University of Ghana http://ugspace.ug.edu.gh COMPUTATIONAL HYDRODYNAMIC MODELLING OF THE FATE AND IMPACT OF NATURAL RADIONUCLIDES IN LIQUID EFFLUENT DISCHARGES FROM THE GOLD PROCESSING PLANT AT ABOSO GOLDMINES IN DAMANG TARKWA, GHANA A THESIS PRESENTED TO THE DEPARTMENT OF NUCLEAR SAFETY AND SECURITY OF THE GRADUATE SCHOOL OF NUCLEAR AND ALLIED SCIENCES, UNIVERSITY OF GHANA, LEGON BY SAMUEL OWUSU (10362796) BSc. PHYSICS (KNUST), 2007 IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF PHILOSOPHY IN RADIATION PROTECTION JULY, 2013. University of Ghana http://ugspace.ug.edu.gh DECLARATION I satisfy that the work in this project was carried out under the supervision of Prof E. O. Darko and Dr Augustine Faanu and that, this project does not incorporate without acknowledgement of any material previously submitted for a degree or diploma in this University, and that to the best of my knowledge and belief, it does not contain any material previously published or written by another person except where due reference is made in the text. Samuel Owusu (Student ID: 10362796) …………………………….. …………………………….. Signature Date Prof E. O. Darko (Supervisor) ………………………………. ……………………………… Signature Date Dr Augustine Faanu (Co-Supervisor) ….…………………………. ……………………………… Signature Date ii University of Ghana http://ugspace.ug.edu.gh DEDICATION This work is dedicated to my parents, Mr James Quainoo and Madam Elizabeth Owusua. iii University of Ghana http://ugspace.ug.edu.gh ACKNOWLEDGEMENTS It is very important to give credit to all whose support and contributions have complemented my effort. I would like to mention first, the Almighty God for His grace, sustenance, mercy and faithfulness throughout my life and the preparation of this piece of work. I am particularly grateful to my supervisors Prof E.O. Darko and Dr Augustine Faanu for their guidance and suggestions especially during the write-up of the thesis. I wish to express my sincere gratitude to the Kristo Asafo Church, Eastern ‘A’ Region for their support. I am also greatly indebted to Mr Konfe Amadou, an M. Phil. Medical Physics student of the Graduate School of Nuclear and Allied Sciences, University of Ghana and Mr Peter Davor, Assistant Research Scientist, Ghana Atomic Energy Commission for their assistance during the challenging aspects of the MATLAB programming. I also remember vividly the immeasurable efforts of my parents Mr James Quainoo and Madam Elizabeth Owusua. I say God bless you. iv University of Ghana http://ugspace.ug.edu.gh TABLE OF CONTENTS CHAPTER PAGE DECLARATION………………………………………………………………………….ii DEDICATION……………………………………………………………………………iii ACKNOWLEDGEMENTS………………………………………………………………iv TABLE OF CONTENTS…………………………………………………………….........v LIST OF TABLES…………………………………………………………………….......x LIST OF FIGURES………………………………………………………………………xi LIST OF SYMBOLS AND ABBREVIATIONS…………………………………….....xiii ABSTRACT…………………………………………………………………………….xvi CHAPTER ONE 1.0 INTRODUCTION ............................................................. 1 1.1 Background ............................................................................................................... 1 1.2 Radionuclide Transport in Surface Water ................................................................. 3 1.3 Radionuclide Transport Modelling Approaches ....................................................... 5 1.4 Statement of the Problem .......................................................................................... 7 1.5 Objectives of the Study ............................................................................................. 8 1.6 Significance of the Study .......................................................................................... 9 1.7 Scope and Limitation of the Study .......................................................................... 10 CHAPTER TWO 2.0 LITERATURE REVIEW………………………………11 2.1 Background ............................................................................................................. 11 2.2 Hazards and Risks associated with Exposure to NORM in the Mining Industry ... 12 v University of Ghana http://ugspace.ug.edu.gh 2.3 Dose Estimation from Radioactive Effluent discharges ......................................... 15 2.4 Gold Mining Industry in Ghana .............................................................................. 16 2.4.1 Contribution of Gold mining to National Economy ......................................... 17 2.4.2 Methods of Gold Mining in Ghana ................................................................... 19 2.4.2.1 Large-Scale mining………………………………………………………19 2.4.2.2 Small-Scale mining………………………………………………………20 2.4.3 NORM Wastes in the Gold mining Industry .................................................... 22 2.5 Models of Radionuclide Transport in Water Bodies ............................................... 24 2.5.1 One -Dimensional Transport Model ................................................................. 26 2.5.2 Two- Dimensional Transport Model ................................................................ 28 2.5.3 Three -Dimensional Transport Model .............................................................. 29 2.5.4 Zero-Dimensional Transport Model ................................................................. 31 2.5.5 Analytical Models............................................................................................. 33 2.5.6 Modelling Radinuclide Exchanges in Water-Suspended Sediment and Bottom Deposition .................................................................................................................. 34 2.5.7 Modelling River Hydrodynamics and Sediment Transport .............................. 36 2.6 Predictive Hydrologic Modelling Software Packages ............................................ 39 2.7 Some study approaches to solving the Advection -Diffusion Equation.................. 40 2.8 The Numerical Approaches to Solving Partial Differential Equations ................... 42 2.8.1 The Classical Random Walk ............................................................................ 42 vi University of Ghana http://ugspace.ug.edu.gh 2.8.2 The Lagrangian Approach to the Advection–Diffusion Equation .................... 43 2.8.3 The Eulerian Approach to the Advection-Diffusion Equation ......................... 44 2.9 The Present Model .................................................................................................. 44 CHAPTER THREE 3.0 MATERIALS AND METHODS……..………………46 3.1 Description of the Study Area ................................................................................. 46 3.1.1 Location and Size ............................................................................................. 