perforated pipe to inject CO2-rich gas into tailings for carbon sequestration. However, the scope of that study did not encompass crucial aspects, namely the fluid flow dynamics and pressure profiles within perforated pipes, which are indispensable for the successful large-scale implementation of the concept. Simulations are necessary to optimize the injection of diesel exhaust using perforated pipes. A perforated pipe can be defined as a cylinder with holes that allow for a uniform distribution of flow throughout the pipe [166, 167]. Studies on perforated pipes can generally be categorized into three types: discrete, analytical, and computational fluid dynamics (CFD) simulations, based on the methodologies adopted to investigate pressure drops and flow [168]. Several studies have used either energy equations [169] or momentum conservation methods [170] to investigate the pressure profile in perforated pipes. Acrivos et al. [171] conducted an extensive experimental and theoretical 32 evaluation by including an empirical alteration of the Bernoulli equation to estimate the flow distribution and pressure variation in a perforated pipe. These findings were later simplified by Greskovich and O'Bara [172] with the assumption of uniform flow through the perforations [173]. Wang [168] explained the pressure response of perforated pipes by deriving an energy balance of the fluid flow in the boundary layer and the pipe center (see also [174]). Several studies have focused on the application of perforated pipes for micro-irrigation applications. Vallesquino and Luque-Escamilla [175] treated lateral irrigation outflow as a discrete event and employed Taylor polynomials to calculate flow rates. Maynes et al. [176] proposed a theoretical solution based on laboratory experiments to calculate the head loss coefficient across a perforated pipe. Discrete or network models have also been employed due to their simplicity [177]. In these models, the perforated pipe or manifold was represented as a combination of several intersections through which fluid traveled. For each intersection, the conservation equation for mass and momentum was applied to derive a system of differential equations. Analytical models provided an explicit analytical solution while considering a continuously branched fluid flow throughout the manifold. Although widely accepted due to their simplistic approach [170], both discrete and analytical approaches have limitations in terms of their applicability to complex cases. The application of CFD models has the potential to solve problems related to perforated pipes. Afrin et al. [178, 179] developed a numerical model and conducted several parametric studies to investigate the hydraulic characteristics of porous pipe underdrains. Minocha et al. [180] employed three-dimensional (3D) CFD simulations to investigate potential design scenarios to optimize the pressure drops in a divided manifold system. Kulkarni et al. [173] performed 3D CFD simulations along with experimental work to investigate the pressure and flow distribution in pipe and ring 33 spargers to achieve a uniform pressure and flow distribution. Though the application of CFD has been extremely useful in this research field, it demands extensive computational resources, which makes it inconvenient for a preliminary analysis. Drawing insights from the comparisons outlined above, which examined various approaches for analyzing flow and pressure profiles within perforated pipes, this study aimed to construct a reduced-order numerical (ROM) model. This model was pursued as the optimal strategy to effectively address the specific problem under investigation. A ROM provides the similar accuracy as 3D CFD models in solving complex scenarios, but requires significantly less computational resources and time [181]. In this chapter, a novel (1+1)D reduced-order numerical model was developed that was validated by the results of an experimental investigation and provided the same accuracy as a 3D finite element (FE) model for different operating and design parameters. This model was applied to establish an energy-efficient large-scale design for injecting flue gas into mine tailings. Two distinctive yet dynamically coupled transport phenomena were identified and evaluated: i) gas transport inside the pipe and ii) gas injection into the porous body of the tailings. This chapter presents two models to investigate these transport phenomena: a three-dimensional (3D) and a one-plus-one-dimensional (1+1D) model. An experimental investigation of the pressure profile through the injection pipe was carried out to validate the models at the lab-scale. To ensure the accuracy of the (1+1)D model developed for potential applications on larger scales, its results were cross-checked with those obtained from the 3D model. To include the effect of the perforations in the pipe on the pressure profile of the (1+1)D model, an analytical fluid velocity profile was developed in relation to geometric and physical parameters related to the proposed system. The 34 performance of the (1+1)D model with this impact factor was then evaluated against the 3D model results for the inlet pressure, pressure profile, and gas outflow distribution under various conditions than those investigated experimentally. The (1+1)D model has undergone thorough rigorous validation to substantiate its suitability for creating an energy-efficient methodology, suitable for large-scale implementation across a diverse range of operational parameters, for the controlled injection of flue gas into mine tailings aimed at carbon sequestration. 3.2 Methodology 3.2.1 Conceptual design The conceptual design proposed in Figure 3-1 would require cooling the exhaust gas with a heat recovery system [22, 73, 74] and transporting the cooled exhaust from the power plant to the dry stack TSF through a pipeline (Transport-1). The exhaust could then be injected into an array of perforated pipes buried in deposited tailings to ensure consistent delivery of CO2. The proposed concept considers dividing the tailings into an array of blocks with similar dimensions. Each block has an injection pipe buried at its center, with each pipe having a certain volume of surrounding tailings. Two concurrent phenomena will occur within the injection pipes: the transportation of the exhaust through the injection pipes (Transport-2) and the injection of the exhaust into the tailings through the pipe perforations (Transport-3). Once a layer of tailings has fully reacted, a new layer can be built up with a new set of injection pipes. 35 Figure 3-1. Schematic of the proposed carbon sequestration method implemented at remote mines. In Transport-1 and 2, frictional pressure losses occur due to the viscosity of the exhaust gas within the respective pipes. During Transport-2, the flue gas outflow creates a momentum loss as the gas exits through the perforations into the tailings, leading to a pressure rise [182]. The total pressure drop in Transport-2 is the net value of the pressure losses and gains and can be denoted as the transportation pressure losses (TPL). Simultaneously, in Transport-3, the system is faced with another pressure drop due to the outflow of the exhaust into the tailings [183]. This can be denoted as the injection pressure loss (IPL). A compressor, a fan, or a blower will be necessary for flowing exhaust into the tailings and providing a steady discharge throughout the entire length of the pipe to ensure a homogeneous reaction of the tailings with CO2. The major design challenge in the large-scale implementation of this concept is to reduce the power required to overcome the pressure drops. The first step to address this challenge is to study the gauge pressure and outflow behavior of gas injected into a perforated injection pipe embedded in a porous medium. Tailings bedTransport-1: Exhaust coming from the power plantCompressor/Fan/BlowerInjection pipes embedded in ultramafic tailingsTransport-3: Exhaust injection into tailings through the perforationsTransport-2: Exhaust transportation in injection pipesDiesel generatorExhaust heat recovery system Initial piping Re-piping Tailings block36 The methodology of this study involved an experimental investigation which was conducted to validate a 3D FE numerical simulation and a (1+1)D ROM. To create the (1+1)D model, the relationship between various perforation arrangements and the pressure profile along the injection pipe was established through a parameter termed the 𝑚-factor. This approach rendered the (1+1)D model decoupled from the 3D FE analysis and avoided the need to run the computationally intensive 3D numerical model. To evaluate the performance of the (1+1)D ROM, the model results were compared against the 3D FE results under different design and operating parameters. 3.2.2 Experimental setup of injection through a perforated pipe A meter-scale injection experimental setup was built to validate the developed (1+1)D model. This setup comprised a perforated injection pipe (1.1 m in length and 0.029 m in diameter) nested within a larger, perforated cylinder (1.024 m in length and 0.15 m in diameter; shown in Figure 3-2). The perforations of the injection pipe and the external cylinder were covered with a gray, breathable fabric membrane. Along the injection pipe, eight precise, low-noise Bosch Sensortec BMP 388 pressure sensors (labeled as S1- S8 in Figure 3-2(b); relative accuracy of ±8 Pa) were installed at approximately equal intervals. The sand was compacted in a large cylinder, around the injection pipe, with the membrane preventing the sand from exiting through the external perforations and from entering the injection pipe. The sand was used as a porous material as it is more homogenous and has a permeability range similar to mine tailings. Two particle size distributions (PSD) of sand were used to achieve different permeabilities, termed coarse sand (CS; < 2 mm and > 425 μm) and fine sand (FS; < 425 μm). The PSD of the sand was assessed by sieving and laser diffraction, with further details and results included in Appendix A . The cylinder was filled first with 26 kg of CS at 3% moisture content and then with 32 kg of FS at 5% moisture 37 content. As the column was filled, the sand was compacted every ~3 kg. The physical conditions of the sand in the cylinder were simulated in a separate column, which allowed the permeability to be measured. Once full, the ends of the large cylinder and injection pipe were sealed with epoxy. Figure 3-2. Experimental setup for studying the outflow from a perforated pipe into a porous medium: (a) entire experimental setup; and (b) perforated pipe. The system was connected to a compressed air cylinder, and a MASS-VIEW MV-306 flow regulator (accuracy of ±2% of the reading for > 100 L/min and ±1% of the reading +0.5% of full scale for < 100 L/min) was used to control the flow rate into the injection pipe. Gas flowed through the perforations of the injection pipe, into the porous medium of the sand, and out through the perforations in the larger cylinder. Air was injected into the CS at three flow rates: 100, 110, and 120 L/min. For the FS, the injection rates were 70, 85 and 100 L/min. Each injection rate was conducted twice to examine the experimental repeatability. The entire surface of the cylinder discharged at ambient pressure (𝑝0), and any air entrapment was prevented by the well-distributed external perforations. The pressure sensors were used to measure the gauge pressure along the 38 injection pipe. The real-time pressure monitoring and data collection were accomplished by a Raspberry Pi 3B +. In measuring both the flow rate and pressure values, the experimental errors were considered, and ranges for these two parameters were calculated with the following equations: 𝑝 = 𝑝𝑚 ± 𝑝𝑒 (3.1) 𝑄 = 𝑄𝑚 ± 𝑄𝑒 (3.2) 3.2.2.1 Permeability measurement A centimeter-scale permeameter was used to measure the permeability of the two sand samples at the same moisture content and density conditions as existed in the m-scale injection pipe setup. The potential variability in permeability for both samples from different density conditions (1.4 × 10−3 –1.8 × 10−3 kg/m3) was also assessed. The permeameter consisted of a polycarbonate column manufactured by W.A. Hammond Drierite, with two Bosch Sensortec BMP 280 pressure sensors (relative accuracy of ±12 Pa) used to measure the gauge pressure at the column inlet and outlet (Figure 3-3). Sand at the targeted moisture content was introduced and compacted to the targeted bulk density in regular intervals. The preparation procedure of the materials and the test conditions for permeability inspection can be found in Appendix A and Appendix B , respectively. Air was injected using a Bronkhorst EL-Flow Prestige mass flow controller at flow rates ranging from 0.5 to 8 L/min. From the pressure drop between the inlet and outlet, the permeability of the sand was calculated using the following equation: 39 𝑘 =2𝑄𝜇𝐿𝑝0𝐴(𝑝𝑖𝑛2 − 𝑝𝑜𝑢𝑡2 ) (3.3) where, 𝐴 (= 0.0025 m2) is the cross-sectional area of the column, 𝐿 is the length of the column filled with sand, 𝜇 (= 1.813 × 10−5 Pa. s) is the dynamic viscosity of air, and 𝑄 is the flow rate. 𝑝0 is the ambient pressure, and 𝑝𝑖𝑛 and 𝑝𝑜𝑢𝑡 are the measured pressures (in Pa) at the inlet and outlet of the column, respectively. Three flow rates were used per test, with the average permeability from the three tests being taken as the final value. Figure 3-3. Permeameter setup 3.2.3 3D Model development To model the experiment, using COMSOL Multiphysics 6.1, a 3D model was developed that coupled the fluid flow in Transport-2 and 3 and solved for the pressure distribution simultaneously. The governing equations describing the turbulent flow in the pipe (Transport-2) in terms of the time-averaged and fluctuating components of the velocity field (𝑈𝑖 , 𝑢𝑖′; 𝑖 = 1 − 3) are described in the form of the Reynolds averaged Navier-Stokes equations. For steady-state incompressible flow of Newtonian fluids, this equation can be written as: Pressure sensorsCompacted sandOutletPolycarbonate column Inlet40 𝜌𝑒𝑥ℎ𝑈𝑗𝜕𝑈𝑖𝜕𝑥𝑗=𝜕𝜕𝑥𝑗[−𝑝𝛿𝑖𝑗 + 𝜇𝑒𝑥ℎ (𝜕𝑈𝑗𝜕𝑥𝑖+𝜕𝑈𝑖𝜕𝑥𝑗) − 𝜌𝑒𝑥ℎ𝑢𝑖′𝑢𝑗′̅̅ ̅̅ ̅̅ ] (3.4) where, 𝜌𝑒𝑥ℎ, 𝜇𝑒𝑥ℎ, and 𝑝 denote the density and viscosity of the exhaust gas and associated pressure for the flow of exhaust through the pipe. The Reynolds stress tensor (−𝜌𝑢𝑖′𝑢𝑗′̅̅ ̅̅ ̅̅ ) in this equation indicates the measure of the turbulent fluctuations in the exhaust flow field. The next step was to solve the momentum equation, a critical exercise that required expressing the Reynolds stress tensor in relation to the time-averaged velocity vector components via the integration of a suitable turbulence model. The Algebraic yPlus model—a choice grounded in the well-established framework of Prandtl's mixing-length theory was employed as the turbulence model. This selection offered the advantage of both accuracy and computational efficiency. Notably, the Algebraic yPlus model exhibited robustness in the face of varying mesh sizes, mitigating sensitivity concerns that may arise in other modeling approaches. The investigations conducted here revealed that this model delivered noteworthy reductions in computational overhead, enhancing overall computational expediency, and rendering it a favorable option for this study. On the other hand, the flow in the tailings (porous domain) was governed by the Brinkman–Forchheimer equation, as mentioned in [97, 184]. 𝛻𝑝 = −𝜇𝑒𝑥ℎ𝐾𝑡𝒖 + 𝜇𝑒𝑥ℎ̅̅ ̅̅ ̅̅ 𝛻2𝒖 − 𝑐𝐹𝐾𝑡−12𝜌𝑒𝑥ℎ𝒖|𝒖| (3.5) This equation is composed of three distinct terms, each contributing to the comprehensive description of the fluid flow phenomena within the porous medium. The initial term on the right-hand side embodies Darcy's law, encapsulating the essential relationship between pressure gradient 41 and flow rate. The second term is the Brinkman extension and encompasses the viscous influences operating within the porous medium, further refining the model's fidelity to real-world conditions. Intertwined with these components, the last term encapsulates the Forchheimer extension, an essential inclusion that effectively characterizes the high turbulent flow regime [185]. The effective viscosity at the wall, 𝜇𝑒𝑥ℎ̅̅ ̅̅ ̅̅ signifies a parameter conveniently assumed to be the same as 𝜇𝑒𝑥ℎ, for the sake of modeling simplicity. For the numerical environment considered here (where, 𝑅𝑒𝐾 < 1), the Forchheimer constant (𝑐𝐹) gravitated towards a value of zero (𝑐𝐹 = 0). So that inertial forces were insignificant. 𝑘𝑡 denotes the permeability of the tailings. The finite element analysis was used to solve Equations (3.4) and (3.5) concurrently for the flow of a fluid in a perforated pipe separated by a thin interface (pipe wall) from a porous medium. The geometry of the domain and the boundary conditions implemented in the FE simulations are shown in Figure 3-4. The symmetry of the model allows the simulations to run over a quarter of the geometry. At the outer boundary of the geometry (𝑟 = 𝑟𝑜𝑢𝑡), the pore pressure is set to the ambient pressure (𝑝 = 𝑝0). Continuity conditions were satisfied at the surface of the pipe where the perforations are located, and the Dirichlet boundary condition is assigned at the fluid-pipe interface. The thickness of the pipe was much smaller than the entire geometry and was therefore neglected in the simulations. A mesh independence analysis was carried out to ensure that the numerical results were independent of the mesh configuration. 42 Figure 3-4. The geometry and the boundary conditions implemented in the 3D FE simulations. 3.2.4 (1+1)D Model development To identify the most suitable injection design scenario, it will be necessary to perform a series of simulations. The 3D model developed in this study demands significant computational resources and time for operation. Conversely, conducting experiments for each design iteration entails high costs and time consumption. Therefore, it is imperative to establish a dependable model that can provide accuracy comparable to the 3D models and can be validated against experimental results. Subsequently, to attain the necessary acceleration in modeling iterations, a (1+1)D numerical model was proposed that could simulate the experimental results and match the 3D model results. The developed model carries forward the calculations for the flow field iteratively through the direction of the flow (along the pipe) and concurrently towards the direction of injection (to the porous media). Therefore, the model is referred to as the (1+1)D model. 43 The model divides the entire length of the pipe (𝐿) into 𝑛𝑧 sections of equal length [s𝑖 =𝑠𝑧 (𝑖 = 1, 2, … , 𝑛)], with each section receiving inputs from the previous one. 𝑠𝑧 is the center-to-center distance between the perforations in the longitudinal direction and is considered as the smallest unit of discretization along a pipe of length 𝐿(= 𝑛𝑧𝑠𝑧). The discretization used in the (1+1)D ROM is shown in Figure 3-5. 𝑄𝑖 is the amount of exhaust transported through the inflow into the 𝑖th section; Δ𝑄𝑖 is the amount of exhaust injected into the tailings from that perforated section; and 𝑄𝑖+1 is the outflow transported from the 𝑖th section to the following section. Figure 3-5. The (1+1)D model development for perforated injection pipes embedded in a porous medium. In Transport-2, the friction between the pipe wall and the flue gas is active along each section. The Darcy-Weisbach equation [186] is used to estimate the contributions of frictional pressure losses (Δ𝑝𝑑𝑖) to TPL from each section: 44 Δ𝑝𝑑𝑖 = − 𝑠𝑧 (𝜌𝑒𝑥ℎ2𝑑ℎ) (𝑄𝑖𝐴𝑖𝑛)2𝜆𝑖 (3.6) In this equation, 𝑑ℎ is the hydraulic diameter of the pipe, which is equal to the diameter of a circular pipe; 𝜆𝑖 is the Darcy-Weisbach friction coefficient [186] corresponding to the 𝑖th section, which in the case of turbulent flow is given as: 𝜆𝑖 = 0.0055(1 + (2 × 104𝛿2𝑟𝑖𝑛+106𝑅𝑒𝑖)13) (3.7) which for laminar flow can be written as: 𝜆𝑖 = 64𝑅𝑒𝑖 (3.8) where, 𝛿 is the absolute roughness of the pipe; 𝑟𝑖𝑛 is the inner radius of the injection pipe; 𝐴𝑖𝑛(= 𝜋𝑟𝑖𝑛2 ) is the cross-sectional area of the pipe inlet; and 𝑅𝑒𝑖(= (2𝑟𝑖𝑛𝜌𝑒𝑥ℎ𝑄𝑖) (𝜇𝑒𝑥ℎ𝐴𝑖𝑛⁄ )) is the Reynolds number for the 𝑖th section. For Transport-3, the perforations drilled on the surface of the injection pipe were numerous enough to guarantee a smooth distribution of flow from the peripheral surface of the pipe. Note that this assumption does not necessarily result in a consistent outflow into the porous medium, as the outflow at each section depends on the local pressure difference between the inside and outside of the pipe, along with the permeability of the surrounding porous medium. In the current configuration, the flue gas injected into the tailings surrounding the injection pipe is in the laminar flow regime (viscous force dominated), and the inclusion of the Brinkman Equation becomes valid. 45 The injection of exhaust into the porous medium through the section has been calculated by adapting Darcy's law for radial coordinates in the following equation [187]: ∆𝑄𝑖 =(𝑝𝑔𝑖 − Δ𝑝𝑑𝑖 2⁄ )𝑠𝑧𝛼 (3.9) Here, α depends on the perforation arrangement applied to the injection pipe and its impact on the pressure profile through the pipe. When the impact of the perforations is negligible, the following equation can be applied: 𝛼 =𝜇𝑒𝑥ℎ4𝑘𝑡{2𝜋𝑙𝑛 (𝑟𝑜𝑢𝑡𝑑ℎ)} (3.10) In this equation, 𝑝𝑔𝑖 is the gauge pressure in the 𝑖th section that is estimated from the (1+1)D model to overcome the coupled TPL and IPL. When the perforation arrangement of the injection pipe impacts the pressure profile, α must be determined in one of two ways. The first method is to use the results from the 3D FE model as an input for the (1+1)D model as shown in the following equation: 𝛼 =𝑝′𝐿𝑄 (3.11) where 𝑝′ is the pressure at the mid-perforation, which was obtained from the 3D FE simulations developed in section 3.2.3. 46 The second method is to determine the value of 𝑝′ by correlating the value of a parameter, termed the 𝑚-factor, to different perforation arrangements. This method would enable the (1+1)D model to operate independently of the 3D FE model and is accomplished through the following process. The perforation arrangement affects the pressure profile because it can cause non-uniform flow patterns as the gas first enters the porous medium (see Figure 3-6). This region (also denoted as Region 1 or the transition zone) extends to approximately ~𝑠 2⁄ within the porous domain for all perforation arrangements and corresponds to significant pressure drops following injection of the fluid into the tailings. In this case, the center-to-center spacings are equal (𝑠𝑧 = 𝑠𝑐 = 𝑠). Further within the porous domain, the flow is more uniform, and this is denoted as Region 2 or the smooth zone. The transition zone occupies the domain defined by 𝑟𝑖𝑛 ≤ 𝑟 ≤ 𝑟𝑖𝑛𝑡(= 𝑟𝑖𝑛 + 𝑠 2⁄ ), and the smooth zone occupies the region where 𝑟𝑖𝑛𝑡 ≤ 𝑟 ≤ 𝑟𝑜𝑢𝑡. The following representation for the radial velocity accounts for the abrupt change in the pressure profile of Region 1: 𝑢𝑟(1)(𝑟) =𝑄2𝜋𝑟𝐿+ [𝑄𝐴𝑝−𝑄2𝜋𝑟𝐿] [1 − (𝑟 − 𝑟𝑖𝑛𝑠/2)𝑚]+ 𝑚 [𝑄𝐴𝑝−𝑄2𝜋𝑟𝑖𝑛𝑡𝐿] (𝑟 − 𝑟𝑖𝑛𝑠/2) (𝑟 − 𝑟𝑖𝑛𝑠/2− 1) ; 𝑟𝑖𝑛 ≤ 𝑟 ≤ 𝑟𝑖𝑛𝑡 (3.12) For Region 2, it takes the following form: 𝑢𝑟(2)(𝑟) =𝑄2𝜋𝑟𝐿 ; 𝑟𝑖𝑛𝑡 ≤ 𝑟 ≤ 𝑟𝑜𝑢𝑡 (3.13) 47 In Equation (3.12), 𝐴𝑝(= 𝜋𝑛𝑐𝑛𝑧𝑟𝑝2) is the total area of the perforations; 𝑛𝑐 is the number of perforations on the circumference of the pipe; 𝑛𝑧 is the number of perforations along the length of the pipe, and 𝑟𝑝 is the radius of the perforations. Figure 3-6. Visual representation of the transition and smooth zone for gas flow into the porous medium. Equation (3.12) is a power function, and 𝑚 (𝑚-factor) is a value that is dependent on the geometry of the perforations and the specific operating parameters. Equations (3.12) and (3.13) account for the continuity of flow variables (𝑝 and 𝑢𝑟) and their derivatives at the interface of the two regions (𝑟 = 𝑟𝑖𝑛𝑡). Here, the effect of the tangential and axial velocities (due to the presence of perforations) on the pressure loss in the porous medium is accounted for by only one velocity component, as characterized in Equation (3.12). By substituting Equations (3.12) and (3.13) separately in Equation (3.5) and integrating with respect to 𝑟, one can find a closed-form relation for pressure in regions 1 and 2, respectively. By solving Equation (3.5) for 𝑚 and making it equal to the mid-perforation pressure obtained from the 3D FE solution for different perforation arrangements, one can correlate the value of 𝑚 with other non-dimensional variables that describe Region 1 (Transition zone)Region 2(Smooth zone)Injection pipePorous medium48 the perforation arrangement and geometry of the design. Later in the study, after making the 𝑚-factor an independent variable, it was introduced to the (1+1)D model as an input to describe the transport characteristics of the fluid into the porous domain from the perforated pipe. Transport-2, and 3 can now be considered together, as these processes are interrelated. Due to the momentum loss from the outflow through the perforations, pressure recovery (rise) occurs from one end of the perforation to the other. As the outflow contains the lower energy fluid from the boundary layer compared to the flow in the middle of the pipe, a pressure rise co-occurs with the friction effect [168]. The following equation [173] has been employed to compute the pressure recovery (Δ𝑝𝑟𝑖) for each pipe section: Δ𝑝𝑟𝑖 = 𝑘𝑖′𝜌𝑒𝑥ℎ(𝑣𝑖2 − 𝑣𝑖+12 ) (3.14) In this equation, 𝑘𝑖′ is the momentum recovery factor that depends on the inflow and outflow velocities of the 𝑖th section (see Figure 5) and is computed in each section by using the following equation [188]: 𝑘𝑖′ = 𝜉 + 𝜒 (𝑣𝑖2 − 𝑣𝑖+12𝑣𝑖2 ) (3.15) The values of 𝜉 and 𝜒 depend on the pipe length to the pipe diameter ratio and have been iterated for each section [188]. Finally, for the (𝑖 + 1)th section, we have: 𝑄𝑖+1 = 𝑄𝑖 − Δ𝑄𝑖 (3.16) 𝑝𝑔𝑖+1 = Δ𝑝𝑑𝑖 + Δ𝑝𝑟𝑖 (3.17) 49 3.3 Results and Discussion 3.3.1 Validation of the numerical models 3.3.1.1 Experimental results Figure 3-7 shows the gauge pressures along the injection pipe for duplicate tests of air injection at three flow rates per sand sample. The results include errors from the sensitivity of the pressure sensors and the flow controller. Measured gauge pressures were consistent with each other along the length of the pipe and were consistent between replicate experiments. Figure 3-7. Comparison between the gauge pressure profiles in the injection pipe from the experimental and numerical results. (The square and diamond-shaped markers represent the results from experimental tests 1 and 2, respectively. Distinct colors distinguish the different flow rates used for the CS and FS. The solid and the dash lines indicate the results obtained from the (1+1)D and the 3D FE results.) 02550751001251501752002252502753000.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00Gauge pressure inside the perforated pipe (Pa)Distance from the inlet, z (m)70 L/min 85 L/min 100 L/min100 L/min 110 L/min 120 L/minFine Sand ( m2)Coarse Sand ( m2)50 The FS having a lower permeability recorded the highest gauge pressures, yielding average pressures of 227, 196, and 153 Pa for injection rates of 100, 85, and 70 L/min, respectively. The CS yielded pressures of 40, 37, and 33 Pa with respective injection rates of 120, 110, and 100 L/min. The measured permeabilities of the CS and FS at the physical conditions of the m-scale experiments were 3.2 × 10−10 m2 and 4.8 × 10−11 m2, respectively. Coarse-grained materials yield larger pores, which enable fluid transport compared to the small pore spaces of finer-grained materials. It was recognized that despite best efforts, the permeability of the sand within the m-scale apparatus would be heterogeneous and not accurately represented by the cm-scale permeameter measurement. The variability of the permeability of the sand at different degrees of compaction resulted in a range of permeability values, as shown in Figure 3-8. Figure 3-8. Comparison between the measured permeability range of the sand samples and the predicted permeability range from the (1+1)D model results. Permeability, kt(m2)Flowrate, Q (L/min)Coarse Sand -Test 1 Coarse Sand -Test 2 Fine Sand -Test 1 Fine Sand -Test 2Permeability test range(Coarse Sand)Higher compactionLower compactionPermeability test range (Fine Sand)Higher compactionLower compaction10−910−1010−1170 85 100 110 12051 The CS’s permeability was as high as 3.8 × 10−10 m2 when loosely compacted and as low as 1.3 × 10−10 m2 when densely compacted. Likewise, the FS varied from 1.3 to 5.8 × 10−11 m2. 3.3.1.2 Comparison of the experimental and numerical results The experimental gauge pressure measurements along the pipe were compared with results from the 3D FE and the (1+1)D model simulations using the sand’s permeability and injected flow rates (shown in Figure 3-7). For all the experiments, the results obtained from both the 3D and (1+1)D numerical models achieved an acceptable agreement with the experimental findings. Both models produced near identical gauge pressures that were uniform along the length of the injection pipe. The average difference between the experimental and numerical results was less than 6%, validating the developed numerical models for further use. However, a few individual experimental gauge pressure values at different points along the injection pipe were inconsistent with the modeling results (for example, see S2 in the FS at 100 L/min during test 1). This could be due to heterogeneous compaction, which promotes the potential for having a nonuniform permeability inside the cylinder, whereas the (1+1)D and 3D numerical models use a uniform permeability as the input. To determine whether the variability in the sand permeability (permeability test range in Figure 3-8) could account for the individual sensors not matching the numerical model results, the pressure data from all sensors were used as an input for the (1+1)D model to back-calculate the permeability that would cause the observed gauge pressures. This process resulted in two permeability ranges, from the minimum to the maximum, from the eight sensor values for each 52 test. Figure 3-8 shows the numerical model values compared to the ranges derived from the centimeter-scale permeameter tests. The calculated permeability ranges derived from the numerical model for each flow rate are nearly identical for both the FS and CS. Furthermore, these ranges fit well within the measured permeability ranges for the FS. However, for each flow rate in the CS, the error bar on the calculated permeability ranges from the numerical model are slightly higher than the measured permeability range. However, the calculated permeability value itself is within the measured range. Therefore, the variability seen in the experimental results can be accounted for by the heterogeneity of the sand permeability. This validates the ability of the (1+1)D numerical model to estimate the outflow from an injection pipe into a porous medium. 3.3.2 Progression of the (1+1)D reduced-order model Following the validation of both the 3D Finite Element (FE) and (1+1)D models, the aim was to make the (1+1)D model independent. The relationship between the perforation arrangement on the injection pipe and the pressure profile was determined from the 3D FE model and used to define the 𝑚-factor for the (1+1)D model. Using the 3D FE model, the relationship between the perforation arrangement and the 𝑚-factor was determined and analyzed to understand which design parameters impact the 𝑚-factor. With the 𝑚-factor value related to design parameters, the (1+1)D model can be used independently without requiring the operation of the 3D FE model. Note that for all 3D FE simulations, the center-to-center distance of the perforations were equal along the circumference and axial direction of the pipe (𝑠𝑧 = 𝑠𝑐 = 𝑠). 53 3.3.2.1 Impact of design parameters on the 𝒎-factor Five parameters were identified as potentially having a significant role on the value of the 𝑚-factor. The effects of these parameters on the value of the 𝑚-factor were studied by varying each while holding the others constant. A visual presentation of the cases studied in this investigation is shown in Figure 3-9. These parameters, and the degree to which they were varied, were: the permeability (𝑘; 10−9 – 10−12 m2), inlet flow rate (𝑄; 25 – 300 L/min), perforation arrangement (including the number of perforations (𝑛𝑐; 4 – 10 or 𝑛𝑧; 44 – 110), the perforated area ratio of the pipe (𝐴𝑟; 10 – 60%), and the ratio of the thickness of the porous domain to the injection pipe diameter (𝑟𝑟; 1 – 30). Note that when the perforation density increased while the total perforated area was kept the same, the size of the perforation (𝑟𝑝) was reduced. The parameter range was chosen based on typical tailings permeabilities, physical constraints from the size of the system, and by considerations of what was physically possible. 54 Figure 3-9. Visual representation of the cases studied: (a) variation in the perforation arrangement for a constant perforation ratio; (b) variation in the perforation ratio for a fixed perforation arrangement; and (c) cross-section of the system and the definition of 𝒓𝒓. The default values for each parameter were chosen such that the permeability was equal to 4.8 × 10−11 m2, the inlet flow rate was 100 L/min, the perforation arrangement had 4 Porous mediumPerforatedpipe(a) (b)(c)55 perforations around the circumference (𝑛𝑐 = 4), and 44 perforations along the axial length of the pipe (𝑛𝑧 = 44), the radius of the perforations resulted in 30% of the pipe surface being perforated (𝐴𝑟 = 0.3), and the ratio of the porous domain thickness to the injection pipe diameter was five (𝑟𝑟 = 5). Figure 3-10 shows the results from the 3D FE model for the required 𝑚-factor to be used as an input for the (1+1)D model. The 𝑚-factor was found unaffected by the change in the permeability of the porous media or by the change in the injection flow rate when larger than 50 L/min. Cases above 50 L/min were related to transitional and turbulent flow regimes through the pipe, with Reynold’s numbers larger than 2000 and 4000, respectively. The results showed a slightly higher 𝑚-factor for the lower flow rate of 25 L/min where the transition zone is in the laminar flow regime. The 𝑚-factor was affected by changes in the perforation arrangement, perforation area, and thickness of the porous domain. The trend for the perforation arrangement and the porous domain thickness was that the 𝑚-factor decreased as each of these parameters increased. For the perforated area, the 𝑚-factor reaches a maximum value at 20% and gradually decreases as the perforation ratio of the pipe increases further. Values below 20% result in 𝑚-factors only slightly lower than the local maximum. 56 Figure 3-10. Effect on the m-factor from changes in the: (a) permeability, (b) inlet flow rate, (c) perforation arrangement, (d) injection pipe perforated area, and (e) thickness of the porous domain. 3.3.2.2 Establishing correlations between Design Parameters and 𝒎-factor From the 3D FE simulations, the value of the 𝑚-factor was found to be dependent on the perforation arrangement of the injection pipe [𝑠, and (𝑛𝑐 or 𝑛𝑧)], the ratio of the perforated area to 0.220.240.260.28m-factorPermeability, k (m2)(a)10−1210−1110−1010−090.220.240.260.280 50 100 150 200 250 300m-factorInlet flowrate, Q (L/min)(b)LaminarTransitionalTurbulentk = m2(or )Ar = 0.30rr = 50.000.100.200.300.05 0.20 0.35 0.50 0.65m-factorPerforated area ratio, Ar(d)Q = 100 L/mink = m2(or )rr = 50.220.240.260.28m-factorPerforation scheme(c)Q = 100 L/mink = m2Ar = 0.30rr = 50.000.100.200.300 10 20 30m-factorRatio of porous domain to injection pipe, rr(e)Q = 100 L/mink = m2(or )Ar = 0.30Q = L/min(or )Ar = 0.30rr = 557 the total surface area of the pipe (𝐴𝑟), and the ratio of the porous domain to the size of the injection pipe (𝑟𝑟). To independently relate the 𝑚-factor value to the design parameters, two of these variables were combined into a dimensionless number, 𝛽, the ratio of the total perforated area (𝐴𝑝) to the area of the cylindrical surface confining the transition zone (𝛽 = 𝐴𝑝 2𝜋𝑟𝑖𝑛𝑡𝐿⁄ ). The 𝑚-factor was then correlated with 𝛽 and 𝑟𝑟 using the 3D FE model. To accomplish that, four different perforation schemes were used: [𝑛𝑐 = 4 (or 𝑛𝑧 = 44), 𝑛𝑐 = 6 (or 𝑛𝑧 = 66), 𝑛𝑐 = 8 (or 𝑛𝑧 = 88), and 𝑛𝑐 = 10 (or 𝑛𝑧 = 110)]. For each of these arrangements, different perforation ratios (𝐴𝑟 =0.1, 0.2, … 0.6) and porous domain thicknesses (𝑟𝑟 = 1, 5, 10, 15, … 30) were considered. In total, one hundred sixty-eight design scenarios were used with various values for 𝛽 and 𝑟𝑟. The 3D Fe model was adapted for each of those scenarios. For every value of 𝑟𝑟, twenty-four values of 𝑚-factor were plotted against the associated values of 𝛽. To approximate a smooth curve through all the values of 𝑚-factor at a specific value of 𝑟𝑟, the B-Spline interpolation of 𝛽 versus the 𝑚-factor was conducted. For different porous domain thicknesses, the values of m-factor against 𝛽 are shown in Figure 3-11. These results indicate that for all values of 𝛽 greater than 0.15, the 𝑚-factor decreases with an increase in 𝑟𝑟. For values less than 0.15, the 𝑚-factor only decreases slightly. This indicates that with an increase in the size of the porous domain compared to the injection pipe diameter, the impact of the perforations on the pressure profile diminishes as the value of m goes to zero. For all values of 𝑟𝑟, the maximum 𝑚-factor value occurs when 𝛽 is between 0.1 and 0.2. Necessary boundary conditions have been incorporated from the input parameters to Figure 3-11 based on what is physically and economically feasible (𝑟𝑟 𝑚𝑖𝑛= 1; 𝛽𝑚𝑖𝑛 = 0.067 and 𝛽𝑚𝑎𝑥 =58 0.59). The effect of the 𝑚-factor on the pressure profile of an injection pipe becomes negligible for values less than 0.05. This implies that in the lower bound of the graph, the velocity of the flow in the entire porous domain is analogous to the velocity profile represented by Equation (3.13). Figure 3-11. Range of m-factor for different porous domain thicknesses and injection pipe perforation schemes. Using this graph to determine the 𝑚-factor as an input for the (1+1)D ROM decouples this model from the 3D FE model, resulting in noteworthy savings in computational resources and time. To quantify the savings in computational resources and time, an example can be illustrated further. The 1-meter long 3D numerical model, discussed in section 3.3.1 had 6,831,881 elements, and an average mesh quality of 0.67. Using a computer with 10 cores, 32 gigabytes of memory, and a processing speed of 1.6 GHz, solving this model took approximately 8.5 hours. In contrast, employing the (1+1)D ROM developed in this study, the same model can be solved in under 5 minutes, representing a reduction of ~99% in computational time. 0.000.050.100.150.200.250.300.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65m-factorβ = 1 = 5 = 10 = 15 = 20 = 25 = 30rrrrrrrrrrrrrrNegligible effect of m-factor (perforations)Nonviable (too small) perforationsPhysically impractical design(compromised pipe strength) Minimum feasible value of rr59 It is also imperative to underscore that real-world designs often encompass lengths spanning hundreds of meters. Attempting to analyze such expansive designs utilizing 3D numerical methods would be impractical, if not entirely unfeasible. 3.3.3 Performance evaluation of the (1+1)D ROM As the (1+1)D model became independent of the 3D FE models by establishing the relationship between the 𝑚-factor and the porous domain thickness and perforation arrangement, the performance of the (1+1)D model was compared with the results obtained from the 3D FE model. For this analysis, three parameters were selected upon which to evaluate the model results: the pressure at the injection pipe inlet (𝑝𝑖𝑛), the pressure throughout the injection pipe, and the outflow distribution throughout the injection pipe. 3.3.3.1 Inlet pressure The pressure at the inlet of the injection pipe is a critical parameter that will be used to determine the power and energy requirements to inject the gas, which will impact the capital cost required for the pressurization equipment. Again, the permeability, inlet flow rate, perforation arrangements, perforated area of the pipe, and the ratio of the porous domain thickness to the injection pipe diameter, were all varied in the analyses. Figure 3-12 shows the inlet pressures obtained from the (1+1)D ROM and 3D FE numerical models. 60 Figure 3-12. Comparison of inlet pressures obtained from the 3D FE and the (1+1)D numerical model at different operating variables: (a) permeability; (b) inlet flow rate; (c) perforation arrangement; (d) perforation ratio; and (e) size of the porous domain. (The blue diamond and red square shaped markers represent the 3D FE and (1+1)D results, respectively.) For each case, the inlet pressure estimated by the (1+1)D model is nearly identical to the results of the 3D FE model but utilizing considerably less resources and time. The most variability occurs 020040060080010 85 160 235 310Inlet pressure (Pa)Flowrate, Q (lpm)(b)1501802102402703000.05 0.15 0.25 0.35 0.45 0.55 0.65Inlet pressure (Pa)Perforated area ratio, Ar(d)1101001,00010,000Inlet pressure (Pa)Permeability, k (m2)(a)10−1210−1110−1010−09185190195200205210Inlet pressure (Pa)Perforation scheme(c)0751502253003754500 5 10 15 20 25 30Inlet pressure (Pa)Ratio of porous domain to injection pipe, rr(e)Q = 100 L/min(or )Ar = 0.30= 5k = m2(or )Ar = 0.30= 5Q = 100 L/mink = m2(or )= 5Q = 100 L/mink = m2(or )Ar = 0.30Q = 100 L/mink = m2Ar = 0.30= 5161 when the perforation density is changed; however, the difference is still minor. The inlet pressure increases with lower permeabilities, higher injection rates and greater porous domain thicknesses. Permeability exerts a linear control on the injection pressure and has the largest impact relative to other factors. Likewise, the injection rate increases linearly with the injection pressure, while for the porous domain thickness, the injection pressure levels off as the porous domain size increases. Additionally, the inlet pressure decreases as the perforation density and perforation area increase. Both these factors appear to reach an asymptote implying the largest impact is seen within the investigated parameter range. 3.3.3.2 Pressure profile throughout the injection pipe The (1+1)D model can estimate the pressure along the injection pipe by considering the concurrent effects of friction, momentum recovery, and the injection of gas through the perforations. The profile of the flue gas pressure is crucial for an optimum design to ensure uniform exposure of the porous medium to CO2. A comparison is made between the pressure profile along the pipe obtained from the (1+1)D model and the 3D FE results in Figure 3-13. For this analysis, a minimum and maximum value were analyzed for each parameter. The results for the pressure profile obtained from the (1+1)D model are in excellent agreement with the 3D FE results for all the cases studied. The pressure distribution through the pipe is largely consistent regardless of the permeability, injection rate and porous domain thickness. With increases in the perforation density and area, the pressure becomes higher the further from the injection point. 62 Figure 3-13. Comparison of the pressure profile along the injection pipe obtained from the 3D FE and (1+1)D numerical models at different operating variables: (a) permeability, (b) inlet flow rate, (c) perforation arrangement, (d) perforation ratio, and (e) size of the porous domain. (The diamond-shaped markers and dashed lines represent the 3D FE and (1+1)D results, respectively.) 101001,0000 0.15 0.3 0.45 0.6 0.75 0.9 1.05Pressure through pipe (Pa)Distance from pipe inlet, z (m)(b)1801851901952002052100 0.15 0.3 0.45 0.6 0.75 0.9 1.05Pressure through pipe (Pa)Distance from pipe inlet, z (m)(c)1401702002302602903200 0.15 0.3 0.45 0.6 0.75 0.9 1.05Pressure through pipe (Pa)Distance from pipe inlet, z (m)(d)0501001502002503003504000 0.15 0.3 0.45 0.6 0.75 0.9 1.05Pressure through pipe (Pa)Distance from pipe inlet, z (m)(e)1101001,00010,0000 0.15 0.3 0.45 0.6 0.75 0.9 1.05Injection pipe Distance from pipe inlet, z (m)(a)Q = 100 L/mink = m2(or )= 5Q = 100 L/mink = m2(or )Ar = 0.30k m2Q = 100 L/min(or )Ar = 0.30= 5k = m2(or )Ar = 0.30= 5Q L/minQ L/minncncQ = 100 L/mink = m2Ar = 0.30= 5ArArrrrrk m2Injection pipe pressure profile (Pa)Injection pipe pressure profile (Pa)Injection pipe pressure profile (Pa)Injection pipe pressure profile (Pa)Injection pipe pressure profile (Pa)163 3.3.3.3 Outflow distribution A uniform outflow from the injection pipe allows for carbon sequestration to occur throughout the entire tailings block in a consistent manner. The outflow for the same design parameters as the pressure profile cases were analyzed. The length of the pipe was discretized into a number of sections. For each section, the outflow was calculated (using Equation (3.9)) and shown as a relative value compared to the average outflow over the length of the pipe (Figure 3-14). Ideally, the outflow should remain ~1 throughout the length of the pipe to ensure a homogeneous outflow distribution. The outflow was found to be almost constant throughout the length of the pipe for most of the cases examined in this section. A slight trend can be observed for the highest and lowest permeability values where the outflow increases along the length of the pipe. Additionally, the 3D and (1+1)D model results differ the most here, but by less than 5%. 64 Figure 3-14. Comparison of the outflow distribution obtained from the 3D FE and (1+1)D numerical models under different operating parameters: (a) permeability, (b) inlet flowrate, (c) perforation arrangement, (d) perforation ratio, and (e) size of the porous domain. (The diamond-shaped markers and dashed lines represent the 3D FE and (1+1)D results, respectively.) 