46 3.1.2 Climate and Vegetation .................................................................................... 48 3.1.3 Geology and Soil .............................................................................................. 48 3.1.4 Topography and Drainage ................................................................................ 50 3.2 Conceptual Model of the Research Problem ........................................................... 50 3.2.1 Basic river characteristics of the Taamang River ............................................. 51 3.2.2 Assumptions made in the Model ...................................................................... 52 3.3 Surface Water Flow Equations ................................................................................ 52 3.3.1 Initial Conditions .............................................................................................. 57 3.3.2 Boundary Conditions ........................................................................................ 58 3.3.3 Contaminant Input ............................................................................................ 59 3.4 Development of the Finite Difference Solution ...................................................... 60 3.4.1 Euler’s Method ................................................................................................. 61 3.5 Model Implementation using MATLAB................................................................. 65 3.6 Committed Effective Dose Estimation from Radioactive Effluent Discharges ...... 66 vii University of Ghana http://ugspace.ug.edu.gh CHAPTER FOUR 4.0 RESULTS AND DISCUSSIONS………………………...68 4.1 Distribution of Short-Lived Natural Radionuclides ................................................ 69 4.1.1 Simulation of Radium-224 ............................................................................... 69 4.1.2 Simulation of Polonium -210 ........................................................................... 71 4.2 Distribution of Long-Lived Natural Radionuclides ................................................ 73 4.2.1 Simulation of Radium-226 ............................................................................... 73 4.2.2 Simulation of Uranium-238 .............................................................................. 75 4.2.3 Simulation of Thorium-232 .............................................................................. 77 4.3 Comparison of Results with Published Data ........................................................... 79 4.4 Activity Concentration and Annual Committed Effective Dose from Ingestion of water from the Taamang River at various Receptor Locations ..................................... 81 CHAPTER FIVE 5.0 CONCLUSIONS AND RECOMMENDATIONS………...83 5.1 Conclusions ............................................................................................................. 83 5.2 Recommendations ................................................................................................... 84 5.2.1 Recommendations for future study ................................................................... 85 5.2.2 Recommendations to Gold mining Companies ................................................ 85 5.2.2.1 Water Management Planning………………………………………..…...85 5.2.2.2 Water use and Recycling…………………….…………………………..86 5.2.2.3 Diversion of Clean Runoff and Consolidation of Wastewater streams….86 viii University of Ghana http://ugspace.ug.edu.gh 5.2.3 Recommendation to the Radiation Protection Board (RPB) and the Environmental Protection Agency (EPA) ................................................................. 87 5.2.3.1 Safe Drinking Water Act……………………………………………...…87 5.2.3.2 Environmental Auditing…………………………………….……………87 REFERENCES ................................................................................................................ 88 APPENDIX A .................................................................................................................. 99 APPENDIX B ................................................................................................................ 102 APPENDIX C ................................................................................................................ 103 APPENDIX D ................................................................................................................ 104 APPENDIX E ................................................................................................................ 105 APPENDIX F ................................................................................................................ 107 APPENDIX G ................................................................................................................ 108 APPENDIX H ................................................................................................................ 111 APPENDIX I ................................................................................................................. 112 ix University of Ghana http://ugspace.ug.edu.gh LIST OF TABLES Table 2.1: Percentage Contribution of Mining and Quarrying to total GDP .............. 18 Table 2.2: Exempt Concentration Levels in kBq/Kg for selected naturally occurring radionuclides for discharge in sanitary landfills . ............................................................. 23 Table 4.1: Comparison of results from current study with data from other Publications.79 Table 4.2: Activity Concentration and Annual Committed Effective Dose from 226 238 232 consumption of Ra, U and Th in the Taamang River at various Receptor Locations…………… ....................................................................................................... 82 Table A: Radionuclide Half-Life and Decay Constants ................................................... 99 Table B: Relationship between River flow rate, River width and River depth using Linear Interpolation between values .......................................................................................... 102 Table C: Examples of Longitudinal Dispersion Coefficients in Rivers ......................... 103 Table D: Examples of Lateral Dispersion Coefficients in Rivers................................... 104 Table E: Chemical symbols and Characteristics of Uranium- 238 Series, Thorium- 232 Series and K-40 Decay Series ......................................................................................... 105 Table F: Default values of intake per person for various critical groups in the world (Adults) ........................................................................................................................... 107 Table G: Committed Effective dose coefficients for ingestion (Sv/Bq) ......................... 108 x University of Ghana http://ugspace.ug.edu.gh LIST OF FIGURES Fig 1.1: Flow diagram of the key-processes of the Radionuclide Transport in Rivers ...... 5 Fig 1.2: Skin rashes as a result of intake of polluted water ............................................... 7 Fig 2.1: Damang gold mine infrastructure ....................................................................... 17 Fig 2.2: Blanket washing of milled ore ............................................................................ 21 Fig 2.3: Formation of gold amalgam after addition of mercury ...................................... 21 Fig 3.1 Location of Damang in Ghana.............................................................................. 47 Fig 3.2: Geology of Ghana showing Damang .................................................................. 49 Fig 3.3: Local geology plan of Damang lease area .......................................................... 50 Fig 3.4: River stream scheme............................................................................................ 51 Fig 3.5: Mass balance of the pollutant transport in x-direction ........................................ 53 Fig 3.6: One-Dimensional Discretisation of the Model Domain ...................................... 62 Fig 4.1: 3-D Plot of Variation of the Concentration of Radium-224 with time and distance from discharge point ........................................................................................... 69 Fig 4.2: 2-D Plot of Variation of the Concentration of Radium-224 with time and distance from discharge point ........................................................................................... 70 Fig 4.3: 3-D Plot of Variation of the Concentration of Polonium-210 with time and distance from discharge point ........................................................................................... 71 Fig 4.4: 2-D Plot of Variation of the Concentration of Polonium-210 with time and distance from discharge point ........................................................................................... 72 Fig 4.5: 3-D Plot of Variation of the Concentration of Radium-226 with time and ......... 73 distance from discharge point ........................................................................................... 73 xi University of Ghana http://ugspace.ug.edu.gh Fig 4.6: 2-D Plot of Variation of the Concentration of Radium-226 with time and distance from discharge point ......................................................................................................... 74 Fig 4.7: 3-D Plot of Variation of the Concentration of Uranium-238 with time and distance from discharge point ........................................................................................... 75 Fig 4.8: 2-D Plot of Variation of concentration of Uranium-238 with time and distance from discharge point ......................................................................................................... 76 Fig 4.9: 3-D Plot of Variation of the Concentration of Thorium-232 with time and distance from discharge point ........................................................................................... 77 Fig 4.10: 2-D Plot of Variation of the Concentration of Thorium-232 with time and distance from discharge point ........................................................................................... 78 xii University of Ghana http://ugspace.ug.edu.gh LIST OF SYMBOLS AND ABBREVIATIONS 0-D Zero-Dimension 1-D One-Dimension 2-D Two-Dimension 3-D Three-Dimension AACP Anacostia Active Capping Project ADE Advection-Diffusion Equation AGL Aboso Goldfields Limited BEIR Biological Effects of Ionizing Radiation BSS Basic Safety Standards BTCS Backward in Time, Centre in Space CaO Lime CEA Commissariat a l’Energie Atomique CEIA Centre for Environmental Impact Assessment CT Computed Tomography DEM Discontinuous Enrichment Method DNA Deoxyribonucleic Acid ECL Exempt Concentration Levels EMS Environmental Management Systems EPA Environmental Protection Agency FTBS Forward in Time, Backward in Space FTCS Forward in Time, Centre in Space GDP Gross Domestic Product xiii University of Ghana http://ugspace.ug.edu.gh GGL Goldfields Ghana Limited GIS Geographic Information System HDM Hydrological Dispersion Model HEC Hydrologic Engineering Center HPS Health Physics Society IAEA International Atomic Energy Agency ICPRB Interstate Commission on the Potomac River Basin ICRP International Commission on Radiological Protection IFC International Finance Co-operation IG Iduapriem Goldfields ISEs Intermediate Scale Experiments K Potassium Kd Distribution Coefficient LET Linear Energy Transfer LLRW Low Level Radioactive Waste LMs Lagrange Multipliers MARS Merrick Advance Remote Sensing NaCN Sodium cyanide solution NAS National Academy of Sciences NORM Naturally Occurring Radioactive Material NPP Nuclear Power Plant NRC National Research Council PCBs Polychlorinated Biphenyls xiv University of Ghana http://ugspace.ug.edu.gh PDE Partial Differential Equation Ra Radium RA Regulatory Authority Rn Radon RPB Radiation Protection Board SDWA Safe Drinking Water Act TAM Tidal Anacostia Model TGL Teberebie Goldfields Limited Th Thorium U Uranium UN United Nations UNSCEAR United Nations Scientific Committee on the Effects of Atomic Radiation USACE U.S. Army Corps of Engineers USNRC United States Nuclear Regulatory Commission UV Ultraviolet VAMP Vancouver Additional Matrix Program WACAM Wassa Association of Communities Affected by Mining WASP Water quality Simulation Program WHO World Health Organisation WNA World Nuclear Association xv University of Ghana http://ugspace.ug.edu.gh ABSTRACT Transport of radioactivity in surface water of mine-origin can occur either due to a controlled release from a working mine site (e.g. release of excess stored water) or uncontrolled release (e.g. erosion of material from a site). The radionuclides could concentrate during mining and mineral ore processing and incorporate in water bodies or traditional food stuffs, and thus contribute to the radiation dose received by the public. Eulerian approach to Partial Differential Equations (PDE) has been used to describe the relevant physical processes during radionuclide transport in the Taamang River. A computer programme has been written in MATLAB to implement the numerical solution of the PDE in order to estimate the activity concentration and annual committed effective dose to the public from natural radionuclides (NORM) in liquid effluent discharges from the gold processing plant at the Aboso goldmines in Damang, Tarkwa Ghana. The 238 232 NORM elements of interest are U and Th decay chains. These