0.70.80.91.01.11.21.31.40 0.2 0.4 0.6 0.8 1Outflow z/L(a)0.70.80.91.01.11.21.31.40 0.2 0.4 0.6 0.8 1Outflow z/L(b)0.70.80.91.01.11.21.31.40 0.2 0.4 0.6 0.8 1Outflow z/L(c)0.70.80.91.01.11.21.31.40 0.2 0.4 0.6 0.8 1Outflow z/L(e)0.70.80.91.01.11.21.31.40 0.2 0.4 0.6 0.8 1Outflow z/L(d)Q = 100 L/mink = m2(or )= 5Q = 100 L/mink = m2(or )Ar = 0.30k m2Q = 100 L/min(or )Ar = 0.30= 5k = m2(or )Ar = 0.30= 5Q L/minQ L/minncncQ = 100 L/mink = m2Ar = 0.30= 5ArArrrrrk m265 3.3.4 Application of the (1+1)D ROM to an optimal design Having shown that the (1+1)D and 3D model results match for the inlet pressure, the pressure profile, and the outflow distribution, the developed (1+1)D model is, therefore, reliable and can be applied to the selection of an optimal design. The ultimate objective of this study was to optimize the pressure profile within the embedded perforated pipes to homogeneously supply flue gas for the carbon to be sequestered by carbonate mineral formation in the tailings. An optimum energy design requires an optimum pressure design. The results for the pressure at the pipe inlet from the 168 design scenarios were tabulated in the form of a heat map, as shown in Figure 3-15. As a reminder, the injection flow rate was 100 L/min, and the permeability of the porous medium was 4.8 × 10−11 m2. Using the model, a similar heat map could be produced for different injection rates or permeabilities. From the heat map, it can be observed that for any perforation arrangement with a certain perforation ratio, the inlet pressure keeps increasing as the porous domain thickness increases. In other words, higher pressures are required for injection into larger porous domains. On the other hand, the inlet pressure starts to decrease with an increase in the perforation surface area for a certain perforation arrangement. For example, the inlet pressure for the case with a 20% perforation area designated as C6-Z66-A20-R1 is 102 Pa. This value drops by 28% to 74 Pa when the perforation area is increased to 50%. Additionally, with the same perforation area, the inlet pressure is lower for denser perforation arrangements. For instance, the inlet pressure for the case designated as C4-Z44-A40-R5 is 193 Pa and decreases by 6% to 182 Pa when a denser perforation arrangement of C10-Z110-A40-R5 is applied. However, it is important to note that these effects are relatively smaller for higher values of 𝐴 and 𝑟𝑟 . From a design perspective seeking 66 to reduce the injection pressure and cost, the major controls are to be found in minimizing the porous domain size and maximizing the perforation area. Additionally, a denser perforation arrangement may have a minor effect on reducing the injection pressures further. Figure 3-15. Heat maps: inlet pressure (in 𝐏𝐚) variation for different perforation arrangements and porous domain sizes. (Red and green color denote the maximum and the minimum values in the range, respectively.) The perforation arrangement has a significant effect on the pressure profile and energy requirements of the injection operation. Figure 3-16 provides the heat map for the difference in the inlet pressure calculation that occurs when the effect of perforations determined by the 𝑚-factor Perforation arrangementPerforated surface area, A (%)Porous domain thickness with respect to the injection pipe size, R1 (R5 (R10 (R15 (R20 (R25 (R30 (C4-Z44()10 181 288 342 375 396 403 40920 121 228 286 320 344 359 37230 98 206 264 300 323 340 35040 85 193 252 288 312 329 33950 77 185 244 280 304 322 33960 73 181 239 275 300 321 339C6-Z66()10 141 249 305 339 362 374 38120 102 210 269 304 329 345 35930 87 195 254 290 315 333 34540 79 187 246 282 307 325 33950 74 182 241 277 302 321 33960 71 179 238 274 300 321 339C8-Z88()10 122 230 287 322 344 359 36720 92 201 260 295 320 338 35330 82 190 249 286 311 329 34240 76 184 244 280 305 324 33950 72 181 240 276 302 321 33960 69 178 237 274 300 321 339C10-Z110()10 110 218 276 311 334 351 35820 87 196 255 291 315 334 34930 79 187 247 282 309 327 34140 74 182 242 278 304 323 33950 71 179 239 275 300 321 33960 69 177 237 274 300 321 33967 was included or excluded. This figure shows when the 𝑚-factor must be included for the modeling results to be reliable in calculating the pressure profile of the perforated injection pipes. Figure 3-16. Heat maps: difference in the inlet pressure calculations with and without considering the effect of the perforation arrangement. (Red and green color denote the maximum and the minimum values in the range, respectively.) The inlet pressure difference decreases as the porous domain thickness, perforated surface area, and perforation arrangement density all increase. For example, in the case of the C6-Z66-A20-R10 configuration, the exclusion of the impact of the perforation could lead to a 16% error (under-designed) in the inlet pressure calculation. This error decreases to 9% when the porous domain Perforation arrangementPerforated surface area, A (%)Porous domain thickness with respect to the injection pipe size, R1 (R5 (R10 (R15 (R20 (R25 (R30 (C4-Z44()10 172% 66% 47% 39% 34% 27% 23%20 82% 32% 23% 19% 17% 14% 11%30 47% 19% 14% 12% 9% 7% 5%40 28% 11% 8% 7% 6% 4% 2%50 16% 7% 5% 4% 3% 2% 2%60 9% 4% 3% 2% 2% 2% 2%C6-Z66()10 112% 44% 31% 26% 22% 18% 14%20 53% 21% 16% 13% 11% 9% 8%30 30% 13% 9% 8% 7% 5% 3%40 18% 8% 6% 5% 4% 3% 2%50 11% 5% 4% 3% 2% 2% 2%60 6% 3% 2% 2% 2% 2% 2%C8-Z88()10 83% 32% 24% 20% 17% 13% 10%20 38% 16% 12% 10% 8% 7% 6%30 23% 10% 7% 6% 5% 4% 3%40 14% 6% 5% 4% 3% 2% 2%50 8% 4% 3% 3% 2% 2% 2%60 4% 3% 2% 2% 2% 2% 2%C10-Z110()10 65% 26% 19% 16% 13% 11% 7%20 31% 13% 9% 8% 7% 6% 5%30 18% 8% 6% 5% 4% 4% 2%40 11% 5% 4% 3% 3% 2% 2%50 6% 4% 3% 2% 2% 2% 2%60 3% 2% 2% 2% 2% 2% 2%68 thickness increases by two and a half times in the C6-Z66-A20-R25 configuration. With a denser perforation scheme such as C6-Z66-A60-R10 or C8-Z88-A40-R25 configuration, this error reduces to 2%. By using both the heat maps given in Figure 3-15 and Figure 3-16, when the inclusion of the 𝑚-factor is needed can be determined, and the required injection pressure can be minimized, guiding toward a cost-effective and efficient design. 3.4 Summary • A 3D FE model and a (1+1)D ROM were developed in this study to assess injection pressures and gas outflow. An experimental investigation was conducted, and the experimental and analytical results were compared to establish the validity of the models. Upon this validation, the effort was made to develop the (1+1)D model as it demanded ~99% lower computational resources and time than the 3D FE model. • A variable called the 𝑚-factor was introduced, and its values were calculated for a wide range of feasible operating and design parameters to correlate the impact of the perforation arrangement on the pressure profile. • The (1+1)D model was compared with the 3D FE model and was found to perform consistently well in estimating the behavior of the gauge pressure through the perforated pipe, the pressure at the pipe inlet, and the outflow through the perforations into the surrounding porous tailings. • Validation of the model with the experimental and FE results established its viability for use in large-scale injection designs. Finally, the developed (1+1)D ROM was employed to 69 establish a strategy for constructing optimum design cases from an energy and pressure perspective. 70 Chapter 4: Cold Climate Impact on Flue Gas Injection into Mine Tailings 4.1 Introduction As mentioned earlier, the mafic or ultramafic mine tailings that are high in Ca and Mg content can react with CO2 and form solid carbonate minerals [12]. This process is natural, and the reaction rate is relatively slow at the surface conditions [41]. Several studies suggested that the carbon removal with the mine waste can be accelerated significantly with the injection of CO2-rich fluids into the tailings [46, 62, 189]. However, the remote mines in the Arctic region face severe freezing weather. On the other hand, the relatively higher-temperature environment also showed a positive influence on the rate of carbonation in mine tailings for different candidate minerals [190-192]. Before the large-scale implementation of diesel exhaust injection in mine tailings for carbon sequestration purpose, it is essential to understand several critical factors comprehensively. These include the flow of the exhaust through the tailings (porous media), the heat transfer mechanisms involved between the exhaust gas and the tailings, and the influence of the weather conditions on the entire process. Adequate understanding of these aspects is crucial to ensure the success and effectiveness of the carbon sequestration initiative. So far, an efficient flue gas injection procedure has been established in Chapter 3 for capturing carbon in dry stack mine tailings. Now, as the diesel exhaust has a higher temperature than the usual sources of carbon (e.g., air), examining the possibility of utilizing the heat in the exhaust to overcome the impact of the harsh weather is a necessary novel step for the large-scale application of carbon sequestration in mine tailings. To the best of the knowledge of the author, no such study has been conducted so far. This chapter of the present study investigated the influence of severe cold climatic conditions of the 71 off-grid mining operations on the tailings block by tracking the amount of frozen body of tailings throughout the year of operation. The freezing would turn the water absorbed in the tailings into ice. Without the presence of adequate liquid water in the tailings, the carbon sequestration process will be hindered [75, 193, 194]. Therefore, the portion of the tailings that went below the freezing temperature was considered inactive for carbon sequestration. The amount of active and inactive zones in mine tailings throughout the year was estimated using the validated numerical models developed here. A series of sensitivity analyses on different parameters were conducted to evaluate the feasibility of continuing carbon sequestration in mine tailings as a year-round operation. Finally, suggestions for mitigating the effects of adverse weather conditions were offered. 4.2 Methodology In the proposed method of carbon sequestration in mine tailings by flue gas injection (described in section 3.2.1), the top surface of the tailings will be directly exposed to the environment and will experience cold climatic conditions of the remote mining operations. In this chapter, one block was selected as the computational domain to estimate the impact of the weather conditions of the remote locations on the continuity of the operation. The simulation was carried out using the finite element solver COMSOL Multiphysics 6.1. Model development started with establishing the computational domain. A single block (2m high and 13.76m wide) along with the perforated pipe (0.1524m diameter) embedded in it, was selected from the bed of tailings (shown in Figure 3-1) as a representation. In this study, computational optimization of the simulation was achieved by utilizing a two-dimensional (2D) representation that specifically encompasses the width and height dimensions of the three-dimensional (3D) 72 rectangular block. Symmetry was applied in the middle of the 2D block to enhance computational efficiency further. The computational field also included the soil below the dry stack filtered tailings. The details of the computational zone for numerical analysis can be found in Figure 4-1. Figure 4-1. Diagrammatic representation of the computational area of the dry stack tailings for carbon sequestration, along with the associated boundary conditions. 4.2.1 Boundary conditions A fixed mass flow rate was integrated over the intel boundary section (pipe surface representation), parallel to the boundary normal, while setting the tangential velocity to zero. A fixed temperature was also specified at the inlet. The top surface of the tailings block was exposed to the weather conditions of a typical remote off-grid mine location. The collected daily average of the temperature and the wind speed data for a typical remote mining operation from [195] were used as inputs to calculate the daily average heat transfer coefficient by using Equations (4.1)-(4.4) (mentioned in [196]). The operating schedule started from the very first day of the year when the temperature of the selected location was above 0°C and continued for 365 days till the following year. SoilExhaust inletSymmetryTailingsOutletExposed to climate 73 ℎ = 𝑁𝑢 × 𝑘𝑎𝑖𝑟𝐿 (4.1) where, ℎ is the convective heat transfer coefficient, and 𝑘𝑎𝑖𝑟 is the thermal conductivity of the air which is dependable on the temperature. 𝑁𝑢 is the Nusselt number representing the ratio of the convective to conductive heat transfer across the top surface of the block [196]. It was calculated by using the following equation. 𝑁𝑢 = (0.037 × 𝑅𝑒𝐿0.8 − 871)𝑃𝑟13 (4.2) where, 𝑅𝑒𝐿 is the Reynolds number, and 𝑃𝑟 is the Prandtl number. 𝑃𝑟 estimates the relationship between momentum transport and thermal transport capacity of the air that was in direct contact with the top surface of the tailings block [197]. These were calculated by using the following equations. 𝑅𝑒𝐿 = 𝜌𝑎𝑖𝑟 × 𝑣𝑎𝑖𝑟 × 𝐿𝜇𝑎𝑖𝑟 (4.3) 𝑃𝑟 = 𝐶𝑝𝑎𝑖𝑟 × 𝜇𝑎𝑖𝑟𝑘𝑎𝑖𝑟 (4.4) where, 𝜌𝑎𝑖𝑟 and 𝜇𝑎𝑖𝑟 are the temperature-dependent density and dynamic viscosity of the air. 𝐶𝑝𝑎𝑖𝑟 is the specific heat of the air. 𝑣𝑎𝑖𝑟 is the daily average wind speed of the location. This calculated heat transfer coefficient along with the external temperature, were used together to apply the daily average convective heat flux on the top surface of the tailings block. The no-slip condition was set, meaning the fluid velocity relative to the wall velocity was zero (𝒖 = 0). The 74 outlets were the pressure outlet where the tangential stress components were set to zero. The shared boundary between the tailings and the soil was considered impermeable for flow but open for heat transfer by setting a lower permeability to the soil than the tailings. As mentioned earlier, symmetry was applied in the middle of the block to make the model computationally more efficient. Like the geometry of the computational domain, the solution outcomes would have mirror symmetry. Vanishing shear stresses, the combination of a Dirichlet condition and a Neumann condition prescribed zero penetration at the symmetry. The no-slip wall condition was applied to the bottom of the soil. 4.2.2 Governing equations As per the theory of the porous media [97, 198], the flow of the exhaust in the tailings and the heat transfer in the systems were modeled. The governing equation for the mass conservation (continuity) was as follows: 𝜕(𝜀𝑡𝜌𝑒𝑥ℎ)𝜕𝑡+ ∇ ∙ (𝜌𝑒𝑥ℎ𝒖) = 0 (4.5) where, 𝜀𝑡 is the porosity or the air volume fraction of the tailings, and 𝜌𝑒𝑥ℎ is the density of the diesel exhaust. As the flow was considered compressible, all the thermal properties of the exhaust were considered temperature dependent. The following equation was used as the governing equation for mass conservation in numerical analysis. 75 𝜌𝑒𝑥ℎ𝜀𝑡{𝜕𝒖𝜕𝑡+ (𝒖 ∙ ∇)𝒖𝜀𝑡}= −∇𝑝 + ∇ ∙ [1𝜀𝑡{𝜇𝑒𝑥ℎ(∇𝒖 + (∇𝒖)𝑻) −23𝜇𝑒𝑥ℎ(∇ ∙ 𝒖)𝑰}] −𝜇𝑒𝑥ℎ𝐾𝑡𝒖+ 𝜌𝑒𝑥ℎ𝑔 + 𝑭 (4.6) where, 𝒖 and 𝜇𝑒𝑥ℎ are the superficial velocity factor and the dynamic viscosity of the exhaust, respectively. 𝑃, 𝑔, and 𝑰 are the pressure, gravitational acceleration, and the identity matrix, respectively. 𝐾𝑡 stands for the permeability of the tailings. The Forchheimer and Ergun drag, termed 𝑭, allowed the additional viscous force that was square of the exhaust velocity in the tailings. However, due to the low velocity of the flow along with the consideration of a homogeneous porous domain, the impact of the Forchheimer and Ergun drag was negligible. For the same reasons, the inertial terms were found to have almost no impact on the simulation results. In the numerical model, a local thermal non-equilibrium scenario was assumed to exist, meaning the energy balances always occurred between phases [18, 97]. In such a scenario, presuming the heat transfer happening between solid and fluid phases, two separate energy equations (one for the solid phase and another for the fluid phase) must be solved numerically. This approach can provide more accuracy in complex heat transfer in porous media. The following equations represent the energy balance between the tailings (solid phase) and the exhaust (fluid phase). 𝜕(𝜀𝑡𝜌𝑒𝑥ℎ𝐶𝑝𝑒𝑥ℎ𝑇𝑒𝑥ℎ)𝜕𝑡+ ∇ ∙ (𝜌𝑒𝑥ℎ𝐶𝑝𝑒𝑥ℎ𝒖𝑇𝑒𝑥ℎ) = ∇ ∙ (𝜀𝑡𝑘𝑒𝑥ℎ∇𝑇) + ℎ𝑒𝑥ℎ𝑡𝑆𝑏(𝑇𝑡 − 𝑇𝑒𝑥ℎ) (4.7) 𝜕[(1 − 𝜀𝑡)𝜌𝑡𝐶𝑝𝑡𝑇𝑡]𝜕𝑡= ∇ ∙ [(1 − 𝜀𝑡)𝑘𝑒𝑥ℎ∇𝑇] + ℎ𝑒𝑥ℎ𝑡𝑆𝑏(𝑇𝑒𝑥ℎ − 𝑇𝑡) (4.8) 76 where, 𝐶𝑝𝑒𝑥ℎ, 𝑇𝑒𝑥ℎ, and 𝑘𝑒𝑥ℎ are the specific heat, temperature, and thermal conductivity of the exhaust, respectively. On the other hand, 𝐶𝑝𝑡, 𝑇𝑡, and 𝑘𝑡 are the specific heat, temperature, and thermal conductivity of the tailings, respectively. Here, 𝑆𝑏 indicates the specific surface area, and ℎ𝑒𝑥ℎ𝑡 represents the corrected interstitial heat transfer coefficient between exhaust and tailings. Based on [97], these crucial parameters were calculated by the following equations. 𝑆𝑏 =6(1 − 𝜀𝑡)𝑑𝑝 (4.9) ℎ𝑒𝑥ℎ𝑡 = 𝑆𝑏ℎ∗ (4.10) 1ℎ∗=𝑑𝑝𝑘𝑒𝑥ℎ𝑁𝑢𝑒𝑥ℎ𝑡+𝑑𝑝𝛽𝑘𝑡 (4.11) 𝑁𝑢𝑒𝑥ℎ𝑡 = (0.255𝜀𝑡)𝑃𝑟1/3𝑅𝑒𝑡2/3 (4.12) Here, 𝑑𝑝 is the particle diameter of the tailings. ℎ∗ is the ancillary convection coefficient, and 𝛽 is the thermal expansion coefficient of the tailings. Considering the tailings bed consisted of spherical particles, 𝛽 = 10 was presumed. 𝑁𝑢𝑒𝑥ℎ𝑡 is the dimensionless fluid-to-solid Nusselt number which is a function of the 𝑑𝑝 based Reynolds number, 𝑅𝑒𝑡, and 𝑃𝑟. Following the relevant research [73, 74, 199] which investigated the potential of utilizing the thermal potential of the diesel exhaust, all the thermo-physical properties for the exhaust were adapted from temperature-dependent properties of air. As the properties governing the heat transfer are similar between the air and the exhaust, it is a common practice to do so for simplification purposes without compromising accuracy. 77 Depending on the characteristics of the feed materials, filtering equipment and dewatering methods, the dry stack filtered tailings can have 15-25% moisture content [92]. The water mass content in tailings will go through a phase change with respect to the temperature change. To include that effect in the analysis, the phase change material module built on the apparent heat capacity approach was added to the numerical model [200, 201]. In this process, instead of adding the latent heat of the water mass content of tailings exactly when the water reaches its phase change temperature (𝑇𝑤𝑝𝑐), it was considered that the phase (𝜃) transformation happened in a specific temperature interval between 𝑇𝑤𝑝𝑐 −Δ𝑇2 and 𝑇𝑤𝑝𝑐 +Δ𝑇2. The Heaviside function [202] was applied for including the transition from phase 1 (𝜃1) to 2 (𝜃2) or vice versa. The specific heat capacity of the tailings, 𝐶𝑝𝑡 is the function of the specific heat capacity of the dry tailings, 𝐶𝑝𝑡𝑎𝑖𝑙𝑖𝑛𝑔𝑠 and the specific heat of the water. 𝐶𝑝𝑤𝑎𝑡𝑒𝑟 absorbed. The variable 𝐶𝑝𝑡 was computed as [201, 203]. 𝐶𝑝𝑡={ (1 −𝑚𝑤) × 𝐶𝑝𝑡𝑎𝑖𝑙𝑖𝑛𝑔𝑠 +𝑚𝑤 × 𝐶𝑝𝑤𝑎𝑡𝑒𝑟𝜃1 𝑇 > 𝑇𝑤𝑝𝑐 +Δ𝑇2(1 − 𝑚𝑤) × 𝐶𝑝𝑡𝑎𝑖𝑙𝑖𝑛𝑔𝑠 +𝑚𝑤 × 𝐶𝑝𝑤𝑎𝑡𝑒𝑟𝑎𝑝𝑝 𝑇𝑤𝑝𝑐 −Δ𝑇2≤ 𝑇 ≤ 𝑇𝑤𝑝𝑐 +Δ𝑇2(1 − 𝑚𝑤) × 𝐶𝑝𝑡𝑎𝑖𝑙𝑖𝑛𝑔𝑠 +𝑚𝑤 × 𝐶𝑝𝑤𝑎𝑡𝑒𝑟𝜃2 𝑇 < 𝑇𝑤𝑝𝑐 −Δ𝑇2 (4.13) where, 𝑚𝑤 represents the water mass or the moisture content of the tailings. 𝐶𝑝𝑤𝑎𝑡𝑒𝑟𝜃1and 𝐶𝑝𝑤𝑎𝑡𝑒𝑟𝜃2are specific heat capacity of water in the liquid and the solid phase, respectively. 𝐶𝑝𝑤𝑎𝑡𝑒𝑟𝑎𝑝𝑝 is the apparent specific heat that occurs during the phase transition temperature interval. It is a function of the latent heat and was computed throughout the simulations using the following equation [203-205]. 78 𝐶𝑝𝑤𝑎𝑡𝑒𝑟𝑎𝑝𝑝 = 𝐶𝑝𝑤𝑎𝑡𝑒𝑟𝜃1{1 − 𝜃(𝑇)} + 𝐶𝑝𝑤𝑎𝑡𝑒𝑟𝜃2 × 𝜃(𝑇) + 𝐿𝑤𝑑𝜃𝑑𝑇 (4.14) where, 𝜃(𝑇) is the temperature-dependent phase transition function mentioned earlier, and 𝐿𝑤 is the latent heat of the water that was considered in the phase transition of the water absorbed in the tailings. 4.2.3 Grid and domain independence Before commencing the simulation, it was imperative to ensure the numerical model was grid independent. To test the grid independence, the comparison was made between fine, finer, extra fine, and extremely fine mesh developed on the COMSOL Multiphysics software. In all these meshing schemes, the sequence was determined by the physics in the interface of the meshing. The number of elements in the domain of the tailings block (shown in Figure 4-1) for fine, finer, extra fine, and extremely fine mesh were 739, 1377, 2463, and 5687, respectively. The average quality of the mesh in the computation domain was, respectively, 0.7837, 0.8029, 0.8076, and 0.8244 for fine, finer, extra fine, and extremely fine mesh. It was found from the analysis that after improving the mesh from fine to finer grade, the change in the simulation results was less than 0.5%. The extra fine mesh was chosen for all the numerical analyses conducted in this study to remain efficient regarding computational resources and time. The soil below the tailings (shown in Figure 4-1) was also included in the numerical analysis to have the impact of it on the heat transfer. As in a practical scenario, the soil would have an infinite domain length below the tailings block, variable domain lengths were considered to replicate that impact. After several iterations, it was seen that a 10m depth of the soil below the tailings block 79 was long enough to include the impact of the soil in the heat transfer analysis. Further increasing the soil depth was found to have no impact on the results. 4.2.4 Model validation To use the developed numerical model for practical use, it was crucial to ensure its outcomes were dependable regarding fluid flow and heat transfer in porous media. To accomplish that, validating the numerical modeling approach developed here with the available experimental studies in heat transfer in the porous domain was necessary. To establish the validity, the numerical model developed here was resized and adjusted to match the experimental setup to store the heat in a packed bed porous medium mentioned in [206, 207]. To assess the efficacy of the numerical model in replicating the fluid flow and heat transfer within the porous media, the functioning parameters of the rescaled numerical system were fine-tuned to correspond with those of the abovementioned pilot-scale thermal energy storage experiment. A comparison was then made between the numerical results and the original experimental data. The temperature distribution and pressure drop throughout the rock bed were scrutinized to verify the heat transfer and fluid flow, respectively. The validation of the temperature distribution is shown in Figure 4-2(a). Here, the temperature of the rocks (solid) and the air (fluid) from the finite element analysis (FEA)-based numerical model developed in this study are represented with the solid and the dashed lines, respectively. The circular markers show the average temperature collected from the experimental tests at different time intervals. The measurements were taken at various distances in the porous domain and presented accordingly. In all the time intervals, the outcomes from the numerical models were 80 found in acceptable agreement with the experimental results for the temperature distributions compared. Figure 4-2. Validation of the developed FEA-based numerical model with the experimental results presented in [206, 207]; (a) temperature distribution at different time intervals; and (b) pressure drop at different operating hours. 0751502253003754505256006750 0.2 0.4 0.6 0.8 1 1.2Temperature ( C)Distance from inlet (m) FEA-Fluid-1200sExperimental-1200sFEA-Solid-1200sFEA-Fluid-1800sExperimental-1800sFEA-Solid-1800sFEA-Fluid-3000sExperimental-3000sFEA-Solid-3000sFEA-Fluid-3600sExperimental-3600sFEA-Solid-3600sFEA-Fluid-4800sExperimental-4800sFEA-Solid-4800sFEA-Fluid-5400sExperimental-5400sFEA-Solid-5400s01020304050607080901001101200 0.5 1 1.5 2 2.5 3 3.5 4Pressure (Pa)Operating hoursExperimentalFEA(b)(a)81 It is essential to mention that the accurate prediction of the pressure drop associated with the fluid flow in the porous media with a numerical model is crucial for its validation and is significantly challenging to achieve. The comparison of the pressure drops across the porous domain between the numerical and the experimental model is shown in Figure 4-2(b), and they were found to be in excellent agreement. The accuracy of the numerical model developed here in predicting the pressure drop and heat transfer in porous media established the validity of the model and made it ready for further investigation. 4.3 Results and Discussions 4.3.1 Base case scenario With the validated numerical model, the investigation started with the base case analysis, for which the key parameters are shown in Table 4-1. These parameters were kept the same throughout the study unless stated otherwise. The selected location for the base case analysis was a remote mine, operating in the Northwest Territories of Canada. Being in proximity to the arctic circle and surrounded by rugged terrain and wilderness, this location experiences an incredibly challenging climate. Figure 4-3(a) shows that the location had 142 continuous days while the daily average temperature was above 0°C. After that, the temperature was below 0°C for the rest of the operating period making the annual average temperature equal to −7.2°C. The maximum and minimum daily average temperature of the location was 21.1°C and −36°C, respectively. The average daily wind speed was 5.4 m/s, with a minimum and maximum value of 3.1 m/s and 7.9 m/s. The high wind speed (shown in Figure 4-3(a)) of the location along with these severe temperature ranges, resulted on average, a very high convective heat transfer coefficient (shown in Figure 4-3(b)) at the top of 82 the tailings block. Such scenarios made the location particularly challenging in terms of utilizing the heat from the exhaust to maintain a favorable condition in the entire block of tailings for carbon sequestration throughout the year. It is necessary to mention again that the above 0°C temperature in the tailings block has been considered a favorable condition. As below 0°C temperature, the water in tailings will be frozen, and the portion of the block below 0°C were considered inactive for carbon sequestration purposes. Table 4-1. Key parameters used in numerical investigations. Parameters Value Density of dry tailings (𝜌𝑡𝑎𝑖𝑙𝑖𝑛𝑔𝑠) 2600 kg/m3 [208] Thermal conductivity of dry tailings (𝑘𝑡𝑎𝑖𝑙𝑖𝑛𝑔𝑠) 2 W/(mK) [209] Specific heat capacity of the dry tailings (𝐶𝑝𝑡𝑎𝑖𝑙𝑖𝑛𝑔𝑠) 989 J/(kgK) [210] Water mass content in tailings (𝑚𝑤) 15% Injection flow rate (𝑄) 9.2 × 10−4 m3/s Air volume fraction of the tailings (𝜀𝑡) 38% [211] Injection temperature 80 °C Permeability of the tailings (𝐾𝑡) 2 × 10−11 m2 Initial temperature of the soil below tailings (𝑡𝑠𝑜𝑖𝑙) 10 °C Phase change temperature interval (Δ𝑇1↔2) 1 °C 83 Figure 4-3. The climatic condition of the base off-grid location of the remote mine; (a) daily average temperature (shown on the left axis) and wind speed of the location (shown on the right axis) (collected from [195]); and (b) ambient air convective heat transfer coefficient at the surface. 2.02.53.03.54.04.55.05.56.06.57.07.58.08.5-40-35-30-25-20-15-10-505101520250 25 50 75 100 125 150 175 200 225 250 275 300 325 350 375Wind speed (m/s)Average daily temperature (ºC)DaysAvg. daily temperature (°C)Avg. Daily Wind Speed (m/s)(a)(b)3.54.04.55.05.56.06.57.07.58.08.59.09.50 25 50 75 100 125 150 175 200 225 250 275 300 325 350 375Daily average convective heat transfer coefficient (W/m2.K)Days84 The temperature distribution in the block was recorded every day and shown as contours for every 25 days in Figure 4-4. There was no sign of freezing for the first 151 days, but by that time, almost 21% of the block had a temperature between 0°C to 5°C. By day 175, nearly 15% of the block had a temperature below 0°C. The percentage of the frozen body in the tailings kept increasing for the rest of the operating period as the average daily temperature was getting harsher. On day 225, almost 55% of the block was frozen, and another 25% was in the 0 − 5°C temperature range. That means more than half of the block could be considered inactive for the carbon sequestration process at that moment. On day 300, only 20% of the block was active for carbon sequestration, having a temperature above 0°C. However, from the contours, it can be seen that after day 275, due to freezing, there was almost no passage left in the block for the exhaust to pass through the next block. Overall, the annualized average of the active (unfrozen) tailings was almost 66%. These analyses, along with other crucial factors, e.g., the reactivity of the tailings, can help in making decisions of continuing the operation year-long or running it only during the favorable weather period. It is important to clarify that the primary objective of this study did not revolve around examining the correlation between temperature and reaction kinetics. Instead, the emphasis lay on assessing the viability of harnessing thermal energy from exhaust gases to mitigate or postpone freezing. Notably, as depicted in Figure 4-4, only a small section of the tailings, particularly near the pipe, exhibited consistently higher temperatures over the operational year. This localized temperature elevation may potentially accelerate carbon mineralization reactions and demand a dedicated exploration as a separate avenue for future investigation. 85 Figure 4-4. Temperature contours of the tailings body throughout the year for base conditions. Before continuing further with the parametric studies, different values for the phase change temperature interval (Δ𝑇1↔2) was investigated. This was conducted as part of the sensitivity Day 25 Day 50Day 75 Day 100Day 125 Day 150Day 175 Day 200Day 225 Day 250Day 275 Day 300Day 325 Day 350Day 365 Temperature ( C)86 analysis to estimate the impact of different ranges of Δ𝑇1↔2 on heat transfer in the system. Also, it helped to investigate the thermal characteristics of the transition. The tested intervals ranged from 0.125°C to 3°C. However, the variance in the phase change temperature interval did not resonate with any significant difference in the simulation results. The rest of the investigation was carried forward with a Δ𝑇1↔2 of 1°C. 4.3.2 Parametric studies 4.3.2.1 Injection flow rate The amount of flue gas injected in mine tailings for carbon sequestration depends on several factors, e.g., the amount of available tailings, the type of tailings, the power demand of the mine, and so on. Among all these factors, the most critical parameter is the sequestration capacity of the tailings. This factor will determine the amount of carbon that can be potentially captured in a certain amount of tailings. The higher reactivity of the tailings will support a higher rate of flue gas injection, depending on its availability. Considering the importance of this factor, the injection flow rate was considered the first for the parametric studies. In this parametric analysis, all but the injection flow rate (𝑄) were kept the same, as mentioned in Table 4-1. The flow rate was reduced by 100 times and increased by 10 times to establish the range of the flow rates to be tested. Here, 5𝑄 flow rate injection means that the tailings that were being used to capture carbon were 5 times more reactive than using the injection flow rate of 𝑄. The target here was to examine the possibility of delaying the freezing or reducing the rate of the freezing with the higher heating content (with higher flow rates). However, for all the flow rates tested, the freezing started on day 152 and kept increasing gradually. The amount (in percentage) 87 of frozen body in the tailings for different injection flow rates are shown in Figure 4-5(a). The higher values of the flow rates performed slightly better in terms of preventing freezing in the block. For instance, on day 250 of the operation, for the flow rate of 0.1𝑄, almost 70% of the block was unavailable for carbon sequestration due to freezing. While for 10𝑄 flow rate, it was around 62%. Figure 4-5. Impact of injection flow rate variance on (a) the amount of frozen tailings body throughout the year, and (b) the annualized average of the frozen and unfrozen amount of tailings body. The annualized averages of the active and inactive amount of tailings for carbon sequestration purposes for different injection flow rates or reactivity capacities of the tailings are displayed in Figure 4-5(b). The assessment showed that the minimum and maximum values for the annualized average of the unfrozen body in tailings were 61% and 68%, respectively, for the lowest and highest rate of the flue gas injection evaluated here. A heat map (green and red colors labeling the lowest and the highest values, respectively) is also presented in Figure 4-5(b) depicting the annualized average of the inactive tailings for different 𝑄. This indicates that even with tailings 0%10%20%30%40%50%60%70%80%90%100%0 30 60 90 120 150 180 210 240 270 300 330 360Frozen tailings bodyDays in operation0.010.10.52.557.510(a)QQQQQQQQ(b)Q = Injection flowrateTemperature< 0°C > 0°C0.01 Q 38.9% 61.1%0.1 Q 35.8% 64.2%0.5 Q 34.2% 65.8%Q 33.7% 66.3%2.5 Q 33.2% 66.8%5 Q 32.6% 67.4%7.5 Q 32.2% 67.8%10 Q 31.7% 68.3%88 that have higher reactivity potential, continuing the operation year-round could be challenging in such harsh weather conditions. 4.3.2.2 Injection temperature Prior to the injection, the diesel exhaust from the generator will go through a DEHR system. Such a system will not only allow the recovery of the heat in the exhaust for other applications but will also establish control over the injection temperature. It was necessary to check the influence of the higher injection temperature of exhaust as a part of the parametric studies. A higher temperature of the exhaust would undoubtedly heat the tailings bed at a higher rate. However, it was also essential to ensure that the temperature in the tailings (especially regions adjacent to the injection pipe) did not reach a temperature at which the absorbed water would risk evaporating. This was avoided to keep a certain amount of liquid water always present in the tailings bed so that the sequestration process could continue uninterrupted. For all these reasons, all the investigations in this study were conducted with an injection temperature of 80°C. However, for impact analysis, 70°C to 120°C was selected as the injection temperature range. The amount (in percentage) of the frozen body in the tailings for different injection temperatures is shown in Figure 4-6(a). Higher injection temperatures performed slightly better than the lower ones, especially in the later days of the operation. For example, on day 270, for the injection temperature of 80°C, there was almost 78% frozen body in the tailings body. This means that only 22% of the bed of tailings was actively available for carbon sequestration. For the injection temperature of 100°C, on the same day of operation, almost 31% of the bed of tailings remained above 0°C and were accessible for carbon sequestration. The assessment, shown in Figure 4-6(b), also displayed that the minimum 89 and the maximum value for the annualized average of the active body in tailings were 65% and 69%, respectively, for the lowest and highest value for the injection temperature of flue gas tested here. A heat map (green and red colors labeling the lowest and the highest values, respectively) is also given in Figure 4-6(b) depicting the annualized average of the inactive tailings for different injection temperatures. The risk of evaporating the water adjacent to the injection pipe with elevated injection temperature outweighed its potential benefits in preventing freezing in the cold climatic conditions in concern. Figure 4-6. Impact of injection temperature variance on (a) the amount of frozen tailings body throughout the year, and (b) the annualized average of the frozen and unfrozen amount of tailings body. 4.3.2.3 Properties of tailings The properties of the tailings that could have an impact on the heat transfer between the exhaust and itself depend on several factors, e.g., mining and processing methods, equipment optimization, ore composition, tailings management strategy, and so on. Three fundamental parameters were selected to analyze the impact of the variance of such properties on the current investigation. They (a) (b)0%10%20%30%40%50%60%70%80%90%0 30 60 90 120 150 180 210 240 270 300 330 360Frozen tailings bodyDays in operation70 °C80 °C100 °C120 °CInjection temperatureTemperature< 0°C > 0°C70 °C 34.6% 65.4%80 °C 33.7% 66.3%100 °C 32.2% 67.8%120 °C 30.9% 68.9%90 were the air volume fraction or the porosity of the tailings (𝜀𝑡), water mass content in the tailings (𝑚𝑤), and the thermal conductivity of the tailings (𝑘𝑡𝑎𝑖𝑙𝑖𝑛𝑔𝑠). A standard range was established for each of these properties, and the base model was altered accordingly to study their influence on the system. Air volume fraction The air volume fraction of the dry stack tailings depends on the compaction, particle size distribution, surface roughness, dewatering techniques, height of the block, and many other factors [211]. As porosity has a direct relation with the surface area and contact points for heat transfer, it was used in this study as a critical input in estimating the interstitial heat transfer coefficient between exhaust and tailings. A wide range of 10% to 50% was selected for 𝜀𝑡 to examine. The amount (in percentage) of the frozen body in the tailings for different 𝜀𝑡 are shown in Figure 4-7(a). The freezing started on days 151 and 158 when the tailings had 50% and 10% air volume fractions, respectively. Higher porosity promoted a higher rate of heat transfer. Hence, the severe weather conditions had a more pronounced and accelerated effect, resulting in quicker freezing when 𝜀𝑡 had a higher value. The evaluation, indicated in Figure 4-7(b), also displayed that the minimum and maximum values for the annualized average of the active body in tailings were 66% and 68%, respectively, for the highest and lowest value of 𝜀𝑡 considered here. This sensitivity analysis showed that though the higher value of 𝜀𝑡 ensured better heat transfer between the tailings and exhaust, it fostered faster heat transfer between the external wind flow and tailings. As the second one was more dominant, the higher air volume fraction of tailings brought comparatively worse outcomes in terms of 91 preventing freezing in the tailings block. A heat map (green and red colors labeling the lowest and the highest values, respectively) is also presented in Figure 4-7(b) depicting the annualized average of the inactive tailings for different values of 𝜀𝑡. Figure 4-7. Impact of air volume fraction of tailings on (a) the amount of frozen tailings body throughout the year, and (b) the annualized average of the frozen and unfrozen amount of tailings body. Water mass content The dewatering technologies available for dry stack tailings all aim at removing water to form a stackable, dry, and stable structure of filtered tailings. Different dewatering techniques followed by other operating constraints result in different amounts of water mass content (𝑚𝑤) in tailings. The quantity of 𝑚𝑤 had a vital role in the heat transfer problem investigated in this study as the latent heat of the water guided the phase change characteristics in the tailings during Δ𝑇1↔2. To inspect the influence, numerical simulations were conducted with a range of 10% to 25%, keeping all the other parameters in Table 4-1 the same. (a) (b)0%10%20%30%40%50%60%70%80%90%0 30 60 90 120 150 180 210 240 270 300 330 360Frozen tailings (%)Days in operation10%20%30%38%50%Air volume fraction of tailingsTemperature< 0°C > 0°C10% 32.2% 67.8%20% 32.7% 67.3%30% 33.3% 66.7%38% 33.7% 66.3%50% 34.4% 65.6%92 The amount (in percentage) of frozen tailings body for different 𝑚𝑤 are shown in Figure 4-8(a). For all the different values of 𝑚𝑤, the freezing started on day 152 of the operation. However, in the later days of the operation, higher values of 𝑚𝑤 performed better in preventing freezing in the tailings block. For example, on day 250, with a 𝑚𝑤 of 10%, only 27% of the block remained available for carbon sequestration. This increased to 43%, with a 𝑚𝑤 of 25%. This happened as with the higher values of 𝑚𝑤, it will require more energy to change the phase of the water absorbed in the tailings due to a more elevated amount of latent heat requirement. Therefore, the freezing happened at a moderately slower pace. Figure 4-8. Impact of the variance of water mass content in tailings on (a) the amount of frozen tailings body throughout the year, and (b) the annualized average of the frozen and unfrozen amount of tailings body. The assessment, depicted in Figure 4-8(b), also displayed that the minimum and the maximum value for the annualized average of the active body in tailings for carbon sequestration were 65% and 70%, respectively, for the lowest and highest value of 𝑚𝑤 tested here. A heat map (green and red colors marking the lowest and the highest values, correspondingly) is also presented in Figure (a) (b)0%10%20%30%40%50%60%70%80%90%0 30 60 90 120 150 180 210 240 270 300 330 360Frozen tailings bodyDays in operation10%15%20%25%Tailings water mass contentTemperature< 0°C > 0°C10% 35.5% 64.5%15% 33.7% 66.3%20% 32.1% 67.9%25% 30.5% 69.5%93 4-8(b) depicting the annualized average of the inactive tailings for different values of water mass content in tailings. Thermal conductivity Porosity, moisture content, particle size, mineralogical compositions, and several other environmental and operational factors determine the value of the thermal conductivity of the tailings (𝑘𝑡𝑎𝑖𝑙𝑖𝑛𝑔𝑠). Thermal conductivity determines how effectively the heat is conducted through the tailings. The higher the value of 𝑘𝑡𝑎𝑖𝑙𝑖𝑛𝑔𝑠, the better the heat transfers. To assess the impact of variance of 𝑘𝑡𝑎𝑖𝑙𝑖𝑛𝑔𝑠 in the present investigations, the base model was adjusted for different tailings thermal conductivity values ranging from 1 W/(mK) to 3 W/(mK). The freezing started on day 151 and 157, respectively, for the lowest and highest value of the 𝑘𝑡𝑎𝑖𝑙𝑖𝑛𝑔𝑠 tested here. It happened because when the external temperature just started to go below 0°C, the heat transfer between the exhaust and the tailings was more dominant than the heat transfer between the tailings and the wind flowing over it. Therefore, higher values of 𝑘𝑡𝑎𝑖𝑙𝑖𝑛𝑔𝑠 allowed to store more heat from the exhaust in the tailings initially, and freezing could be delayed a bit. However, in the later days of the operation, when the temperature outside became even harsher, the heat transfer between the tailings and the wind flowing over it became more influential than the heat transfer between the exhaust and the tailings. Therefore, the amount of frozen body in the tailings was less on the later days of the operation for the lower values of 𝑘𝑡𝑎𝑖𝑙𝑖𝑛𝑔𝑠. For example, on day 300, with a 𝑘𝑡𝑎𝑖𝑙𝑖𝑛𝑔𝑠 of 1 W/(mK), only 28% of the block remained available for carbon sequestration. But this decreased to 18%, when 𝑘𝑡𝑎𝑖𝑙𝑖𝑛𝑔𝑠 increased by three times. The amount (in percentage) of the frozen body in the tailings for different 𝑘𝑡𝑎𝑖𝑙𝑖𝑛𝑔𝑠 are presented in Figure 4-9(a). 94 Figure 4-9. Impact of different thermal conductivities of tailings on (a) the amount of frozen tailings body throughout the year, and (b) the annualized average of the frozen and unfrozen amount of tailings body. The computation results, illustrated in Figure 4-9(b), also showed that the minimum and the maximum value for the annualized average of the active body in tailings for carbon sequestration were 65% and 70%, respectively, for the highest and lowest value of 𝑘𝑡𝑎𝑖𝑙𝑖𝑛𝑔𝑠 tested here. A heat map (green and red colors labeling the lowest and the highest estimates, correspondingly) is also presented in Figure 4-9(b) depicting the annualized average of the inactive tailings for different thermal conductivities of the tailings. 