radionuclides and 226 some progenies such as Ra are long-lived. The key to understanding their distributions, therefore, is to understand the distribution of the source materials, and the physical and geochemical processes that lead to elevated concentrations of these radionuclides under specific conditions. The results obtained from the study revealed that the concentration of NORM in the Taamang River in Damang increases with time at the point of release and decreases due to its decaying character. For short-lived radionuclides, the concentration decreases rapidly as pollutants travel along the river corridor and approaches zero for 224 210 both Ra and Po at 300 m from the discharged point. However, for long-lived radionuclides, the average activity concentrations were 0.06 Bq/L, 0.54 Bq/L and 0.78 226 238 232 Bq/L for Ra, U and Th respectively at 500 m from the discharged point where the water is used by the public. The corresponding average annual committed effective doses xvi University of Ghana http://ugspace.ug.edu.gh 226 238 232 estimated were 0.01 μSv/y, 0.06 μSv/y, and 0.11 μSv/y for Ra, U and Th respectively. The results indicate an insignificant exposure of the public to Natural Occurring Radioactive Materials (NORM) from the activities of the Goldmine. The model designed will serve as an essential tool for use in the regulatory control of routine discharges of radionuclides into the environment and also in planning measures to be taken in the event of accidental releases from the mine. xvii University of Ghana http://ugspace.ug.edu.gh CHAPTER ONE 1.0 INTRODUCTION 1.1 Background Environmental releases of radionuclides have occurred over the last 50 years from a variety of sources, including global fallout, nuclear accidents such as the Chernobyl accident, effluents from nuclear installations, and natural radionuclides released as a by- product of mining. Releases from these sources have the potential of causing significant exposure of radiation to humans and the environment. The basic understanding of radionuclide distribution and dynamics in lakes and rivers, as well as in their respective catchments, has been achieved from experimental studies in different hydrogeologic systems and geographic regions [Nylen, 1997; Burrrough et al.,1999; Abraham et al., 2000; Sanchez-Cabeza et al., 2000; Matsunaga et al., 1999; Malmgren and Jansson, 1995]. It is important to note that protection of the public and workers from the harmful effects of ionizing radiation has been a concern of radiation protection professionals since the early part of the 20th century when harmful effects were first observed. Due to this, a range of models useful for predicting radionuclide migration characteristics in surface water have been developed [IAEA, 2001]. The International Basic Safety Standards (BSS) for Protection against Ionizing Radiation and for the Safety of Radiation Sources established basic and detailed requirements for protection against the risks associated with exposure to radiation and for the safety of radiation sources that may deliver such exposure [IAEA, 2011]. The standards are based 1 University of Ghana http://ugspace.ug.edu.gh primarily on the 2007 Recommendations of the International Commission on Radiological Protection (ICRP) and other International Atomic Energy Agency (IAEA) Safety Series publications [ICRP, 2007]. The BSS placed requirements on both the Regulatory Authority (RA) and on the legal person responsible for the practice [IAEA, 2011]. This Safety standard provides the information necessary to allow the legal person to “make an assessment of the nature, magnitude and likelihood of the exposures attributed to the source” [IAEA, 2011]. It provides a practical generic methodology for assessing the impact of radionuclide discharges in terms of the resulting individual and collective radiation doses. Also, the principle of radioactive waste management requires the implementation of measures that afford protection of human health and the environment, now and in the future. In view of this, the IAEA has issued safety standards and other publications that provide framework for the control of releases of radionuclides into the environment [IAEA, 2010]. A significant step that should promote the development of mechanisms to implement effective management of wastes and residues, including those containing Naturally Occurring Radioactive Materials (NORM) should be taken into account by governments, research institutions, and the general public. 238 232 The NORM elements of interest are U and Th decay chains. These radionuclides as 226 well as their progenies such as Ra are long-lived. The distribution of these radionuclides in the geosphere depends on the distribution of the geological media from which they are derived and the processes which concentrate them at a specific location in specific media. The key to understanding these distributions, therefore, is to understand 2 University of Ghana http://ugspace.ug.edu.gh the distribution of the source materials and the physical and geochemical processes that lead to elevated concentrations of radionuclides under specific conditions [IAEA, 2003a]. In some developing countries, industries which have the potential to generate NORM have not been duly investigated and as a result, no radiological regulatory control is applied. In Ghana, data on radionuclide concentrations in raw materials, residues and waste streams, and public exposures are limited [Darko et al., 2005]. As a result, there is general lack of awareness and knowledge of the radiological hazards and exposure levels by legislators, regulators and operators. The aim of this work is to model the transport of natural radionuclides in liquid effluent discharges from the gold processing plant at the Aboso gold mine in Damang, Tarkwa in order to assess the magnitude of the impact on the public and the environment. The model will serve as a vital tool for monitoring of radionuclide transport in the event of accidental spillage or deliberate discharge into a river, lake or reservoir. The results from the study will be used to estimate the level of contamination of NORM elements in the Taamang River in Damang. 1.2 Radionuclide Transport in Surface Water The transport of radionuclides in surface water systems has attracted the attention of nuclear geochemists and hydrogeologists because of concerns over the release of radioactive contaminants associated with nuclear installations and radioactive waste disposal facilities. Understanding the long-term migratory behaviour of radionuclides in surface water can be improved through studies of the cumulative effects of the mobility of naturally-occurring decay-series nuclides over geological times [Ku et al., 1992]. 