4.3.2.4 Operating conditions Since the effect of operating conditions is pivotal in determining year-round operation feasibility, it was essential to assess the range of variations in these conditions. After careful consideration, three operating conditions were selected for the sensitivity analysis. They were the initial temperature of soil below the tailings block (𝑡𝑠𝑜𝑖𝑙), time in the year for starting the operation and different operating locations or weather conditions. (a) (b)0%10%20%30%40%50%60%70%80%90%0 30 60 90 120 150 180 210 240 270 300 330 360Frozen tailings bodyDays in operations0.50.7511.251.5ktailingsktailingsktailingsktailingsktailings ktailings = 2 (W/m.K)Tailings thermal conductivity(W/m.K)Temperature< 0°C > 0°C1 30.4% 69.6%1.5 32.5% 67.5%2 33.7% 66.3%2.5 34.5% 65.5%3 35.0% 65.0%95 Initial soil temperature The initial soil temperature can depend on several factors, including the elevation, latitude, geographical conditions of the operating location, etc. As it influenced the heat transfer in the tailings block under investigation, the impact of the variance of 𝑡𝑠𝑜𝑖𝑙 was needed to measure. To do so, a wide range starting from −20°C to 20°C was established at an interval of 5°C for 𝑡𝑠𝑜𝑖𝑙. The base model was then modified for each of these values of 𝑡𝑠𝑜𝑖𝑙, and in total, nine numerical simulations were conducted. The amount (in percentage) of the frozen body in the tailings for different values of 𝑡𝑠𝑜𝑖𝑙 is presented in Figure 4-10(a). It was obvious that the lowest values of 𝑡𝑠𝑜𝑖𝑙 performed the worst in preventing or delaying freezing in the tailings block. The freezing was observed from the very first day of the operation for 𝑡𝑠𝑜𝑖𝑙 valued below or equal to −10°C. For 𝑡𝑠𝑜𝑖𝑙 value of −10°C, the freezing stopped after 59 days of operation and did not recur till day 149. For 𝑡𝑠𝑜𝑖𝑙 of −15°C and −20°C, the freezing continued throughout the operation. The freezing could be delayed slightly with the higher soil initialization temperatures. For instance, the freezing started on days 150 and 154, respectively, for 𝑡𝑠𝑜𝑖𝑙 of −5°C and 20°C. At the later stages of the operation, the amount of the frozen body was lower for the simulations with the higher initial temperature for the soil. For example, on day 275, with a 𝑡𝑠𝑜𝑖𝑙 of −15°C, only 14% of the block remained active for carbon sequestration. This increased to 20% and 26%, with an initial soil temperature of 5°C and 15°C, respectively. The estimates, conveyed in Figure 4-10(b), also displayed that the minimum and the maximum value for the annualized average of the active body in tailings for carbon sequestration were 52% and 68%, respectively, for the lowest and the highest value of 𝑡𝑠𝑜𝑖𝑙 examined here. A heat map 96 (green and red colors labeling the lowest and the highest values, correspondingly) is also exhibited in Figure 4-10(b) portraying the annualized average of the inactive tailings for different values of the initial soil temperature. Figure 4-10. Impact of different soil initialization temperatures on (a) the amount of frozen tailings body throughout the year, and (b) the annualized average of the frozen and unfrozen amount of tailings body. (The negative values for the temperatures are shown in parentheses) Starting time of the operation The next operating parameter evaluated here was the starting day of the operation. It has been mentioned earlier that the chosen timeframe started with the first day that had above 0°C average daily temperature and continued for the next 365 days. To assess the influence of the certain starting point, the starting days for each calendar month were pointed out in Figure 4-11(a) (shown with diamond-shaped markers along with the daily average of the temperature and the wind speed). Then the base case was altered, considering each of these twelve months as a starting point of the operation. Here, a periodic climatic condition was adopted. This means that if the operation was (a) (b)0%10%20%30%40%50%60%70%80%90%0 30 60 90 120 150 180 210 240 270 300 330 360Frozen tailings bodyDays in operation20 °C15 °C10 °C5 °C0 °C(5) °C(10) °C(15) °C(20) °CSoil initialization temperatureTemperature< 0 C > 0 C(20) °C 47.8% 52.2%(15) °C 44.0% 56.0%(10) °C 40.8% 59.2%(5) °C 39.0% 61.0%0 °C 35.6% 64.4%5 °C 34.7% 65.3%10 °C 33.7% 66.3%15 °C 32.7% 67.3%20 °C 31.6% 68.4%97 considered to start on the first day of month 3, the first 2 months were added at the end of month 12 to have a complete 365 days of operation cycle. This way, for all 12 numerical simulations conducted here, the minimum, maximum, and mean values of the daily average temperature and wind speed remained the same. All the other constraints were kept the same as mentioned in the base case analysis. Therefore, the only parameter that could impact the outcomes was the simulation initiation time in the calendar year. The amount (in percentage) of the frozen body in the tailings for different initiation points of operation is presented in Figure 4-11(b)-(d). For the numerical simulations initiated on months 1 to 5 and 12, freezing was observed for the very first day of the operations. Starting on months 9, 10, and 11, the freezing started on days 57, 27, and 6, respectively. By commencing the operation on months 6, 7, and 8, the freezing could be avoided for the first 146, 113, and 86 days. The operations started from months 3 to 7 had more than 100 days of operations without any freezing in the entire duration. The operation began on month 6 had the highest 146 days in the total operating span without encountering any freezing. It was followed by months 5 and 4, having, respectively, 141 and 125 days of operation without any freezing in the tailings block. The operation started on month 12 had no day without freezing, and for month 11, there were only 5 days that did not go through any freezing. The assessments results portrayed in Figure 4-11(e) also displayed that the minimum and the maximum value for the annualized average of the active body in tailings for carbon sequestration were 55% and 73%, respectively, for the operations initiated on month 11 and 4. A heat map (green and red colors designating the lowest and highest values, correspondingly) is also exhibited 98 in Figure 4-11(e) depicting the annualized average of the inactive tailings for different starting points in the calendar year for the operation. This detailed analysis suggested that the starting time of the entire operation should be chosen with caution as it could impact the amount of active tailings available for carbon sequestration purposes. Figure 4-11. Impact of different starting times on the carbon sequestration operation: (a) daily average temperature (shown on the left axis) and wind speed of the location (shown on the right axis) (collected from [195]) accompanied by the starting points marked with diamond-shaped black markers; the amount of frozen tailings body throughout the year for starting the operation on month (b) 𝟏 to 𝟒, (c) 𝟓 to 𝟖, (d) 𝟗 to 𝟏𝟐, and (e) the annualized average for the frozen and the amount of tailings body for different starting points. 2.002.503.003.504.004.505.005.506.006.507.007.508.008.50-40-35-30-25-20-15-10-505101520250 30 60 90 120 150 180 210 240 270 300 330 360Wind speed (m/s)Average daily temperature (ºC)DaysAvg. daily temperature (°C)Avg. Daily Wind Speed (m/s)0%20%40%60%80%100%0 30 60 90 120 150 180 210 240 270 300 330 360Frozen tailings (%)Days in operationMonth 1Month 2Month 3Month 40%20%40%60%80%100%0 30 60 90 120 150 180 210 240 270 300 330 360Frozen tailings (%)Days in operationMonth 9Month 10Month 11Month 120%20%40%60%80%100%0 30 60 90 120 150 180 210 240 270 300 330 360Frozen tailings (%)Days in operationMonth 5Month 6Month 7Month 8(a)(c)(b)(d)(e)Seasonal variability: Different starting month of the operations Temperature 1 2 3 4 5 6 7 8 9 10 11 12<0 °C 37.2% 32.1% 27.7% 26.8% 29.5% 34.7% 43.0% 41.9% 43.5% 44.4% 44.7% 42.4%>0 °C 62.8% 67.9% 72.3% 73.2% 70.5% 65.3% 57.0% 58.1% 56.5% 55.6% 55.3% 57.6%99 Locations So far, with all the different parametric and sensitivity analyses, it is clear that the most significant factor that would impact the carbon sequestration in mine tailings through the injection of diesel exhaust at remote locations is the weather conditions. Consequently, it became essential to compare the performance of the system in different climatic conditions. Four new sites in Canada were selected to compare the impact of the weather scenarios with the base case. Location A (Asbestos) was a southern subcentral continental interior in Quebec. Location B (Fort St. James) was a subcentral continental interior in British Columbia. Location D (Raglan) was in the Nunavik region of northern Quebec, amid the subarctic terrain and rugged landscapes along the shores of the north of the Arctic Ocean. Location E (Turnagain) was in the south-central of British Columbia, overlooking the northern shores of the Gulf of Alaska. All the selected sites are shown on a map of Canada in Figure 4-12. 100 Figure 4-12. Geographical locations of the selected places for investigating the impact of different weather conditions on the carbon sequestration in mine tailings through diesel exhaust injection. The daily average data for the temperature and the wind speed were gathered (from [212-215]) for the four new locations (Location A, B, D, and E) and presented here with the base case (Location C) in Figure 4-13(a) and Figure 4-13(b), respectively. Locations C and D had the lowest mean for the daily average temperature recorded as −7.2°C. However, the lowest daily temperature for all these five locations was recorded as −36°C at location C. Location D had 257 days when the average daily temperature was below 0°C, which was the highest among all the location considered here. On the other hand, the highest recorded daily temperature for all these locations was 23.6°C, Location ALocation BLocation CLocation DLocation E101 experienced at location B. However, location A had the maximum of 242 days with a temperature above 0°C, followed by location B with 228 days. Figure 4-13. The climatic condition of different remote locations; (a) daily average temperature, (b) average daily wind speed (collected from [212-215]), and (c) calculated ambient air convective heat transfer coefficient applied on the top surface. Among all the locations, locations B and E were comparatively less windy, having a mean of 3.6 m/s, and 3.7 m/s, respectively, for daily average wind speed. Location D was the windiest having a mean of 5.8 m/s for the average daily wind speed recorded. Using equations 4.1-4.4, the average convective heat transfer coefficients (ℎ) applied on the top surface of the tailings block 0246810120 30 60 90 120 150 180 210 240 270 300 330 360Avg. daily wind speed (m/s)Days in operation-40-30-20-1001020300 30 60 90 120 150 180 210 240 270 300 330 360Avg. daily temperature ( C)Days in operation(a) (b)01234567891011120 30 60 90 120 150 180 210 240 270 300 330 360Daily average convective heat transfer coefficient (W/m2.K)Days in operation(c)Location ALocation ELocation BLocation CLocation D102 were calculated and shown in Figure 4-13(c). Location B and D had the lowest and highest means for ℎ, respectively, 4.7 W/(m2K), and 6.7 W/(m2K). The amount (in percentage) of the frozen body in the tailings for all five locations is presented in Figure 4-14(a). Freezing was first observed at location D on day 102 of operation. For locations C and E, no freezing was observed for the first 152 and 186 days of the operation, respectively. It was location A that had the highest 249 days without freezing, followed by location B with 202 days. On any day of the operation, location A had more active (unfrozen) tailings for carbon sequestration available compared to any other location. Figure 4-14. Impact of different climatic conditions on (a) the amount of frozen tailings body throughout the year, and (b) the annualized average frozen and unfrozen amount of tailings body. The evaluations articulated in Figure 4-14(b) also showed that the minimum and the maximum value for the annualized average of the active body in tailings for carbon sequestration were 64% and 93%, respectively, for the operations initiated at locations D and A. A heat map (green and 0%10%20%30%40%50%60%70%80%90%0 30 60 90 120 150 180 210 240 270 300 330 360Frozen tailings (%)Days in operationAsbestosFort St. JamesGahcho KuéRaglanTurnagain(a) (b)Locati n ALocation EL cation BLocati n CLocation DLocationTemperature< 0°C > 0°CA 7.0% 93.0%B 10.8% 89.2%C 33.7% 66.3%D 36.1% 63.9%E 15.6% 84.4%103 red colors designating the lowest and highest values, correspondingly) is also exhibited in Figure 4-14(b) portraying the annualized average of the inactive tailings for all the weather conditions of different locations investigated here. 4.3.3 Approaches toward minimizing the impact of harsh weather All the parametric studies conducted so far made it clear that in extreme weather conditions, even with the utilization of the heat available in the diesel exhaust, it could be challenging to keep the entire block of the tailings actively available for year-round carbon sequestration. To continue carbon sequestration throughout the year, the impact of the extreme wind speed and temperature must be minimized. Reduction of wind speed can be attained in several ways. One of them would be to use wind fences or windbreaks. Carefully designed windbreaks or fences hold the potential to reduce the wind speed significantly [216]. It also can help to control the emission of loose particles caused by the wind blow [217]. To understand the importance of the wind fence and its potential usage in dry stack tailings facilities, four more numerical simulations were conducted. In these hypothetical cases, it was assumed that the external temperature remained the same as shown in Figure 4-3(a), but the wind speed was reduced by 30%, 50%, 70%, and 90%. Such a decrease in the wind speed also resulted in a reduction in the ℎ applied on the top surface of the tailings. The numerical simulations were carried forward with the reduced values of ℎ, keeping all the other parameters the same as the base case. The temperature distribution in the block was recorded every day and shown as contours for every 25 days starting from day 150 for all the reduced values of ℎ along 104 with the base case contours in Figure 4-15. In this figure, ℎ denotes the base case. 0.7ℎ, 0.5ℎ, 0.3ℎ, and 0.1ℎ indicate the cases with 30%, 50%, 70%, and 90% reduction in the wind speed. Figure 4-15. Temperature contours of the tailings body throughout the year for different ambient air convective heat transfer coefficients at the surface. From the contours, it can be identified that the freezing could be delayed for a while and controlled with measures taken to weaken the wind speed. The amount (in percentage) of frozen body in the tailings for all the values of ℎ are presented in Figure 4-16(a). With a 30% reduction in the wind speed, the freezing can be prevented for 6 more days compared to the base case. This increased to 11, and 20 days with a 70%, and 90% reduction in the wind speed. Reduced wind speed cases performed comparatively well at the later stages of the operation. For instance, on day 300 of the operation, when the base case had only 19% of the body of the tailings unfrozen, with a 70% reduced wind speed, 30% became available for carbon sequestration. The estimates, displayed in 150175200225250275300325350365Day h 0.7h 0.5h 0.3h 0.1hTemperature ( C)105 Figure 4-16(b), showed that the annualized average for the active tailings was 66% for the base case. It increased up to 69% and 85%, respectively, with a 50%, and 90% reduction in the wind speed. A heat map (green and red colors indicating the lowest and highest values, respectively) is also demonstrated in Figure 4-16(b) portraying the annualized average of the inactive tailings for all the cases investigated here. Figure 4-16. Impact of the reduced ambient air heat transfer coefficient because of reduced wind speed on (a) the amount of frozen tailings body throughout the year, and (b) the annualized average frozen and unfrozen amount of tailings body. The other strategy to minimize the impact could be having an insulation layer over the tailings bed. This layer needs to be less permeable than the tailings so that the exhaust can only flow through the tailings, and it can be achieved with planned compaction [218]. Also, to prevent the impacts of the harsh temperature outside, this layer needs to be constructed with materials with lower thermal conductivity than the tailings bed underneath it. Considering all these factors, three more numerical simulations were conducted. Here, an insulation layer was considered installed over the tailings block that was a thousand times less permeable than the tailings. The thermal 0%10%20%30%40%50%60%70%80%90%100%0 30 60 90 120 150 180 210 240 270 300 330 360Frozen tailings bodyDays in operation0.70.50.30.1(a)hhhhh(b)Reduced wind speed casesTemperature< 0°C > 0°C0.1h 15.4% 84.6%0.3h 27.5% 72.5%0.5h 30.9% 69.1%0.7h 32.4% 67.6%h 33.7% 66.3%106 conductivity of the material in this layer was also assumed to be one-third of 𝐾𝑡. These presumptions were made based on the available literature [43, 165]. Apart from these, all the other parameters were kept the same as mentioned in the base case analysis. Three different heights (0.25m, 0.50m, and 0.75m) for the insulation layer were considered, and the amount (in percentage) of the frozen body in the tailings for all these investigations, along with the base case, is given in Figure 4-17(a). With 0.25m of the insulation layer, the freezing could be prevented for additional 18 days than the base case. With a 0.75m height of insulation layer, the freezing was prevented till 237 days of operation which is 86 days more than the base case. Also, on any day of the operation, the models with the insulated layers performed significantly better than the case with no layer. For example, without any protective layer, only 22% of the block remained unfrozen and could be considered available for carbon sequestration. However, 56%, 78%, and 94% of the block became available on the same day of the operation, respectively, with 0.25m, 0.50m, and 0.75m of layer of insulation. The estimates, presented in Figure 4-17(b), showed that the annualized average for the active tailings was 66% for the base case. It increased to 83%, 92%, and 98%, respectively, with 0.25m, 0.50m, and 0.75m of insulative layer. A heat map (green and red colors indicating the lowest and the highest values, correspondingly) is also demonstrated in Figure 4-17(b) portraying the annualized average of the inactive tailings for different heights of insulative layers investigated here. 107 Figure 4-17. Impact of insulation layers on (a) the amount of frozen tailings body throughout the year and (b) the annualized average frozen and unfrozen amount of tailings body. 4.4 Summary • In this chapter, a comprehensive investigation was conducted to investigate the feasibility of carbon sequestration in mine tailings through diesel exhaust injection in remote, cold climates. A finite element-based numerical model was developed and validated to examine the viability of utilizing the heat in the diesel exhaust to prevent or delay the freezing in dry stack tailings bed to continue the carbon sequestration as a year-round operation. • The results tracked the amount of the frozen tailings body throughout the operational year, along with an annualized average for the above and below 0°C temperature regions. The results for the base case scenario in an extremely harsh weather conditions showed that the annualized average for the active (unfrozen) tailings for carbon sequestration was 66%. 0%10%20%30%40%50%60%70%80%90%0 30 60 90 120 150 180 210 240 270 300 330 360Frozen tailings bodyDays in operation No topsoil0.25m topsoil0.50m topsoil0.75m topsoil(a) (b)Protective layer heightTemperature< 0°C > 0°CNo layer 33.7% 66.3%0.25m 17.2% 82.8%0.50m 7.6% 92.4%0.75m 2.5% 97.5%layer108 • A series of sensitivity analyses on the various related parameters was conducted to estimate the impact of each factor. Higher injection rate and temperature showed slightly better performance in preventing or delaying freezing. Among all the thermo-physical properties of the tailings tested here, the impact of the thermal conductivity was found to be the dominating one. Operating conditions, e.g., the initiation time of the operation in a calendar year, should be chosen carefully as the outcomes could be considerably dependent on it. • Weather conditions of the operating location were identified as the key impacting parameter. There was a 29% difference in the annualized average for the above 0°C temperature regions in the tailings block between the best and the worst case investigated as part of the sensitivity analysis on the various weather locations. • Investigations on the installations of wind fences or protective layers showed that even in the most extreme cold climatic conditions, the carbon sequestration in mine tailings can be continued as a year-round operation, if necessary measures are taken. However, further scrutiny and experimental investigations should be prioritized for such procedures as a part of future studies. 109 Chapter 5: Techno-Economics of Flue Gas Injection into Mine Tailings for Carbon Sequestration 5.1 Introduction The potential to capture and permanently store carbon within mine tailings presents a promising avenue for the mining industry to spearhead the carbon removal initiative offering sustainable solutions. This current study so far paved the way for achieving energy-optimal design scenarios concerning flue gas injection into mine waste for carbon sequestration, achieved through installing perforated pipes embedded in dry stack tailings. The attainment of large-scale carbon sequestration in mine tailings through flue gas injection successfully will not only mitigate the environmental footprint but also position mining as a significant player in the carbon market. However, it is essential to understand the underlying challenges for large-scale implementation of carbon sequestration in mine tailings through diesel exhaust injection and take the necessary steps to overcome those [219]. One of these challenges is the lack of financial analysis that can evaluate the economic viability of this concept. To bridge this knowledge gap, this chapter of the dissertation further developed an existing strategy (outlined in [24]) to devise an energy-optimal approach for flue gas injection into mine tailings for carbon sequestration. Drawing upon this outline, a comprehensive cost analysis was undertaken to assess the potential operational expenses linked with injecting diesel exhaust into mine waste for carbon sequestration. Moreover, a range of sensitivity analyses were performed on relevant operational parameters to gauge the potential variations in the performance of the concept proposed here from an economic standpoint. 110 5.2 Methodology The proposed concept in Chapter 3 involves partitioning the tailings into discrete blocks of identical dimensions, each featuring a central injection pipe enveloped by a specific volume of surrounding tailings. The dimensions of these blocks will be an operating decision depending on the permeability, reactivity capability, and availability of the tailings. These injection pipes will facilitate two concurrent processes: the conveyance of exhaust through the pipes (Transport-2) and its dispersion into the tailings through the pipe perforations (Transport-3). Upon the complete reaction of a given tailings layer, a fresh layer can be established, accompanied by the introduction of a new set of injection pipes. The incorporation of a compressor, fan, or blower becomes crucial to enable the smooth flow of exhaust, effectively mitigating pressure drops incurred during these transportation activities. This integration of the air handling unit is essential for propelling the exhaust into the tailings, thereby ensuring a consistent and uninterrupted discharge along the entire length of the pipe. Solid understanding and optimizing the pressure phenomena involved in Transport-1, 2, and 3 are critical for running the operation efficiently. Thus far, in Chapter 3, a (1+1)D reduced-order model (ROM) was developed to predict the pressure profile for a perforated pipe embedded in a cylindrical block [24]. However, in practical scenarios, the tailings blocks will typically have a rectangular shape (illustrated in Figure 3-1), necessitating the extension of the validated (1+1)D model to cater to the real-world application. In this chapter, this research gap was addressed by further extending the previously developed reduced-order model to accurately predict the fluid flow and the pressure profile during carbon sequestration in mine tailings with perforated injection pipes within a rectangular block scenario. The necessary accuracy of this extended (1+1)D ROM was attained by comparing the relevant 111 outcomes form it with a commercially available finite element solver, COMSOL Multiphysics 6.1. Afterwards, the (1+1)D ROM was coupled with a cost model developed here to estimate the variance in the operating expenditure (OPEX) to sequestrate 1 tonne of CO2 at different operating and design constraints. 5.2.1 Extension of (1+1)D reduced-order model For all the cases investigated here, the perforation scheme was selected based on the strategy established and rigorously tested in Chapter 3. In this configuration, the center-to-center distance of the perforations, known as pitch (𝑠), was the same in both axial (along the length of the pipe) and radial (along the circumference of the pipe) directions. First, the number of perforations around the circumference (𝑛𝑐) of the pipe was chosen. Based on that, the pitch can be computed. Depending on the 𝑠 and 𝑛𝑐, the number of the perforations in the axial direction (𝑛𝑐) was determined. The size of the perforations (𝑟𝑝) controlled the perforated surface area ratio (𝐴𝑟) of the pipe. 5.2.1.1 3D Numerical model development for rectangular block The 3D FE models were developed based on the numerical methodology that was previously established and validated in section 3.2.3 for flue gas injection in mine tailings for carbon sequestration. The flow through the injection pipe (Transport-2), and the outflow through the perforation into the porous tailings (Transport-3) were modeled together based on their designated governing equations shown in Equation (3.4) and (3.5). The computational domains and the associated boundary conditions of the 3D FE models are shown in Figure 5-1. The Free and Porous Media Flow interface was activated in COMSOL Multiphysics 6.1. This allowed the flow in the 112 free channel (through the pipe) to be governed by the Reynolds Averaged Navier-Stokes (RANS) equations. Figure 5-1. Diagram illustrating the computational domain of the rectangular tailings block for carbon sequestration, accompanied by the pertinent boundary conditions for the numerical modeling. A constant mass flow rate was integrated across the inlet boundary section (shown as exhaust inlet, 𝑟𝑖𝑛, in Figure 5-1), aligned parallel to the normal to the boundary, with the tangential velocity set to zero. Employing two symmetry planes allowed confining the analysis to one-quarter of the geometrical domain. This reduced the computational resource requirement while ensuring the integrity of the numerical analysis. Enforcing a no-slip condition at the top surface ensured that the fluid velocity relative to the wall velocity remained zero (𝒖 = 0). A pressure outlet boundary condition was employed at the outlets, where the tangential stress components were prescribed to be zero. Continuity conditions were upheld at the perforated surfaces of the pipe, and a Dirichlet boundary condition was assigned at the interface between the fluid and the pipe. Due to its significantly smaller dimension compared to the overall geometry, the thickness of the pipe was deemed insignificant and consequently omitted in the simulation analysis. A rigorous grid independence study was conducted before commencing simulations using the newly formulated TailingsOutletExhaust inletSymmetryInjection pipe radius ( )Transition zoneSmooth zone(Linear flow)(Radial flow)SymmetryZone 1 Zone 2113 3D finite element model. This meticulous investigation aimed to ascertain that the outcomes from the model remained impervious to alterations in the mesh configuration, ensuring the robustness and reliability of the subsequent analyses. 5.2.1.2 (1+1) ROM development for tailings block Following the previously established methodology for the (1+1)D ROM for cylindrical blocks, the whole length of the pipe, 𝐿, was partitioned into 𝑛 number of segments having equal length of 𝑠. These segments were interconnected sequentially, where information flowed from one segment to the next. The rectangular shape of the tailings block was considered partitioned into two zones, as shown in Figure 5-1 with the dashed red lines. Darcy's law for radial flow was applied to the zone on the left (zone 1) assuming a cylinder originating from the center of the setup with a diameter that was equal to the height of the block. The zone on the right (zone 2) was presumed to have Darcy’s law of linear flow active. It has already been proved in [24] that the arrangement of the perforations could impact the pressure profile by resulting in abrupt flow patterns in the porous domain very adjacent to the perforations. This region was denoted as transitions zone (shown in Figure 5-1) and was found to expand to approximately half of the length of the pitch used. Subsequently, the flow evolves into a uniform pattern as it enters the smooth zone. The radial velocity of the exhaust in the transition and the smooth zone can be represented, respectively, with the Equations (3.12) and (3.13). It has been demonstrated that the 𝑚-factor plays a crucial role in quantifying the influence of the employed perforation scheme on the pressure profile within the perforated pipes integrated into the tailings for flue gas injection. The 𝑚-factor is a dimensionless number and is a function of the 114 perforations scheme applied on the injection pipe and the geometric specifications of the tailings block. 𝑚 = ∫(𝛽, 𝑅′) (5.1) Here, 𝛽 is a dimensionless number referring to the ratio of the total area of the perforations on the injection pipe surface (𝐴𝑝) to the surface area of the enclosing cylindrical boundary encompassing the transition zone (2𝜋𝑟𝑖𝑛𝑡𝐿). 𝑅′ (shown in Figure 5-1) indicates the ratio between the height of the block (ℎ) and the size of the injection pipe diameter. Based on 𝛽 and 𝑅′, the value of 𝑚-factor was approximated from the map given in Figure 5-2 for using in the Equation (3.12). Figure 5-2. Variability in 𝒎-factor across distinct heights of tailings blocks and various patterns of perforations in the injection pipe (modified from [24]). 0.000.050.100.150.200.250.300.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65m-factorβ = 1 = 5 = 10 = 15 = 20 = 25 = 30R’R’R’R’R’R’R’Negligible effect of m-factor (perforations)Nonviable (too small) perforationsPhysically impractical design(compromised pipe strength) Minimum feasible value of R’115 Afterward, the pressure profile through the mid-perforation for the zone 1 (𝑝𝑧𝑜𝑛𝑒1′ ) where the radial flow was activated was estimated by using Equation (5.2). Adding the linear pressure drop in zone 2 (𝑝𝑧𝑜𝑛𝑒2′ ) to 𝑝𝑧𝑜𝑛𝑒1′ produced the total mid-perforation pressure profile (𝑝′). 𝑝𝑧𝑜𝑛𝑒1′ = ∫ 𝑢𝑟(1)(𝑟)𝑟𝑖𝑛𝑡𝑟𝑖𝑛+∫ 𝑢𝑟(2)(𝑟)𝑟𝑜𝑢𝑡𝑟𝑖𝑛𝑡 (5.2) 𝑝𝑧𝑜𝑛𝑒2′ = 𝑄 × 𝜇𝑒𝑥ℎ ×{1 +1𝑅𝑤ℎ(1 −𝜋4)}𝑤 − ℎ4𝑘𝑡ℎ𝐿 (5.3) 𝑝′ = 𝑝𝑧𝑜𝑛𝑒1′ + 𝑝𝑧𝑜𝑛𝑒2′ (5.4) where, 𝑅𝑤ℎ represents the ratio of the width (𝑤) of the tailings block to its height (ℎ). Equation (5.3) also includes the dark grey shaded area of the block (shown in Figure 5-1) in the calculation, which was not included in the cylindrical flow assumption for zone 1 earlier. This was included by making necessary modifications to Darcy’s law for linear flow. With the higher values of 𝑅𝑤ℎ, the impact of this zone on the total pressure profile will become insignificant. As earlier mentioned, the operating configurations examined here were in the laminar flow regime in the porous domain, the amount of outflow in each section was calculated based on Darcy’s law for radial coordinates [187] using Equation (3.9). In this context, the parameter 𝛼 is contingent upon the specific arrangement of perforations employed in the injection pipe, as well as its influence on the pressure distribution along the pipe. Equations (3.11) and (5.5) can be utilized combinedly to ascertain the value of 𝛼, catering to 116 scenarios where the effect of the perforation arrangement holds significance or can be disregarded (pressure-optimized cases) correspondingly. 𝛼 = 𝜇𝑒𝑥ℎ2𝑘𝑡[1𝜋𝑙𝑛 (ℎ𝑑ℎ) +{1 +1𝑅𝑤ℎ(1 −𝜋4)}𝑤2ℎ− 0.5] (5.5) Based on this extended methodology, the gauge pressure, 𝑝𝑔𝑖, mentioned in Equation (3.9) was computed, using the (1+1) ROM in every 𝑖th section with the following equation for rectangular tailings block. This is the combined pressure drop of TPL and IPL for simultaneously occurring in Transport-2, and 3, respectively. The associated Equations (3.14) – (3.17) involved in the computation were kept the same. 5.2.2 Financial analysis The primary focus of the financial analysis of the concept was estimating operating costs. The installation of the necessary air handling units and construction of the piping for Transport-1 were regarded as capital expenditures. These were kept out of discussion in this investigation as these will be a one-time manageable capital investment. The economics of the entire operations can be evaluated by understanding and controlling the operating expenses involved. Therefore, the target became to estimate the OPEX to sequestrate 1 tonne of CO2 in every operating year. The major costs contributing to the OPEX were the cost of piping, electricity, and materials handling. The materials handling cost indicated the arrangement of dry stack tailings bed and preparing it for diesel exhaust injection. However, as the dry stack tailings will have long-term operational benefits in tailings management cost, the associated expenditure related to materials handling was decided 117 to exclude from the current investigation. This makes the total operating expenditure to capture 1 tonne of CO2 in every operating year (𝑜𝑥𝑡) in mine tailings solely a function of the associated operating cost of piping (𝑜𝑥𝑝𝑖𝑝𝑖𝑛𝑔), and the electricity cost (𝑜𝑥𝑒𝑙𝑒𝑐). 𝑜𝑥𝑡 = 𝑜𝑥𝑝𝑖𝑝𝑖𝑛𝑔 + 𝑜𝑥𝑒𝑙𝑒𝑐 (5.6) As previously mentioned, the total pressure drop (Δ𝑝) that the installed air handling units must counteract will equal the sum of the pressure differentials experienced across Transport-1, 2, and 3. The pressure drop in Transport-1 was estimated by altering Equation (3.6). The (1+1)D ROM provided with the pressure drop associated in Transport-2, and 3. Based on Δ𝑝, and the total flow rate of the exhaust injection, the air handling unit could be chosen. Also, an additional 5% pressure drop was included in the calculations as a contingency. The energy consumed by the fan (𝑊𝑓𝑎𝑛) and the compressor (𝑊𝑐𝑜𝑚𝑝) in the operations was estimated by using equations (5.7) and (5.8), respectively. 𝑊𝑓𝑎𝑛 =(Δ𝑝)𝑄𝑡𝜂𝑓𝑎𝑛 (5.7) 𝑊𝑐𝑜𝑚𝑝 =𝜌𝑒𝑥ℎ × 𝑄𝑡 × 𝐶𝑝𝑒𝑥ℎ𝜂𝑐𝑜𝑚𝑝{(1 +Δ𝑝𝑝𝑎𝑡𝑚)(1−1𝛾)− 1}𝑇 (5.8) where, 𝜂𝑓𝑎𝑛 and 𝜂𝑐𝑜𝑚𝑝 represent the efficiency of the fan and the compressor, respectively. 𝑄𝑡 is the total volumetric flow rate and 𝐶𝑝𝑒𝑥ℎ is the specific heat of the exhaust, respectively. 𝑝𝑎𝑡𝑚, 𝛾, and 𝑇 indicate respectively the atmospheric pressure, adiabatic index, and the temperature of the exhaust before it enters the compressor. As the operation under discussion here was found to be 118 dealing with higher pressure drops, especially with tailings of low permeability, all the investigations here were carried out with compressors as the air handling unit. The thermal characteristics of the exhaust were derived from the temperature-dependent thermophysical properties of air. This methodology aligns with the established practices observed in comparable studies focusing on the versatile utilization of diesel exhaust [73, 74, 199]. The available quantity of CO2 in the diesel exhaust was estimated from the exhaust flow rate of the diesel generators mentioned in the datasheet provided by the manufacturers, assuming a 10% volumetric concentration of CO2 [47]. Using the following equation, 𝑜𝑥𝑒𝑙𝑒𝑐 was evaluated in every scenario investigated where 𝑢𝑐𝑒𝑙𝑒𝑐 denotes the cost of electricity per kWh, and 𝑀𝐶𝑂2 represents the amount (in tonnes) of CO2 sequestrated. 𝑜𝑥𝑒𝑙𝑒𝑐 =𝑊𝑐𝑜𝑚𝑝 × 365 × 24 × 𝑢𝑐𝑒𝑙𝑒𝑐𝑀𝐶𝑂2 (5.9) The required energy to operate the air handling unit for injecting flue gas in mine tailings to capture CO2 is needed to be delivered from the diesel-based power plant running in the mine site. Therefore, it was necessary to keep a check on the energy requirement for running the operation throughout the study. To do so, a term noted as energy ratio (𝑅𝛦) was introduced. It signifies the percentage ratio of the power needed for the sequestration operation to the sequestrated power. The entire dry stack tailings bed was divided into identical blocks with the same ℎ, 𝑙, and 𝑤. The effective execution of the envisioned concept hinges upon a uniform outflow of exhaust through the perforations into the tailings, spanning the entirety of the length of the embedded injection pipe. In the cases of high permeable tailings, where IPL was significantly lower than TPL, the 119 injection of the gas into the tailings became easier than transporting inside the pipe. Such a scenario resulted in a major portion of the gas injection within the initial segment of the block. The smoothness of the outflow distribution could be determined by the flow uniformity index (𝑓𝑢𝑖) given by 𝑓𝑢𝑖 =(Δ𝑄1)𝐿𝑄𝑡𝑠 (5.10) where, Δ𝑄1 indicates the outflow from the 1st discretized section of the pipe. In an ideal smooth distribution scenario, 𝑓𝑢𝑖 will be equal to 1. In case of an abrupt distribution of the outflow (𝑓𝑢𝑖 >1), a substantial portion of the tailings will not be sequestrated because of the exhaust failing to reach them. To avoid this mishap, the dimensions of the injection pipe, to be situated at the center of each block, were subsequently established by evaluating the ratio between TPL and IPL. Having injection pipes with larger diameters resulted in less frictional losses and a lower value in TPL and brought the necessary balance between TPL and IPL. In all the investigations conducted here, this exercise was followed thoroughly to find the optimum diameter for the injection pipe. It was observed that an acceptable smooth distribution of the outflow was present when IPL was at least 15 times higher than TPL. In general, the low permeability of the tailings required the installation of injection pipes with larger diameters. The number of perforation pipes (𝑛𝑝𝑖𝑝𝑒) was equal to the number of the tailings blocks employed in the operation. The total operating cost for injection piping was estimated based on the total length of piping required (𝑛𝑝𝑖𝑝𝑒𝐿) and the cost of the piping per meter (𝑢𝑐𝑝𝑖𝑝𝑖𝑛𝑔). Using the following equation, 𝑜𝑥𝑝𝑖𝑝𝑖𝑛𝑔 was evaluated in every scenario investigated here. 120 𝑜𝑥𝑝𝑖𝑝𝑖𝑛𝑔 =𝑛𝑝𝑖𝑝𝑒𝐿 × 𝑢𝑐𝑝𝑖𝑝𝑖𝑛𝑔𝑡𝑝𝑖𝑝𝑖𝑛𝑔 ×𝑀𝐶𝑂2 (5.11) where, 𝑡𝑝𝑖𝑝𝑖𝑛𝑔 refers to the re-piping period. As previously mentioned, after full sequestration in one layer of tailings, a new layer of tailings will be needed with a new set of injection pipes. The frequency of re-piping activity was measured with 𝑡𝑝𝑖𝑝𝑖𝑛𝑔 (in years). If 𝑡𝑝𝑖𝑝𝑖𝑛𝑔 was less than 1 year, that meant that a new layer of tailings with new sets of injection pipes were needed to be installed even before completing 1 year of operation. In such cases, the cost of piping in an operating year will be higher. This could be experienced when the tailings had a lower capacity to sequestrate CO2 than the available or targeted amount. On the other hand, tailings with a higher reactivity potential could have operations where 𝑡𝑝𝑖𝑝𝑖𝑛𝑔 was more than 1 year. However, this was an operating parameter and could be controlled by appropriately setting up the operation. It is pertinent to note that the term "operating year" utilized in this study does not necessarily denote a calendar year. The operating year indicates an operating period of 365 days where diesel exhaust is injected into the tailings for capturing CO2. However, these 365 days do not necessarily need to be continuous. Considering the application of the present study in remote, off-grid locations, it is essential to mention that the operational continuity may not be sustained throughout the entire year due to harsh climatic conditions and other challenges. Therefore, the term "operating year" was introduced and consistently employed throughout the study to enhance investigations clarity. As the carbon sequestration was guided by the reactivity potential of the tailings, it was important to include that in evaluating the financial aspects of the proposed concept here. A parameter called reactivity index (𝑅𝐼) was introduced and was computed as 121 𝑅𝐼 =𝑀𝐶𝑂2𝑀𝑡𝑎𝑖𝑙𝑖𝑛𝑔𝑠 (5.12) where, 𝑀𝑡𝑎𝑖𝑙𝑖𝑛𝑔𝑠 indicates the amount of the tailings (in tonnes) that was required to sequestrate 𝑀𝐶𝑂2. 𝑅𝐼 is a crucial parameter which is dependent on the geo-physical characteristics of tailings and some other operational conditions. The average power demand of the mine, and the amount of the available tailings along with 𝑅𝐼 governed 𝑀𝑡𝑎𝑖𝑙𝑖𝑛𝑔𝑠 which influenced the system design. 5.3 Results and Discussion 5.3.1 Establishment of energy-optimum scenario Before investigating the financial details of the proposed concept, it was essential to check the viability of the application of the extended (1+1)D ROM in estimating the pressure profile for perforated pipes embedded in rectangular tailings block. To evaluate the actuality of the (1+1)D ROM, four perforation designs (𝑛𝑐 = 4, 6, 8, and 10) introduced in [24] were selected. For each perforation case, two different perforation ratios (𝐴𝑟 = 30%, and 50%) were picked. Two different heights were chosen for the tailings blocks, along with four different width-to-height ratios (𝑅𝑤ℎ). In total, sixty-four different configurations were prepared for perforated injection pipes installed in the tailings bed for the extended (1+1)D ROM. Simultaneously, the same configurations were replicated with the 3D FE model. The key parameters used in the investigations conducted in this section of the study are given in Table 5-1. 122 Table 5-1. Key parameters used in constructing the (1+1)D ROM and 3D FE models for results comparison. Parameters Value Density of the tailings (𝜌𝑡𝑎𝑖𝑙𝑖𝑛𝑔𝑠) 2600 kg/m3 [208] Height of the tailings block (ℎ) 2 m Length of the tailings block or the injection pipe 1.02 m Injection flow rate (𝑄) 1.7 × 10−3 m3/s Air volume fraction or porosity of the tailings (𝜀𝑡) 35% [211] Injection temperature 80 °C Permeability of the tailings (𝐾𝑡) 4.8 × 10−11 m2 The results for the inlet pressure obtained for all the sixty-four cases from the (1+1) ROM were compared with the outcomes from the 3D FE models. The comparisons for all these configurations are shown in Figure 5-3, and Figure 5-4, respectively for the tailings blocks that had 𝑅′ of 5, and 12. 123 Figure 5-3. Comparison of the inlet pressures obtained from the 3D FE models and (1+1)D ROM for rectangular tailings block (𝑹′ = 𝟓) for different perforation configurations, based on the number of the perforations around the circumference of the pipe: (a) 𝒏𝒄 = 𝟒, (a) 𝒏𝒄 = 𝟔, (a) 𝒏𝒄 = 𝟖, and (a) 𝒏𝒄 = 𝟏𝟎. For all the cases tested here, the (1+1)D ROM and the 3D FE models were found to be in good agreement in predicting the inlet pressures of the perforated pipes embedded in the rectangular blocks of the tailings. The maximum difference between the results obtained was less than 3%, and it was observed for the smallest width-to-height ratios tested here. With the larger-sized blocks, and higher intensity of the perforations, the effect of perforations in the pressure profile became insignificant. The target of this section of the study was to prove that the injection of diesel exhaust in mine tailings for carbon sequestration can be designed in an optimal way for energy management. To achieve such a scenario, two factors were necessary to confirm. One of them was to ensure that the outflow through the perforations of the injection pipe was consistent into the 05001,0001,5002,0002,5003,0003,5000 5 10 15 20 25Inlet Pressure (Pa)Width to height ratio of the block3D FE (A30)(1+1)D ROM (A30)3D FE (A50)(1+1)D ROM (A50)05001,0001,5002,0002,5003,0003,5000 5 10 15 20 25Inlet Pressure (Pa)Width to height ratio of the block3D FE (A30)(1+1)D ROM (A30)3D FE (A50)(1+1)D ROM (A50)05001,0001,5002,0002,5003,0003,5000 5 10 15 20 25Inlet Pressure (Pa)Width to height ratio of the block3D FE (A30)(1+1)D ROM (A30)3D FE (A50)(1+1)D ROM (A50)05001,0001,5002,0002,5003,0003,5000 5 10 15 20 25Inlet Pressure (Pa)Width to height ratio of the block3D FE (A30)(1+1)D ROM (A30)3D FE (A50)(1+1)D ROM (A50)(a) (b)(c) (d)124 tailings throughout the length of the tailings block. This could be ensured by sizing the perforation schemes previously established in [24]. The second one was to ensure that the pressure drop the system would need to overcome was mostly the pressure drop due to the injection in porous tailings. This can be achieved if the impact of the perforations on the pressure profile becomes insignificant. When the pressure drop is optimal, the required energy to overcome that will also be the same. This was previously shown as attainable in a cylindrical block [24]. Here, the investigations were continued to ensure the possibility of reaching such a setup in rectangular tailings blocks. Figure 5-4. Comparison of the inlet pressures obtained from the 3F FE models and (1+1)D ROM for rectangular tailings block (𝑹′ = 𝟏𝟐) for different perforation configurations based on the number of the perforations around the circumference of the pipe: (a) 𝒏𝒄 = 𝟒, (a) 𝒏𝒄 = 𝟔, (a) 𝒏𝒄 = 𝟖, and (a) 𝒏𝒄 = 𝟏𝟎. (a) (b)(c) (d)05001,0001,5002,0002,5003,0003,5000 5 10 15 20 25Inlet Pressure (Pa)Width to height ratio of the block3D FE (A30)(1+1)D ROM (A30)3D FE (A50)(1+1)D ROM (A50)05001,0001,5002,0002,5003,0003,5000 5 10 15 20 25Inlet Pressure (Pa)Width to height ratio of the block3D FE (A30)(1+1)D ROM (A30)3D FE (A50)(1+1)D ROM (A50)05001,0001,5002,0002,5003,0003,5000 5 10 15 20 25Inlet Pressure (Pa)Width to height ratio of the block3D FE (A30)(1+1)D ROM (A30)3D FE (A50)(1+1)D ROM (A50)05001,0001,5002,0002,5003,0003,5000 5 10 15 20 25Inlet Pressure (Pa)Width to height ratio of the block3D FE (A30)(1+1)D ROM (A30)3D FE (A50)(1+1)D ROM (A50)125 A combination of multiple heat maps is given in Figure 5-5, showing the variations in the inlet pressures for different perforation schemes applied on the injection pipes installed in different dimensions of rectangular tailings block. For each block size, a heat map is curated, demonstrating the effect of different perforation schemes on the inlet pressure. These maps can be applied in the decision-making process for choosing a perforating scheme for the system design. For example, when the tailings block had 5-times height of the injection pipe diameter along with the 𝑅𝑤ℎ of 1 (square-shaped block), the least-dense perforation scheme (4 perforations around the circumference of the pipe with 30% of the pipe surface perforated) applied here resulted in an inlet pressure drop of 238.4 Pa. This could be reduced by 8.5% by making 50% of the pipe surface perforated. It can be further reduced to 214.8 Pa by increasing the number of perforations around the circumference of the pipe by 2. Further densifying the perforation scheme did not bring any significant reduction in the inlet pressure estimates. From the heat maps, it can also be understood that the larger block sizes required a less dense perforation scheme to achieve the pressure-optimum scenario. For example, blocks with 𝑅′ = 12, which had a 𝑅𝑤ℎ of 4, the difference between the inlet pressure obtained with the least and most dense perforation arrangement evaluated here was 3.3%. That means that using the least dense perforation scheme could result in an additional 3.3% pressure drop in comparison to the pressure-optimum case. However, this value decreased to 0.7% when the 𝑅𝑤ℎ became 20. Such analyses showed that it was possible to achieve an energy-optimum design for flue gas injection in mine tailings for carbon sequestration with the extended (1+1)D ROM. Further calculations on the financial aspects of the proposed concept were carried out with presuming an energy-optimum design applied. 