3 University of Ghana http://ugspace.ug.edu.gh Any pollutant in a river is transported by the water flow (advection processes) and its concentration is altered by the simultaneous influence of turbulent diffusion processes [Heling et al., 1999]. The radionuclides can also interact with suspended sediments and bottom depositions. The pollutant transfer between the river water and suspended sediments can be described as an adsorption-desorption process. The transfer between river water and the upper layer of the bottom deposition is determined by adsorption- desorption and diffusion processes. The sedimentation of contaminated suspended sediments and the bottom erosion are also important pathways of the “water column- bottom” exchange of radionuclides. The fate of radionuclides in surface water is in general driven by: 1. Dissolved contaminant transport by the river/reservoir flow, 2. Particulate contaminant (pollution absorbed by sediment) transport by the river/reservoir flow and 3. Contamination dynamics in the upper active layer of bottom sediments. The main physical exchange mechanisms are the sedimentation of contaminated suspended matter into the river bed and resuspension of the sediments into water. They are controlled by hydraulic factors (e.g. river flow, sediment transport), and depend strongly on the sediment size fractionation (e.g. clay, silt, sand and gravel). The pollutants in rivers are transported by the water flow (advection process) with simultaneous influence of the turbulent diffusion process. The radionuclides can interact with the suspended sediments and bottom depositions. A pollutant transfer between the river water and suspended sediment is described by the adsorption-desorption processes. 4 University of Ghana http://ugspace.ug.edu.gh The transfer between the river and the upper layer of the bottom deposition is under the influence of adsorption-desorption and diffusion processes. The main processes governing the radionuclide transport in river systems are presented on the scheme of figure1.1 [Heling et al., 1999]. Advection Concentration Concentration of in Biota sediments S Uptake A d s o r p t i o n Concentration in Concentration on suspended in solute C sediment Cs Desorption Diffusion Adsorption Desorption Sedimentation Re suspension Concentration in upper bottom layer Concentration in deep bottom deposition Fig 1.1: Flow diagram of the key-processes of the Radionuclide Transport in Rivers 1.3 Radionuclide Transport Modelling Approaches The transport and behaviour of radionuclides in surface water can be predicted using various sophisticated methods, ranging from a simple algebraic mass-balance approach to 5 University of Ghana http://ugspace.ug.edu.gh a multi-dimensional numerical solution of the problem. The basis of all the computer models is on the law of mass conservation of any contaminant. It can be expressed in terms of the advection-diffusion equation in Cartesian coordinates. There are three basic types of models used to estimate radionuclide transport in surface water [IAEA, 2001]. 1. Numerical models usually transform basic equations describing radionuclide dispersion/diffusion into finite difference or finite element forms. 2. Box type models that treat the entire water body or sections of a water body as homogeneous compartments. These models often include some sediment– radionuclide interactions. 3. Analytical models that solve the basic radionuclide transport equations. Simplifying assumptions are made regarding water body geometry, flow conditions and dispersion processes in order to obtain analytical solutions to the governing equations. In addition, Monte Carlo methods may be used to model water body geometry and to simulate particle transport. This type of model is not based on the solution of the mathematical equation but, rather describes the movement of particles step by step. Each particle, representing a pollutant in its various forms, is followed when discharged from a certain source. The random movement is calculated by means of the model. There is no numerical dispersion problem in this approach, and is therefore an attractive alternative from the advection-dispersion/diffusion method [Heling et al., 1999]. It is also possible to derive several groups of models from the basic mass-balance equation. 6 University of Ghana http://ugspace.ug.edu.gh 1.4 Statement of the Problem Several complaints have been made by inhabitants of the communities in the operational areas of the Aboso Gold Fields Ghana Limited, a mining company operating in Damang, Tarkwa that the gold processing plants have been discharging poisonous effluents into the Taamang River. A baseline study conducted by the Centre for Environmental Impact Assessment (CEIA) Ghana, and the Wassa Association of Communities Affected by Mining (WACAM) in 2008 revealed that in the Tarkwa mining area, all the 117 rivers and streams have been polluted by mining activities. This is because indigenes in those areas have since 2004 reported thousands of cases of skin diseases and type II diabetes caused by the high intake of some pollutants associated with gold ores [Smith-Asante, 2011]. Fig 1.2: Skin rashes as a result of intake of polluted water [Source: Smith-Asante, 2011] 7 University of Ghana http://ugspace.ug.edu.gh Effluents discharged into the Taamang River undergo hydrodynamic flow and reach a receptor location where the critical group resides. The effluents may contain natural radionuclides that may be concentrated due to the processing activities of the mines. This may lead to concentration of these radionuclides and other elements, wastes and tailings to a level that may call for concern from the radiation protection point of view. Naturally occurring radionuclides and particularly their decay products are transported in ground water and surface water. As a result, these radionuclides may enter the food chain through irrigation waters, water supply through groundwater wells and surface water such as streams and rivers, and hence expose the public [UNSCEAR, 2000]. 1.5 Objectives of the Study The primary objective of the study is to determine the concentration of NORM elements in radioactive discharges using computational hydrodynamic modelling in order to assess the magnitude of the impact on the public and the environment. The study will address the following specific objectives: 1. To formulate the governing equations of contaminant transport in surface water flow and to analyze the corresponding initial and boundary conditions of contaminant concentration. 2. To derive a finite difference solution for the governing equations formulated in (1) without tributary inflow. 