126 Figure 5-5. Heat maps illustrating variations in inlet pressure for tailings blocks of different dimensions and various perforation arrangements. (Red and green color denote the maximum and the minimum values in the range, respectively.) 5.3.2 Financial analysis As mentioned earlier, in the proposed concept, the injection of diesel exhaust will start with one-layer dry stack tailings in which the initial set of injection pipes will be embedded. After the complete reaction of one layer of tailings, a fresh layer can be established by employing a new set of injection pipes. This process was denoted as re-piping in this study, and the time difference between the piping and the re-piping process was called the re-piping period. Two hypothetical Porous domain height with respect to the injection pipe size, Block width to height ratio ( )Perforated surface area,( or ) ( or ) ( or ) ( or ) 5 130 238.4 228.3 223.2 220.050 218.2 214.8 213.2 212.35 430 697.4 687.2 682.1 678.950 677.2 673.8 672.2 671.25 1030 1616.0 1605.1 1600.0 1596.850 1595.1 1591.7 1590.1 1590.15 2030 3145.2 3135.0 3128.0 3128.050 3124.9 3121.5 3118.0 3118.012 130 312.7 303.2 298.3 295.450 292.6 289.7 288.6 287.812 430 771.6 762.1 757.3 754.350 751.7 748.7 747.5 746.712 1030 1689.6 1680.0 1676.5 1672.250 1669.6 1666.7 1666.6 1664.612 2030 3219.4 3209.9 3205.3 3202.050 3199.4 3199.4 3195.3 3195.3512127 scenarios were constructed, based on the duration of the re-piping periods. In the first one, a fixed re-piping period of 1 year was considered. For the second one, the re-piping period was kept variable. For each scenario, the operating expenditure was evaluated for a range of permeabilities (𝐾𝑡) and reactivity indexes (𝑅𝐼) of the tailings along with the dimensions of the tailings blocks. The primary parameters used in the investigations conducted in this section of the study are given in Table 5-2, unless mentioned otherwise. Table 5-2. Base parameters used in the financial aspects analysis. Parameters Value Density of the tailings (𝜌𝑡𝑎𝑖𝑙𝑖𝑛𝑔𝑠) 2600 kg/m3 [208] Height of the tailings block (ℎ) 2 m Length of the tailings block or the injection pipe 1000 m Transport-1 distance 2000 m Air volume fraction or porosity of the tailings (𝜀𝑡) 35% [211] Injection temperature of the exhaust 80 °C Number of perforations around the circumference of the pipe (𝑛𝑐) 10 Perforated surface area of the injection pipe (𝐴𝑟) 50% Efficiency of the air handling equipment 65% Cost of electricity (𝑢𝑐𝑒𝑙𝑒𝑐) C$0.26/kWh Volumetric percentage of CO2 in diesel exhaust 10% 128 The cost for piping (𝑢𝑐𝑝𝑖𝑝𝑖𝑛𝑔 = C$67/m) was established based on data obtained from a reputable manufacturer for a specific size (16 inches diameter) of a pipe. To account for the variations in pipe diameters used in this study, a functional relationship between the diameter of the pipe and its corresponding cost was developed. This approach ensured that the cost estimation remained accurate and adaptable to different pipe sizes as needed throughout the study. By utilizing the manufacturer's data and incorporating a scalable cost model, a realistic representation of expenses associated with piping in this research was maintained, promoting transparency and accuracy in our economic evaluations. 5.3.2.1 Fixed re-piping period approach At first, based on 𝑅𝐼, a relationship between the amount of the tailings and the amount of the exhaust being injected into that tailing was established. To sequester the same amount of power, depending on the 𝑅𝐼 of the tailings, different amounts of tailings will be required. Higher 𝑅𝐼 of the tailings will advocate for higher rate carbon sequestration potential, which means that it will require less amount of tailings to sequestrate the same amount of power in comparison to the tailings with lower values of 𝑅𝐼. Considering the injection temperature of 80°C, the mass flow rate of diesel exhaust injection was estimated for 1 MW of power sequestration. For an operating span of 1 year, the amount of the tailings required for sequestrating 1 MW of power was evaluated using 𝑅𝐼. That exact amount of tailings was considered available and utilized in 1 year, and using that, the ratio of the mass of the tailings to the mass of the exhaust being injected into that was expressed as 𝛤 in Figure 5-6. The relationship between 𝛤 and 𝑅𝐼 exhibited a direct proportionality. 129 Figure 5-6. Relationship between the reactivity indexes of the tailings and the ratio of the mass of the tailings to the mass of the exhaust injection. After understanding the significance of 𝛤, the 𝑜𝑥𝑝𝑖𝑝𝑖𝑛𝑔 for sequestrating 1 MW of power in mine tailings with different values of 𝑅𝐼 and 𝐾𝑡was evaluated. Values of 𝑅𝐼 ranging from 0.1% to 5% were selected, along with a possible range for 𝐾𝑡 for the mine tailings. The amount of the tailings utilized here was directly determined from the associated values of 𝑅𝐼. That means that with the lower values of 𝑅𝐼, the same amount of exhaust gas was injected in a higher volume of tailings compared to the tailings with the higher values of 𝑅𝐼. For example, for 𝑅𝐼 of 0.5% (𝛤 = 30.6), 1.7 million tonnes (MT) of tailings will be required over the span of 1 year of operating period to sequestrate 1 MW of power (equivalent to 8.6 MT of CO2). This will reduce to 0.3 MT for 𝑅𝐼 of 2.5% (𝛤 = 6.1). However, for both cases, the same amount of diesel exhaust will be injected, and the 𝑀𝐶𝑂2will be the same. After having an estimate for the quantity of tailings to be employed (𝑀𝑡𝑎𝑖𝑙𝑖𝑛𝑔𝑠) for each value of 𝑅𝐼, attention was paid to sizing the tailings blocks. Keeping the same height for all the blocks, the 1101001,0000% 1% 2% 3% 4% 5% 6% 7% 8% 9% 10%Mass of tailings/Mass of gas, Reactivity Index, RI130 width was made variable. Based on 𝑀𝑡𝑎𝑖𝑙𝑖𝑛𝑔𝑠 and 𝑅𝑤ℎ, the number of blocks (or perforated injection pipes) needed was determined. For all cases investigated here, 𝑡𝑝𝑖𝑝𝑖𝑛𝑔 was presumed to be 1 year, meaning that the 𝑀𝑡𝑎𝑖𝑙𝑖𝑛𝑔𝑠 determined were considered available and prepared for the injection prior to the initialization of the operation. Then the injection of flue gas was continued for 1 year. The 𝑜𝑥𝑡 for each scenario was evaluated and then shown in Figure 5-7. The results are categorized by the values of 𝐾𝑡, and 𝑜𝑥𝑡 (on the left axis) along with their associated 𝑅𝛦 (on the right axis) values presented together. Thresholds of C$100 (indicated with the solid black line) and 1% (indicated with the dashed black line) were set respectively for 𝑜𝑥𝑡 and 𝑅𝛦 for performance evaluation of the proposed design concepts. For higher values of 𝐾𝑡, many cases fell under the threshold for both 𝑜𝑥𝑡 and 𝑅𝛦. With the lower values for 𝐾𝑡, though there were some cases under the threshold value for 𝑜𝑥𝑡, almost no case remained under the threshold value that was set for 𝑅𝛦. For example, for 𝐾𝑡 = 2 × 10−10 m2, only 3 cases had 𝑅𝛦 above 1%. Moving to 𝐾𝑡 = 10−13 m2, there were only 3 cases that had 𝑅𝛦 below 1% for all the values of 𝑅𝐼 considered. It happened as the system needed to overcome a huge IPL when the tailings had lower permeabilities. This necessitated a significant amount of energy consumption by the installed air handling units to counteract the induced pressure losses. 131 Figure 5-7. Total operating expenditure and the associated energy ratios per tonne of 𝐂𝐎𝟐 captured targeting 𝟏 𝐌𝐖 power sequestered in the reactivity-index driven amount of mine tailings for different permeabilities at fixed re-piping period scenarios: (a) 𝑲𝒕 = 𝟏𝟎−𝟏𝟎 𝐦𝟐, (b) 𝑲𝒕 = 𝟏𝟎−𝟏𝟏 𝐦𝟐, (c) 𝑲𝒕 = 𝟏𝟎−𝟏𝟐 𝐦𝟐, (d) 𝑲𝒕 =𝟏𝟎−𝟏𝟑 𝐦𝟐, and (e) 𝑲𝒕 = 𝟏𝟎−𝟏𝟒 𝐦𝟐. (Operating expenditures (solid lines, left axis) and energy ratios (dashed lines, right axis) depicted for varying reactivity indexes of the tailings, distinguished by distinct colors.) 0%1%10%1101001,00010,0000 10 20 30 40 50 60 70 80 90Energy ratioTotal OPEX (C$/tonne of CO2)Width to height ratio of the block0%1%10%100%1101001,00010,0000 10 20 30 40 50 60 70 80 90Energy ratioTotal OPEX (C$/tonne of CO2)Width to height ratio of the block0%1%10%100%1101001,0000 10 20 30 40 50 60 70 80 90Energy ratioTotal OPEX (C$/tonne of CO2)Width to height ratio of the block0%1%10%100%1000%1101001,0000 10 20 30 40 50 60 70 80 90Energy ratioTotal OPEX (C$/tonne of CO2)Width to height ratio of the block1%10%100%1000%1101001,00010,0000 10 20 30 40 50 60 70 80 90Energy ratioTotal OPEX (C$/tonne of CO2)Width to height ratio of the block(e)(a) (b)(c) (d)Total OPEX (C$/tonne of CO2)Energy ratio (%)0.1% 0.1%.1%0.1%RI = 0.1%RI = 0.25%RI = 0.5%RI = 0.75%RI = 1%RI = 2.5%RI = 5%132 For the same reason, the minimum value for 𝑜𝑥𝑡 was observed with the higher values of 𝑅𝑤ℎ for cases with higher values of 𝐾𝑡. For example, in Figure 5-7(b) (𝐾𝑡 = 10−11 m2), for 𝑅𝐼 = 0.75%, the minimum 𝑜𝑥𝑡 was observed with the design when tailings blocks had a 𝑅𝑤ℎ of 44. This decreased to 4, in Figure 5-7(d) (𝐾𝑡 = 10−13 m2), for the same reactivity index of the tailings. As mentioned earlier, 𝑜𝑥𝑡 had only two active components: operating expenditure for piping and electricity. When the permeability of the tailings is high, the operating expenditure per tonne of CO2 sequestrated was dominated mainly by the 𝑜𝑥𝑝𝑖𝑝𝑖𝑛𝑔. In such cases, as IPL was very low, going with a higher 𝑅𝑤ℎ resulted in the lowest 𝑜𝑥𝑡. However, with the decrease in 𝐾𝑡, IPL increased, and the 𝑜𝑥𝑒𝑙𝑒𝑐 became dominant in the 𝑜𝑥𝑡. This resulted in the observation of the minimum 𝑜𝑥𝑡 in the cases that had lower values of 𝑅𝑤ℎ for low permeable tailings. Identifying the optimal point between 𝑜𝑥𝑒𝑙𝑒𝑐 and 𝑜𝑥𝑝𝑖𝑝𝑖𝑛𝑔 was vital in the cost estimation for 𝑜𝑥𝑡. The optimal point did not necessarily have the lowest value for either 𝑜𝑥𝑒𝑙𝑒𝑐 or 𝑜𝑥𝑝𝑖𝑝𝑖𝑛𝑔. However, the combination of them generated the minimum 𝑜𝑥𝑡. The minimum operating expenditure to sequestrate 1 tonne of CO2 in every operating year for each case, presented in Figure 5-7, was identified. Figure 5-8(a) shows these minimum 𝑜𝑥𝑡 (on the left axis) values gathered and their designated 𝛤 (on the right axis) with respect to 𝑅𝐼. The associated 𝑅𝑤ℎ and 𝑅𝛦 for these minimum 𝑜𝑥𝑡 cases are shown on the left axis in Figure 5-8 (b) and Figure 5-8 (c), respectively. The results were categorized based on the permeability of the tailings. 133 Figure 5-8. Correlation analysis elucidating the interdependence of reactivity indexes of the tailings and the mass ratio between tailings and exhaust injection in (a) the minimum OPEX for each reactivity cases displayed in Figure 5-7, (b) the associated width to height ratio of the block size for the minimum OPEX cases, and (c) the associated energy ratio for each of the minimum OPEX cases. (Visualization of the mass ratio between tailings and exhaust injection, shown as solid red lines on the right axis of each figure, alongside minimum OPEX, width to height ratio of the block, and energy ratio (depicted by dashed lines, on the left axis) within the designated graph. Different colors denote distinct tailings permeabilities.) In Figure 5-8(a), all but 2 cases had an 𝑜𝑥𝑡 below C$100 . In almost all cases, the higher permeability configurations resulted in lower 𝑜𝑥𝑡. The cases with 𝑅𝐼 of 0.75% can be discussed as examples here. For 𝐾𝑡 = 10−14 m2, the minimum operating expenditure to sequestrate 1 tonne of CO2 in every operating year was C$48 . This dropped to C$26 when 𝐾𝑡 was 10−11 m2. Though 11010010001101001,0000 1 2 3 4 5 6 7 8 9 10Mass of tailings to mass of gas, Total OPEX (C$/tonne of CO2)Reactivity Index (%)11010010000%1%10%100%0 1 2 3 4 5 6 7 8 9 10Mass of tailings to mass of gas, Energy ratioReactivity Index (%)11010010001101001,0000 1 2 3 4 5 6 7 8 9 10Mass of tailings to mass of gas, Block width to height ratioReactivity Index (%)(a) (b)(c)Mass of tailings to mass of gas0.1%134 almost all the configurations had an 𝑜𝑥𝑡 that was lower than the threshold value set, the majority of these were above the individual threshold set for 𝑅𝛦. As shown in Figure 5-8(c), only a few configurations that had the highest permeability tested here had a 𝑅𝛦 below 1%. This was also reflected in Figure 5-8(b), where the 𝑅𝑤ℎ associated with the minimum 𝑜𝑥𝑡, in most cases, was less than 11. While the 𝑅𝑤ℎ was low, the 𝑜𝑥𝑡 was dominated by the 𝑜𝑥𝑝𝑖𝑝𝑖𝑛𝑔, as IPL in such cases was comparatively lower. Therefore, the energy needed to operate the air handling units was also on the lower side. However, with the increase of 𝑅𝑤ℎ, pushing the gas in the lateral direction became difficult, and this made the 𝑜𝑥𝑒𝑙𝑒𝑐 the most contributing to the 𝑜𝑥𝑡. That is why the highest permeability cases had the minimum 𝑜𝑥𝑡 observed where they had comparatively higher 𝑅𝑤ℎ. In these cases, the operating expenditures were mostly dominated by the 𝑜𝑥𝑝𝑖𝑝𝑖𝑛𝑔. Because the high permeable tailings required injection pipes with larger diameters to make TPL reasonably lower than IPL for a smooth outflow distribution. However, it is also important to mention that pushing the exhaust in the lateral direction for such a long distance could be challenging to execute. A holistic approach is crucial to find out the optimal point for all these factors. So far, in the financial analysis, the amount of the tailings utilized for carbon sequestration was guided by 𝛤. This generalized approach was a good strategy to initiate the discussion around the financials of carbon sequestration operation in mine tailings through the injection of diesel exhaust. However, restricting 𝑀𝑡𝑎𝑖𝑙𝑖𝑛𝑔𝑠 based on 𝛤, resulted in some complications in the results shown in Figure 5-7 and Figure 5-8. For lower values of 𝐾𝑡, the higher values of 𝑅𝐼 cases had higher 𝑜𝑥𝑡 than those with lower 𝑅𝐼 values in multiple configurations. The design configurations, where 𝐾𝑡 =10−13 m2 can be discussed as examples. For 𝑅𝐼 of 0.25%, the 𝑜𝑥𝑡 was C$42 , when 𝑅𝑤ℎ was 8. 135 For the exact dimension of the tailings blocks, the 𝑜𝑥𝑡 increased to C$74 when the reactivity index became 10 times higher (𝑅𝐼 = 2.5%). The reactivity of the tailings is the most crucial factor for the successful large-scale implementation of carbon sequestration in mine tailings through flue gas injection. The higher the reactivity of the tailings, the lower the 𝑜𝑥𝑡 should be. The reason behind such misleading results was the constraint set for 𝑀𝑡𝑎𝑖𝑙𝑖𝑛𝑔𝑠 by 𝛤. This resulted in an equal amount of gas injection across varying quantities of tailings. When the reactivity was lower, a larger amount of tailings was required. Conversely, as 𝑅𝐼 increased, the 𝑀𝑡𝑎𝑖𝑙𝑖𝑛𝑔𝑠 decreased. The injection of the same amount of flue gas (as all cases targeted to sequestrate 1 MW of power) resulted in tremendously higher IPLs, when the 𝑀𝑡𝑎𝑖𝑙𝑖𝑛𝑔𝑠 was lower (in higher values of 𝑅𝐼) because of higher injection flux. Interpretations of such results could be deceptive, and to avoid that, the constraints set for the financial analysis was shaped to represent the results differently. In a practical scenario, a mining operation will always have a certain quantity of tailings available annually, along with a specific power demand for operations. Both will vary from mines to mines and depend on several factors, e.g., mining method, ore type, processing technology, operating practices, and so forth. Therefore, in the real-life implementation of the proposed concept, the reactivity index of the tailings will be first estimated. After having a comprehensive understanding of the reactivity potential, based on the quantity of tailings available from the operation, a certain percentage of power will be targeted to sequestrate in a specific operating period. To further explain the approach, the necessary parameters were adapted for a mine operating at a remote, off-grid location in the Northwest Territories of Canada from [220]. This mine had an average power demand of 8.05 MW, and around 4.5 MT of tailings was available yearly. Three different values for 𝑅𝐼 were selected, and they were 0.1%, 0.5%, and 1.5%. Based on the methodology established 136 in this study, it was evaluated that employing 4.5 MT of tailings in an operating period spanning 1 year, 0.5 MW, 2.7 MW, and 8.05 MW of power can be sequestrated, respectively, with the chosen values for 𝑅𝐼. The operating expenses (depicted with the solid lines on the left axis) and the energy ratio (depicted with the dashed lines on the right axis) for each scenario are shown in Figure 5-9 for a range of permeabilities. For all the cases shown here, the minimum 𝑜𝑥𝑡 was consistently observed in the middle of the permeability range tested here, regardless of the reactivity index. Based on the analysis, the most suitable operating point could be found between 𝐾𝑡 of 10−11 m2 and 10−12 m2, in terms of permeability. In that range, the power consumption by the air handling units were found to be acceptable and having a good ratio between TPL and IPL allowed to use a reasonable injection pipe size. Before that (for higher permeabilities), the 𝑜𝑥𝑡 was primarily dominated by the 𝑜𝑥𝑝𝑖𝑝𝑖𝑛𝑔 because of the required installation of the larger-sized injection pipes. Afterward (for lower permeabilities), the 𝑜𝑥𝑒𝑙𝑒𝑐 became more impacting, which resulted in an increase in the 𝑜𝑥𝑡. For all the configurations tested here, in the higher end of the permeability range (10−9 m2 and 10−10 m2), the lowest 𝑜𝑥𝑡 was achieved with the largest block sizes because of the very low IPL occurred in such cases. For example, for 𝐾𝑡 = 10−10 m2, the minimum 𝑜𝑥𝑡 was witnessed with a 𝑅𝑤ℎ of 99 for all reactivity index cases tested here. With a decrease in permeability afterwards, the 𝑅𝑤ℎ associated with the minimum 𝑜𝑥𝑡 dropped, except for 𝑅𝐼 = 0.1% cases, as the injection flow rate was still significantly low in this configuration. For 𝐾𝑡 = 10−12 m2, the minimum 𝑜𝑥𝑡 could be achieved with a 𝑅𝑤ℎ of 15 while targeting to sequestrate 2.7 MW (𝑅𝐼 = 0.5%), and 137 8.05 MW (𝑅𝐼 = 1.5%) of power. In these two cases of 𝑅𝐼, for the lowest permeability tested here (𝐾𝑡 = 10−14 m2), the minimum 𝑜𝑥𝑡 was achieved with the lowest value of 𝑅𝑤ℎ(= 2). Figure 5-9. Total operating expenditure per tonne of 𝐂𝐎𝟐 captured and the associated energy ratio for sequestrating (a) 𝟎. 𝟓 𝐌𝐖, (b) 𝟐. 𝟕 𝐌𝐖, and (c) 𝟖. 𝟎𝟓 𝐌𝐖 of power in 𝟒. 𝟓 𝐌𝐓 of tailings with reactivity index of 𝟎. 𝟏%, 𝟎. 𝟓%, and 𝟏. 𝟓%, respectively, in a fixed re-piping period scenario. (Operating expenditures (solid lines, left axis) and energy ratios (dashed lines, right axis) are depicted for varying permeabilities of the tailings, distinguished by different colors in each figure.) The sequestration of 0.5 MW, 2.7 MW, and 8.05 MW of power would result in the decarbonization of approximately 6.2%, 33.5%, and 100% of the average electricity generation of the mine. Therefore, it was important to check the energy ratios for the cases considered here. For 𝐾𝑡 =10−9 m2, all the minimum 𝑜𝑥𝑡 cases had a 𝑅𝛦 below 1% for all the values of 𝑅𝐼 investigated here. Total OPEX (C$/tonne of CO2)Energy ratio (%)(a) (b)(c)0%0%0%1%10%100%1000%1101001,00010,000100,0000 10 20 30 40 50 60 70 80 90 100Energy ratioOPEX (C$/tonne of CO2)Width to height ratio of the block.001%.01%.1%0%1%10%100%1000%1101001,00010,0000 10 20 30 40 50 60 70 80 90 100Energy ratioOPEX (C$/tonne of CO2)Width to height ratio of the block.1%0%0%1%10%100%1000%1101001,00010,0000 10 20 30 40 50 60 70 80 90 100Energy ratioOPEX (C$/tonne of CO2)Width to height ratio of the block0.01%0.1%138 The reduction in the permeability afterward resulted in the increased standings of 𝑅𝛦. For example, for 𝐾𝑡 = 10−11 m2, the minimum 𝑜𝑥𝑡 cases had a 𝑅𝛦 of 2%, 2%, and 4%, respectively, for 𝑅𝐼 of 0.1%, 0.5%, and 1.5%. In some cases, due to the lower permeability of the tailings, the 𝑅𝛦 could be significantly higher than the previously set threshold of 1%. For example, the minimum 𝑜𝑥𝑡 case for 𝐾𝑡 = 10−14 m2, had a 𝑅𝛦 of 6% and 15%, respectively, for 𝑅𝐼 of 0.5%, and 1.5%. However, it is also important to take into consideration that these cases targeted to decarbonize the one-third and the entire average power generation of the mine, correspondingly. When choosing an optimal design zone for operating, such factors should also be included in the decision-making process. In this representation of the cost analysis (shown in Figure 5-9), different amounts of CO2 (different injection rates) were sequestrated in the same amount of tailings based on their 𝑅𝐼. On the other hand, in the previous representations (shown in Figure 5-7 and Figure 5-8) the same amount of CO2 (same injection rate) was captured in different amounts of tailings, guided by the associated values of 𝑅𝐼. Both situations were governed by the ratio of the mass of the tailings to the mass of the exhaust injection (𝛤). However, in the first one (Figure 5-7), it was used to determine the amount of the tailings to be utilized, and in the later one (Figure 5-9), it was utilized to estimate the exhaust injection rate. Both tactics have the potential to be adopted in the decision-making process for carbon sequestration in mine tailings through flue gas injection. 5.3.2.2 Variable re-piping period approach The analyses conducted thus far had a fixed re-piping period of 1 year meaning a new layer of tailings with a new set of injection pipes would be installed after 1 year of operation. Therefore, 139 the amount of tailings laid down at the beginning had enough potential to capture carbon for 1 year of operation. While this scenario could be deemed ideal, it may not always be assured. In real-world applications, the power generation of a mine and the tailings available from the operation could lead to a re-piping period of more or less than 1 year. If the tailings are highly reactive and the mine has a comparatively low power demand, the re-piping period is likely more than 1 year of operation. Here, the cost of piping will be lower as it will be less frequent. On the other hand, if the reactive potential of the mine tailings is on the lower spectrum of 𝑅𝐼, then the targeted power may require multiple layers of tailings installation, making the operating period less than 1 year. In such cases, the piping cost will go higher as installation of a set of injection pipes will be required more frequently. In this hypothetical scenario, it was assumed to have access to additional stockpiles of tailings to support the multiple re-piping activity in the same operating period. To illustrate this approach, the quantity of available tailings and the average power demand of the mine were adapted from the previous analysis shown in Figure 5-9. The target was set to decarbonize 12.4% (1 MW), 37.3% (3 MW), and 100% (8.05 MW) of the average power demand with an initial layering of 4.5 MT of tailings. A wide range was considered for 𝑅𝐼, ranging from 0.05% to 10%. The cost model was run to estimate the operating expenditures and the energy ratio for each scenario selected for the variance of the permeability. The results are categorized according to the permeability values and shown in Figure 5-10, Figure 5-11, and Figure 5-12, respectively, for 1 MW, 3 MW, and 8.05 MW of power sequestrated. In all three figures, for 𝐾𝑡 =10−09 m2 and 10−10 m2, the 𝑜𝑥𝑡 progressively decreased as 𝑅𝑤ℎ increased. As in such high permeable tailings, due to low IPL, the 𝑜𝑥𝑡 was mostly contributed by 𝑜𝑥𝑝𝑖𝑝𝑖𝑛𝑔. 140 Figure 5-10. Comparison of the total operating expenditure per tonne of 𝐂𝐎𝟐 captured and the corresponding energy ratio for the sequestration of 𝟏 𝐌𝐖 power in 𝟒. 𝟓 𝐌𝐓 of tailings, considering distinct permeabilities under a variable re-piping period scenario: (a) 𝑲𝒕 = 𝟏𝟎−𝟗 𝐦𝟐, (b) 𝑲𝒕 = 𝟏𝟎−𝟏𝟎 𝐦𝟐, (c) 𝑲𝒕 = 𝟏𝟎−𝟏𝟏 𝐦𝟐, (d) 𝑲𝒕 = 𝟏𝟎−𝟏𝟐 𝐦𝟐, (e) 𝑲𝒕 = 𝟏𝟎−𝟏𝟑 𝐦𝟐, and (f) 𝑲𝒕 = 𝟏𝟎−𝟏𝟒 𝐦𝟐. (Operating expenditures (solid lines, left axis) and energy ratios (dashed lines, right axis) depicted for varying reactivity indexes of the tailings, distinguished by distinct colors in each graph.) 0%0%1%10%100%1101001,00010,0000 10 20 30 40 50 60 70 80 90 100Energy ratioTotal OPEX (C$/tonne of CO2)Width to height ratio of the block0.01%.1%0%0%0%1%10%100%1101001,00010,000100,0000 10 20 30 40 50 60 70 80 90 100Energy ratioTotal OPEX (C$/tonne of CO2)Width to height ratio of the block0%0%1%10%100%1101001,00010,0000 10 20 30 40 50 60 70 80 90 100Energy ratioTotal OPEX (C$/tonne of CO2)Width to height ratio of the block0%1%10%100%1000%1101001,0000 10 20 30 40 50 60 70 80 90 100Energy ratioTotal OPEX (C$/tonne of CO2)Width to height ratio of the block1%10%100%1000%1101001,0000 10 20 30 40 50 60 70 80 90 100Energy ratioTotal OPEX (C$/tonne of CO2)Width to height ratio of the blockRI = 0.1%RI = 0.25%RI = 0.5%RI = 0.75%RI = 1%RI = 2.5%RI = 5%Energy ratio (%)RI = 0.05% RI = 10%RI = 7.5%(a) (b)(c) (d)(e) (f)0%0%0%1%10%100%1101001,00010,000100,0000 10 20 30 40 50 60 70 80 90 100Energy ratioTotal OPEX (C$/tonne of CO2)Width to height ratio of the block0.001%.01%.1%.001%.01%.1%0.01%.1%.1%141 Also, as the lower values of 𝑅𝐼 required more frequent installations of pipes, higher 𝑅𝑤ℎ helped the operation to continue with fewer number of pipes (or blocks). That was why the 𝑜𝑥𝑡 kept on decreasing with the increase of 𝑅𝑤ℎ. For these two permeabilities, 𝑅𝛦 was always below or close to 1% for all configurations investigated. In all cases (regardless of the permeabilities), considering the re-piping period as a variable in the calculation revealed a clear trend: higher reactivity index (𝑅𝐼) values corresponded to lower values of 𝑜𝑥𝑡. From 𝐾𝑡 = 10−11 m2, the impact of the energy cost was observed to be influence the 𝑜𝑥𝑡, and the 𝑅𝑤ℎ associated with the minimum 𝑜𝑥𝑡 started to decrease. 𝑅𝐼 = 0.75% cases can be discussed here as an example. The minimum 𝑜𝑥𝑡 was C$11 , C$23 , and C$41 , for the sequestration of 1 MW, 3 MW, and 8.05 MW of power respectively, as depicted in Figure 5-10(c), Figure 5-11(c), and Figure 5-12(c). The associated 𝑅𝑤ℎ with these minimum 𝑜𝑥𝑡 were 70, 50, and 41. The variance in the operating cost per tonne of CO2 sequestrated observed here was due to the different re-piping periods and associated piping costs involved. For the 1 MW case, in every 4 years of operation, a new layer of 4.5 MT of tailings was needed along with a new set of injection pipes, whereas for the 3 MW and 8.05 MW cases, the re-piping period shrank to 1.6, and 0.5 years, respectively. 142 Figure 5-11. Comparison of the total operating expenditure per tonne of 𝐂𝐎𝟐 captured and the corresponding energy ratio for the sequestration of 𝟑 𝐌𝐖 power in 𝟒. 𝟓 𝐌𝐓 of tailings, considering distinct permeabilities under a variable re-piping period scenario: (a) 𝑲𝒕 = 𝟏𝟎−𝟗 𝐦𝟐, (b) 𝑲𝒕 = 𝟏𝟎−𝟏𝟎 𝐦𝟐, (c) 𝑲𝒕 = 𝟏𝟎−𝟏𝟏 𝐦𝟐, (d) 𝑲𝒕 = 𝟏𝟎−𝟏𝟐 𝐦𝟐, (e) 𝑲𝒕 = 𝟏𝟎−𝟏𝟑 𝐦𝟐, and (f) 𝑲𝒕 = 𝟏𝟎−𝟏𝟒 𝐦𝟐. (Operating expenditures (solid lines, left axis) and energy ratios (dashed lines, right axis) depicted for varying reactivity indexes of the tailings, distinguished by distinct colors in each graph.) 0%0%1%10%100%1101001,00010,000100,0000 10 20 30 40 50 60 70 80 90 100Energy ratioTotal OPEX (C$/tonne of CO2)Width to height ratio of the block0%0%1%10%100%1101001,00010,000100,0000 10 20 30 40 50 60 70 80 90 100Energy ratioTotal OPEX (C$/tonne of CO2)Width to height ratio of the block0.01%0.1%RI = 0.1%RI = 0.25%RI = 0.5%RI = 0.75%RI = 1%RI = 2.5%RI = 5%Energy ratio (%)RI = 0.05% RI = 10%RI = 7.5%(a) (b)(c) (d)(e) (f)0.01%0.1%0%0%1%10%100%1101001,00010,0000 10 20 30 40 50 60 70 80 90 100Energy ratioTotal OPEX (C$/tonne of CO2)Width to height ratio of the block0%1%10%100%1101001,00010,0000 10 20 30 40 50 60 70 80 90 100Energy ratioTotal OPEX (C$/tonne of CO2)Width to height ratio of the block0.1%0%1%10%100%1000%1101001,00010,0000 10 20 30 40 50 60 70 80 90 100Energy ratioTotal OPEX (C$/tonne of CO2)Width to height ratio of the block1%10%100%1000%1101001,00010,0000 10 20 30 40 50 60 70 80 90 100Energy ratioTotal OPEX (C$/tonne of CO2)Width to height ratio of the block0.01%0.1%0.1%143 Also, to balance TPL and IPL ratio, it was necessary to employ larger-sized injection pipes where injection flow rates were higher (higher power sequestration cases). This analysis was analogous to all the other cases examined here. In Figure 5-10(d), the minimum 𝑜𝑥𝑡 for each case was accomplished when 𝑅𝑤ℎ ranged between 8 to 50. This range shrunk to 8 to 33, and 8 to 27, respectively, in Figure 5-11(d) and Figure 5-12(d). Another trend can also be seen in all the results shown in Figure 5-10, Figure 5-11, and Figure 5-12. The 𝑅𝑤ℎ responsible for the minimum 𝑜𝑥𝑡 in any design configuration decreased with the increase of 𝑅𝐼. The results shown in Figure 5-12(e) can be discussed here for further explanation. The 𝑅𝑤ℎ leading to the minimum 𝑜𝑥𝑡, was 8, for 𝑅𝐼 = 0.5%. It decreased to 2 when 𝑅𝐼 increased by 10 times. As with a higher reactivity index, the injection pipes will need to be installed less frequently, the 𝑜𝑥𝑡 became dominated by the 𝑜𝑥𝑒𝑙𝑒𝑐, and the optimum design point was found with a relatively smaller 𝑅𝑤ℎ. In the cases with lower permeabilities, designing the system with low 𝑅𝑤ℎ can be recommended as it can keep the 𝑅𝑒 under a reasonable value. For instance, in Figure 5-11(f), increasing 𝑅𝑤ℎ above 4, would make the 𝑅𝑒 higher than 20%. However, the percentage of the total power that was being sequestrated was also essential to consider in making the final decision on choosing a suitable operating point. 144 Figure 5-12. Comparison of the total operating expenditure per tonne of 𝐂𝐎𝟐 captured and the corresponding energy ratio for the sequestration of 𝟖. 𝟎𝟓 𝐌𝐖 power in 𝟒. 𝟓 𝐌𝐓 of tailings, considering distinct permeabilities under a variable re-piping period scenario: (a) 𝑲𝒕 = 𝟏𝟎−𝟗 𝐦𝟐, (b) 𝑲𝒕 = 𝟏𝟎−𝟏𝟎 𝐦𝟐, (c) 𝑲𝒕 =𝟏𝟎−𝟏𝟏 𝐦𝟐, (d) 𝑲𝒕 = 𝟏𝟎−𝟏𝟐 𝐦𝟐, (e) 𝑲𝒕 = 𝟏𝟎−𝟏𝟑 𝐦𝟐, and (f) 𝑲𝒕 = 𝟏𝟎−𝟏𝟒 𝐦𝟐. (Operating expenditures (solid lines, left axis) and energy ratios (dashed lines, right axis) depicted for varying reactivity indexes of the tailings, distinguished by distinct colors in each graph.) 10%100%1000%1101001,00010,0000 10 20 30 40 50 60 70 80 90 100Energy ratioTotal OPEX (C$/tonne of CO2)Width to height ratio of the block1%10%100%1000%1101001,00010,0000 10 20 30 40 50 60 70 80 90 100Energy ratioTotal OPEX (C$/tonne of CO2)Width to height ratio of the block0%1%10%100%1101001,00010,0000 10 20 30 40 50 60 70 80 90 100Energy ratioTotal OPEX (C$/tonne of CO2)Width to height ratio of the block0%1%10%100%1101001,00010,0000 10 20 30 40 50 60 70 80 90 100Energy ratioTotal OPEX (C$/tonne of CO2)Width to height ratio of the block0%1%10%100%1101001,00010,000100,0000 10 20 30 40 50 60 70 80 90 100Energy ratioTotal OPEX (C$/tonne of CO2)Width to height ratio of the blockRI = 0.1%RI = 0.25%RI = 0.5%RI = 0.75%RI = 1%RI = 2.5%RI = 5%Energy ratio (%)RI = 0.05% RI = 10%RI = 7.5%(a) (b)(c) (d)(e) (f)0.1%0. 1%0%1%10%100%1101001,00010,000100,0000 10 20 30 40 50 60 70 80 90 100Energy ratioTotal OPEX (C$/tonne of CO2)Width to height ratio of the block0.1%0.1%145 It was important to compile the results presented in Figure 5-10, Figure 5-11, and Figure 5-12 to show how variance of the re-piping period in different operating constraints that could impact the decision-making process. A correlation between the available quantity of tailings and the amount of power that could potentially be sequestrated within it, contingent on the reactivity index of the tailings, was visually depicted in Figure 5-13(a) using colour-contour representations. The contour map serves as a guide for estimating the potential power that can be decarbonized through flue gas injection into the mine waste, considering the quantity of available tailings in a mining operation, and categorizing them based on their reactivity potential. In the same figure, re-piping periods are also shown by using dashed lines, considering 4.5 MT of tailings available annually to commence the operation. Based on the information presented in this figure, achieving power sequestration of 10 MW with 4.5 MT of tailings (over a re-piping period of 1 year) through flue gas injection necessitates that the tailings possess a reactivity index of 2%. The dashed lines representing the re-piping period in Figure 5-13(a) will vary depending on the initially available quantity of tailings. Nevertheless, the colour-contour map will remain unchanged, serving as a consistent general reference. 146 Figure 5-13. (a) Contour plot showing tailings quantity required for sequestering specific power levels, considering tailings reactivity, and dashed lines representing the re-piping period with an annual availability of 𝟒. 𝟓 𝐌𝐓 of tailings. (b) Re-piping periods for the carbon sequestration cases targeting to capture 𝟏, 𝟑, and 𝟖. 𝟎𝟓 𝐌𝐖 power for cases considering 𝟒. 𝟓 𝐌𝐓 of tailings available yearly. 0.010.11100.01 0.1 1 10 100Reactivity Index (%)Re-piping period (years)1 MW3 MW8.05 MWOperational period < 1 yearOperational period = 1 yearOperational period > 1 year(a)(b)147 The re-piping periods for all the cases presented in Figure 5-10, Figure 5-11, and Figure 5-12 were plotted in Figure 5-13(b) against the reactivity index of the tailings. For the 1 MW scenarios examined in this study, any reactivity index (𝑅𝐼) exceeding 0.25% resulted in an operational (re-piping) period extending beyond 1 year. The 𝑅𝐼 had to be above 0.75% and 2.5%, for the 3 and 8.05 MW cases tested here, respectively, for the re-piping period to be above 1 year. 5.4 Summary • The reduced-order model established here showed potential to be included in designing a pressure and energy-optimum scenario while targeting to capture the carbon in mine tailings by injecting the diesel exhaust from the power plant. • The techno-economic cost model was developed to evaluate the expenses associated with carbon sequestration, considering factors such as piping, and energy operational expenditures. The meticulous consideration of the intricate factors, such as, piping infrastructure and operational energy expenditures shaped this study to be used in the decision-making to assess the operating expenses involved in carbon sequestration in mine tailings through flue gas injection. • Tailings possessing higher permeabilities exhibited reduced energy consumption for operation, and the operating cost was primarily driven by the piping costs. Conversely, in the case of low-permeable tailings, energy expenses played a more significant role in the total operating cost. Striking the right balance between power costs and piping expenditures is pivotal for successful implementation of the proposed concept at a larger scale. This 148 study can be incorporated in the decision-making processes aiming at identifying the optimal operating zone. • The findings showed that the operating expenditure of carbon sequestration within mine tailings can effectively be managed under the threshold of C$100 per tonne of CO2 sequestrated considered in this study. These findings underscored the potential for meaningful greenhouse gas reduction and reinforced the practicality of large-scale adaptation of carbon sequestration strategies in mine tailings within industrial standards. • The present research demonstrated that through efficient design decisions, the energy requirements for the entire sequestration process can be maintained under 1% of the power sequestrated. The targeted energy ratio is an operating decision, and the threshold for it should be adjusted accordingly to the targeted amount of CO2 that needs to be sequestrated. 149 Chapter 6: Contributions and Recommendations 6.1 Core contribution Each chapter in this dissertation concluded with a comprehensive summary containing all the core findings of each segment of the research. Here, the comprehensive conclusion of the whole study was drawn based on the objectives set up at the beginning of the study. As this study was one of the first to propose a concept for large-scale carbon sequestration in mine tailings through flue gas injection, the first objective was to conceptualize the large-scale application process and identify its key components. Following that, a strategy was developed involving installing the perforated pipes in the tailings block to ensure that exhaust can be injected into the entire length of the tailings bed smoothly through the perforations of the injection pipes. The suggested concept seeks to operate the process under energy-optimal conditions, most importantly due to the fact that the additional energy required will be generated using fossil fuel-powered generators in remote mine sites. The crucial determinant for achieving an energy-optimal scenario in this context was the ability to comprehend and regulate the pressure profile within the perforated pipes embedded in the tailings bed. Accordingly, the most significant contribution or objective was to develop reliable tools for investigating the flow and pressure characteristics of perforated pipes injecting diesel exhaust into mine tailings. Preliminary investigations underlined the absence of an amenable numerical tool to predict the fluid flow and pressure profile of a perforated pipe embedded in the mine tailings for flue gas injection to capture carbon. Addressing this knowledge gap, a (1+1)D reduced-order model was established. Being one of the core contributions of this research, this model offers the accuracy of 150 the 3D numerical models built on commercially available simulation software but requires significantly less computational resources and time. Ensuring the viability of this model for real-world application was the next objective, which was fulfilled by validating the developed model with lab-scale experimental investigation. Rigorous examinations utilizing this model revealed that an energy-optimum scenario will occur when the impact of the perforations on the pressure profile of the perforated injection pipe is minimal. A strategy was then provided to establish a guideline for attaining a pressure or energy-optimum scenario in different design and operational conditions. The subsequent objective of this research was to investigate the feasibility of utilizing the thermal energy of diesel exhaust to overcome the impact of the cold climatic conditions of remote mining operations. The finite element-based numerical models were developed and validated against experimental studies available. The core contribution of this novel step was identifying the crucial operating parameters that can influence the effectiveness of enduring the carbon sequestration operation year-round in remote locations. A series of sensitivity analyses showed the viability of injecting flue gas into mine tailings throughout the year for carbon sequestration if necessary actions can be taken. The final objective of this study was to evaluate the economic feasibility of capturing carbon by injecting flue gas into tailings bed. The development of a techno-economic cost model allowed for evaluating of the cost associated with such carbon sequestration operations. By accounting for intricate factors, such as, piping infrastructure, energy operational expenditures, and tailings permeability, this study offered a valuable tool for decision-making processes aimed at optimizing operating expenses. The research acknowledged the critical operating point between power costs 151 and piping expenditures, enabling the identification of optimal operating zones for the successful implementation of carbon sequestration initiatives. By demonstrating that the operating expenditure for carbon sequestration can be managed efficiently under a crucial threshold, the study emphasizes the potential for meaningful greenhouse gas reduction. Moreover, the findings show that a precise design can help maintain the energy requirements below 1% of the sequestered flue gas power source and provide a sustainable pathway for integrating carbon sequestration into mining operations without imposing substantial energy burdens. 6.2 Future work recommendations This novel research is one of the first to offer a techno-economic feasibility assessment of capturing CO2 in mine tailings through flue gas injection in remote locations at large scale. Derived from the outcomes of this research, directing attention towards the following aspects can supplement the feasibility of effectively operating a large-scale system for carbon sequestration in mine tailings. • The subsequent phase of the study should comprehend pilot-scale experimental validation, with a preference for conducting the experiment at a remote mining site. • Investigations into protective measures such as wind fences and protective layers open avenues for exploring the robustness of carbon sequestration operations under extreme conditions. 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Available: https://www.miningdataonline.com/reports/Gahcho_Kue_Technical_Report_03162018.pdf 170 Appendices Appendix A Material Characterization for experimental setup First, the CS was manually sieved to determine the PSD, and the particles below 425 μm (FS) were separated for further analysis. The particle size of the FS was analysed using a Malvern Mastersizer 2000 Laser Diffraction Particle Size Analyser. To do this, a 5% solid suspension was made by combining a representative sample of the sand with deionized water. Before drawing an aliquot for particle size analysis, the suspension was stirred for 10 minutes. To disaggregate particle clusters, treatment with ultrasonic waves (at 0 min, 0.5 min, 1 min, 1.5 min, etc.). The effect of the ultrasonic treatment time on the particle size (e.g., 𝑑50) was investigated. Increasing the ultrasonic treatment time from 2 minutes to 2.5 minutes did not result in a notable change in the value of 𝑑50. Therefore, further ultrasonic treatment was not considered necessary. The cumulative distribution and the distribution density of the FS, along with the particle size analysis for the CS, are presented in Figure A- 1. 171 Figure A- 1. (a) Particle size analysis of the CS, (b) Cumulative distribution (%), and (c) distribution density of the FS used in the experiment. 0%5%10%15%20%25%30%35%20001190850600425<425Percentage (wt.%)Particle size (µm)(a)Fine sand0204060801000.01 0.1 1 10 100 1000Cumulative distribution (%) Particle size (µm)(b)No treatment0.5 min ultrasound1 min ultrasound1.5 min ultrasound2 min ultrasound2.5 min ultrasound02356890.01 0.1 1 10 100 1000Distribution densityParticle size (µm)(c)No treatment0.5 min ultrasound1 min ultrasound1.5 min ultrasound2 min ultrasound2.5 min ultrasound172 Appendix B Sand Permeability Variability Testing A series of tests were conducted to identify the necessary conditions to achieve certain permeabilities with both CS and FS. All these tests were conducted with the experimental setup introduced in Figure A- 1. The following table contains a summary of the results. Table B- 1. Summary results of different tests conducted to measure the sand permeability at various conditions. Sand type Moisture Content Bulk Density Length Flow rate Permeability Average Permeability (Wt. %) (kg/m3) (m) (m3/s) (m2) (m2) CS 3 1.58 × 103 0.151 6.7 × 10−5 1.28 × 10−10 1.27 × 10−10 1.0 × 10−4 1.27 × 10−10 1.3 × 10−4 1.26 × 10−10 3 1.51 × 103 0.134 3.3 × 10−5 2.05 × 10−10 1.99 × 10−10 1.0 × 10−4 1.86 × 10−10 6.7 × 10−5 2.05 × 10−10 2 1.46 × 103 0.127 3.3 × 10−5 2.85 × 10−10 2.71 × 10−10 1.0 × 10−4 2.56 × 10−10 6.7 × 10−5 2.73 × 10−10 2 1.52 × 103 0.135 3.3 × 10−5 1.50 × 10−10 1.43 × 10−10 1.0 × 10−4 1.37 × 10−10 6.7 × 10−5 1.43 × 10−10 173 3 1.39 × 103 0.165 3.3 × 10−5 3.40 × 10−10 3.79 × 10−10 1.0 × 10−4 4.13 × 10−10 6.7 × 10−5 3.84 × 10−10 FS 5 1.70 × 103 0.128 3.3 × 10−5 1.71 × 10−11 1.71 × 10−11 5.0 × 10−5 1.70 × 10−11 1.7 × 10−5 1.73 × 10−11 5 1.75 × 103 0.119 1.7 × 10−5 1.28 × 10−11 1.28 × 10−11 2.5 × 10−5 1.28 × 10−11 1.3 × 10−5 1.27 × 10−11 5 1.73 × 103 0.127 8.3 × 10−6 1.45 × 10−11 1.44 × 10−11 3.3 × 10−5 1.43 × 10−11 2.5 × 10−5 1.44 × 10−11 5 1.47 × 103 0.132 1.7 × 10−5 5.95 × 10−11 5.78 × 10−11 5.0 × 10−5 5.66 × 10−11 3.3 × 10−5 5.73 × 10−11 2 1.64 × 103 0.124 1.7 × 10−5 1.61 × 10−11 1.61 × 10−11 5.0 × 10−5 1.61 × 10−11 3.3 × 10−5 1.62 × 10−11 174 Appendix C Additional Publications The following list comprises additional peer-reviewed journals that are relevant to the present research but are not part of this thesis. These publications were authored by me during the doctoral program. • D. Baidya, M. A. R. de Brito, and S. A. Ghoreishi-Madiseh, “Techno-economic feasibility investigation of incorporating an energy storage with an exhaust heat recovery system for underground mines in cold climatic regions,”, Applied Energy, vol. 273, no. March, pp. 115289, Sep 2020, doi: 10.1016/j.apenergy.2020.115289. • D. Baidya, M. A. R. de Brito, and S. A. Ghoreishi-Madiseh, “Diesel generator exhaust heat recovery fully-coupled with intake air heating for off-grid mining operations: An experimental, numerical, and analytical evaluation,” Int. J. Min. Sci. Technol, vol 32, no. 1, pp. 155-169, Jan 2022, doi: 10.1016/j.ijmst.2021.10.013. • H. Kalantari, D. Baidya, and S. A. Ghoreishi-Madiseh, “A Numerical Investigation on Utilizing Jacket Water Waste Heat of Power Generation Units in Remote Mines,” Mining, Metallurgy & Exploration, vol 40, pp.1409-1421, July 2023, doi:10.1007/s42461-023-00801-6.
Thesis/Dissertation
eng
Mining Engineering
Vancouver : University of British Columbia Library
Attribution-NonCommercial-NoDerivatives 4.0 International
Graduate
Ghoreishi-Madiseh, Seyed Ali
Dipple, Gregory
Study of fluid flow and heat transfer for carbon mineralization in mine wastes
Text