3. To conduct numerical simulations in order to quantify the specific natural 238 232 radioactive elements such as U, Th, etc. using MATLAB computer programme. 8 University of Ghana http://ugspace.ug.edu.gh 4. To estimate the annual committed effective dose to the public from ingestion of NORM due to the discharge and 5. To provide recommendations to stakeholders about how radiological health and safety policies of gold mining companies in Ghana can be improved. 1.6 Significance of the Study Water is life, water is wealth and water is health. Freshwater contamination due to releases of radionuclides into the environment is an issue of global concern. Comprehensive planning of resource protection strategies requires the characterization of radionuclide migration patterns and processes and the ability to simulate these processes in aquatic environment [IAEA, 2002]. Assessment of the release of radioactivity into the environment is therefore important for the protection of public health; especially if the released radioactivity can enter the food chain. Environmental assessment models are used for evaluating the radiological impact of actual and potential releases of radionuclides into the environment. They are essential tools for use in the regulatory control of routine discharges into the environment and also in planning measures to be taken in the event of accidental releases; they are also used for predicting the impact of releases which may occur far into the future, for example, from underground radioactive waste repositories. Dispersion models thus allow the activity concentration of a radionuclide in the air or water medium, into which it is discharged, to be assessed as a function of time and distance from the source. Given that authorizations are based on a prospective assessment, an environmental modelling approach is always essential. 9 University of Ghana http://ugspace.ug.edu.gh The environmental transfer information that would be obtained could be used to assess activity concentrations in other environmental media (e.g. sediment or food products) based on time varying or equilibrium assumptions. The model was used to predict the level of NORM contamination in rivers as a result of gold processing at different times and distances. Hence, the Environmental Protection Agency (EPA) and the Radiation Protection Board (RPB) will have a solid reference on which authorization of gold processing facilities could be based. Finally, the results from the study could be used to assess the impact of liquid effluent discharge into the environment, by assessing the dispersion and accumulation of the radionuclides in other environmental materials such as air. It will also lead to improvements in the understanding, often tested by comparison of the models with measured data. 1.7 Scope and Limitation of the Study In the present study, a computational model is developed to predict the activity concentration of NORM in the Taamang River in Damang. It is recognized that surface water flow and contaminant discharge include a number of potential issues such as temperature fluctuations, pH, salinity, radionuclide decay, variable density flow, tributary inflow, river velocity, river depth, diffusion/dispersion coefficient etc. In this study, attention is focused on river velocity, river depth, dispersion coefficient and radionuclide decay as the basic characteristics of the river flow required in order to model contaminant transport in rivers. 10 University of Ghana http://ugspace.ug.edu.gh CHAPTER TWO 2.0 LITERATURE REVIEW This section presents an overview of literature relevant to the study. Different dispersion models and model software packages are discussed. The models consider various factors that influence surface water flow and contaminant transport and conclusions made by prior authors as to the various aspects of how each factor, or the combination of these factors, affect the flow and transport pattern in rivers, lakes and reservoirs. 2.1 Background As the environmental awareness of the world’s populace increases, the remediation of contaminants in the environment has become an increasing priority for governments, research institutions, and the general public. Although pollutants may be present in any environmental media (e.g. soil, water, and/or air), contaminated sub-aqueous sediments pose a particular health risk as they serve as a prime pathway for chemical migration from contaminated groundwater to overlying surface water. Once in these surface waters, the contaminants present an exposure hazard to both local marine life and the human population [Luyben, 1995]. Recently, much attention has been focused on the development of accurate equations of state for the prediction of several process parameters including pollutant transport in environmental media. Much effort has also been applied to the development of several equilibrium calculation algorithms for handling some numerical complexities that are inherent in the modelling of waste systems. Computing power, data acquisition, simulation, optimization and information systems also have greatly improved effluent 11 University of Ghana http://ugspace.ug.edu.gh management in recent years. To maintain set pollutant discharge standards to the environment, it is imperative to adopt the most efficient effluent monitoring and management system [Austin, 1984]. 2.2 Hazards and Risks associated with Exposure to NORM in the Mining Industry It is important to assess the risk associated with exposure of radiation to the public as well as the environment. According to the National Research Council (NRC) of USA, Risk is defined as the characterization of the potential adverse health effect of human exposures to environmental hazards [NRC, 1999]. Due to the stochastic nature of the adverse effects of the exposure, together with their extremely low probability of occurrence, risk assessments/estimates have always been based on studies on large population groups using mathematical models. The most current of such studies is that by the U.S. National Academy of Sciences Committee on the Biological Effects of Ionizing Radiation (BEIR Committee) known as BEIR V Report and the latest version of BEIR VII: Health Effects of Exposure to low levels of Ionizing Radiation. Low doses are doses in the range of near zero up to 100 mSv of low-LET radiation [NAS, 1990; NAS, 2006]. This assessment was based on a review of new scientific information from several different studies including: 1. Epidemiological studies of Japanese survivors of nuclear bombing during World War II; 2. Radiation accidents; 3. Patients who had been exposed to radiation during the course of their medical treatments; 12 University of Ghana http://ugspace.ug.edu.gh 4. Laboratory studies on chemistry, physics and biology of ionizing radiation [Cember and Johnson, 2009]. Studies by American Health Physics Society have also recommended quantitative estimation of radiation health risk below an individual dose of 50 mSv per year, additional to background radiation. The reason is that, there is no conclusive evidence of health risks for low dose rate up to 50 mSv/year [HPS, 1996]. It should however be noted that health risks involve not only neoplastic diseases but also somatic mutations that may contribute to other illnesses (including birth defects and ocular maladies) and heritable mutations that may increase the risk of diseases in future generations. Low dose radiation-induced cancer in humans depends on several variables, and most of these variables are not possible to correct for, in any epidemiologic study [Von et. al., 2012]. Some of the confounding factors include: 1. Interaction of radiation with other physical (UV light), chemical, and biological mutagens and carcinogens in a synergistic manner; 2. Variation in repair mechanisms that depend on dose; 3. Variation in sensitivity of bystander cells to subsequent radiation exposure that depends on whether they have been pre- or post-irradiated; and 4. Variation in adaptive response that depends on radiation doses and protective substances (antioxidants). It is important to note that both the linear no-threshold-response and the threshold- response models might not be suitable in predicting cancer risk at low radiation doses in a quantitative sense. Low doses of ionizing radiation should not be considered 13 University of Ghana http://ugspace.ug.edu.gh insignificant for risks of somatic and heritable mutations as well as neoplastic and nonneoplastic diseases in humans. In studies on a human skin tissue model, researchers at Pacific Northwest National Laboratory used a systems biology approach to show that an ionizing radiation dose mimicking that received during a Computed Tomography (CT) scan is sufficient to alter genes in two cell layers. The researchers found 1452 genes altered in the dermis and 428 genes altered in the epidermis. Genes altered in the two layers showed little overlap, but the affected signaling pathways were similar [Von et. al., 2012]. Biological effects of NORM are concentrated mainly on the effects of low doses of ionizing radiations. Low doses of ionizing radiation exposure has the probability of inducing cancer proportional to the dose received which show up after a latency period [IAEA, 2003b]. Direct estimate of the risk associated with NORM from a combination of epidemiological and radiobiological studies at the molecular and cellular levels is a useful tool for elucidating the consequences of low doses of ionizing radiations. The main effects that manifest in later life due to changes or damage to the DNA structure include: 1. Changes in the genetic code resulting in the death of the cell progeny. 2. Cancer induction due to damage to single cells. Cancer initiation involves a loss of regulation of growth or reproduction and development in somatic stem cells i.e. loss of control over cell production cycle and differentiation process. 14 University of Ghana http://ugspace.ug.edu.gh Point mutation and Chromosomal abrasion or damage play important roles in the initiation of cancer formation (neoplasia). 3. Hereditary effects which occur due to changes in genetic codes being transmitted. This may become manifest as hereditary disorders in the descendants of the exposed individuals [Hilson, 2002a]. The World Nuclear Association (WNA) therefore recognizes the need to address concerns among policymakers and the public about the potential health impact of low levels of exposure to ionizing radiation. In this effort, it is a valuable asset that risks of cancer associated with radiation are much better documented than similar risks arising from other hazardous material such as chemicals. 2.3 Dose Estimation from Radioactive Effluent discharges The basic approach to radiation protection consistent all over the world is based on the recommendations of the ICRP in its publications 60 and 103 [ICRP, 1990; 2007]. The recommendations stipulate that, any exposure above the natural background radiation be kept as low as reasonably achievable but below the individual dose limits, which for occupationally exposed workers is 20 mSv average over 5 years but not exceeding 50 mSv in any single year and for members of the public is 1 mSv/year. The dose limits were set based on prudent approach by assuming that, there is no threshold dose below which there would be no effect [ICRP, 1990; 2007]. Individual doses are calculated for the transfer of particular radionuclides through particular pathways. For generic assessment purposes the total hypothetical critical group dose due to a particular source is estimated by summing the doses from all pathways and 15 University of Ghana http://ugspace.ug.edu.gh all radionuclides. Thus the hypothetical critical group is assumed to represent those members of the public most exposed from the source from all possible pathways. In practice this is unlikely to occur, although it is a reasonable assumption for generic purposes. The calculations are based either on the assumption that equilibrium is reached or on the assumption of a continuous buildup of long lived radionuclides in the environment [IAEA, 2001]. 2.4 Gold Mining Industry in Ghana West Africa has for centuries been one of the world’s most important gold mining regions. Today the most significant gold producing country in this area is Ghana [Hilson, 2002a]. At present a total of about 237 companies (154 Ghanaian and 83 foreign) are prospecting for gold and another 18 are operating gold mines in Ghana [Hilson, 2002a]. Prospective gold regions are localized in the western part of the country. Tarkwa, Prestea and Obuasi are the major towns in Ghana where gold is mined [Hilson, 2002a]. From 1992, the mineral industry has become the single largest foreign exchange earner and gold accounts for 95 % of this [Hilson, 2002a]. The gold mine under study is the Aboso gold mine in Damang, owned by Gold Fields Ghana Limited. The Aboso goldmine operates under mining lease no. ML 1409/96 granted to Gold Fields Ghana Limited on April 19, 1995 for a period of 30 years. It was 2 amended on 4th April 1996 to cover an area of 52.39 km . Mining at Damang is carried out by conventional open pit methods. The mine exploits oxide and fresh hydrothermal mineralisation in addition to Witwatersrand-style palaeoplacer gold. The hydrothermal mineralisation is located in Tarkwaian sediments and is the only deposit of its kind located on the Eastern side of the Ashanti Belt in South-West Ghana. Damang’s main ore 16 University of Ghana http://ugspace.ug.edu.gh body is located close to the closure of an antiform, while all other known palaeoplacer mineralisation is located on the Eastern and Western limbs of the anticline [Gold Fields Ghana Limited, 2004]. The Damang gold mine has a Mineral Resource of 4.7 million gold ounces and a Mineral Reserve of 2.1 million ounces [Hilson, 2002a]. It is estimated that the current Mineral Reserve will be depleted in 2024 [Gold Fields Ghana Limited, 2004].There are also several illegal and uncontrolled artisanal mineral productions in Ghana [Addy, 1998]. Other big key sectors in Ghana are cocoa and forestry [Aryee, 2001]. Fig 2.1: Damang gold mine infrastructure [Source: Gold Fields Ghana Limited, 2004 2.4.1 Contribution of Gold mining to National Economy The United Nations (UN) definition of a mineral economy is those economies where mining generates at least 10 % of Gross Domestic Product (GDP) and mineral exports are at least 40 % of their foreign exchange earnings [Aryee, 2001]. Ghana is not exactly classified as a mineral economy by the UN definition. About 40 % of gross foreign 17 University of Ghana http://ugspace.ug.edu.gh exchange earnings come from the mining sector and it generates 5.7 % of GDP [Aryee, 2001]. The industry also has linkages to other sectors and is a major employer in rural areas. Mining contributes to the development of these areas by engaging in community activities and adding to infrastructure by building schools, hospitals and roads [Addy, 1998; Hilson 2002b]. Table 2.1: Percentage Contribution of Mining and Quarrying to total GDP [Source: Akabzaa and Darimani, 2001] YEAR CONTRIBUTION % YEAR CONTRIBUTION % 1970 2.4 1984 1.1 1971 2.4 1985 1.2 1972 2.5 1986 1.1 1973 2.3 1987 1.1 1974 1.8 1988 1.2 1975 2.0 1989 1.3 1976 2.0 1990 1.3 1977 - 1991 1.3 1978 1.7 1992 1.4 1979 1.5 1993 1.5 1980 1.3 1994 1.5 1981 1.0 1995 1.5 1982 1.2 1996 1.5 Gold Fields Ghana Limited has since mid-1990s to date invested 2.4 billion dollars in productive sectors of the economy. It has also spent 34 million dollars on community projects since 2002. In 2011, Royalties of 3% - 12% of mineral revenue were paid to the Government of Ghana. The current 3% royalty rate is based on a 30% operating ratio. 18 University of Ghana http://ugspace.ug.edu.gh Damang gold mine produces 6,772 kg (218,000 ozs) of gold with capital expenditure of 88 million US dollars. The Damang gold mine delivers tangible and lasting benefits to its stakeholder communities towards ensuring sustainable community development. The social investment spent in 2011 focused on the various sectors of the local economy including education, health, water and sanitation and alternative livelihood. The Damang gold mine has offered scholarships to students from local communities to enhance education. Small town water system initiated at Kyekyewere has been completed and a borehole at Koduakrom to provide potable water has been drilled [Gold Fields, 2011]. 2.4.2 Methods of Gold Mining in Ghana In Ghana there are both small-scale mining and large-scale mining. The general processing techniques are handpicking, amalgamation, cyanidation, flotation, electrowinning and roasting of ore [Akosa et al., 2002]. The techniques differ between large and small-scale mining and also vary depending on the type of deposit and its location [Ntibery et al., 2003]. Mining at Damang is carried out by conventional open pit methods [Gold Fields, 2011]. 2.4.2.1 Large-scale mining Large-scale mining is today conducted as surface mining. Cyanidation is the most common technique in the study area and is used for non-sulphidic paleplacer ore [Kotatsi, 2004]. Non-sulphidic paleplacer ore occurs mainly in hard rocks. It is particularly associated with the banket conglomerates of the Tarkwa formation. Teberebie Goldfields Limited and the Iduapriem Goldfields use this ore [Kotatsi, 2004]. This technology is typically conducted as drilling, blasting, haulage of the ore, crushing and screening, 19 University of Ghana http://ugspace.ug.edu.gh agglomeration, haulage and stacking. Lime (CaO) is applied to the ore to raise the pH to between 10.5 and 11.0. Sodium cyanide solution (NaCN) is used for dissolution of the gold [Kuma and Younger, 2001]. In the Wassa West district, there are seven large-scale mines which extract and process two metals, gold (six mines) and manganese (one mine). A number of these are located in the study area namely; Iduapriem Goldfields (IG), Teberebie Goldfields Limited (TGL), Goldfields Ghana Limited (GGL), Ghana Manganese Company (GMC) in Nsuta and Aboso Goldfields Limited (AGL) at Damang [Avotri et al., 2002]. 2.4.2.2 Small-scale mining Small-scale mining in Ghana is defined as “mining by any method not involving substantial expenditure by any individual or group of persons not exceeding nine in number or by a cooperative society made up of ten or more persons” [Kuma and Younger, 2001]. They are estimated to number over 150,000 in Ghana, of which many operate illegally on concessions belonging to large scale operators, or in restricted areas [Kuma and Younger, 2001]. The illegal small-scale miners account for approximately 10% of the gold production in Ghana [Addy, 1998]. These are locally referred to as galamsey [Addy, 1998]. The technique mostly used for small-scale mining is amalgamation [Akosa et al., 2002]. In this process mercury is mixed with gold concentrate to form gold amalgam and then heated to separate the gold [Ntibery et al., 2003]. Both legal and illegal small scale mining are practised in the Wassa West district [Avotri et al., 2002]. In the Tarkwa area, small-scale mining is carried out both in the forest and along the rivers. It is practised all year round and number about 20 000 in the 20 University of Ghana http://ugspace.ug.edu.gh Wassa West district. Of these small-scale miners, about 90 % are illegal. At the moment 168 small-scale mining concessions are valid in the Western region [Ntibery et al., 2003]. Fig 2.2: Blanket washing of milled ore [Source: Ntibery et al., 2003] Fig 2.3: Formation of gold amalgam after addition of mercury [Source: Ntibery et al., 2003] 21 University of Ghana http://ugspace.ug.edu.gh 2.4.3 NORM Wastes in the Gold mining Industry The radioactive wastes generated in mining and mineral processing operations, especially those involving naturally occurring radioactive material (NORM), typically contain low concentrations of radioactive material. However, large volumes of these wastes are produced annually by mining industries throughout the world. The bulk of mining and ore processing waste is the soil or rock that must be removed to gain access to the ore. This waste material includes the overburden from surface mines, underground mines, development rocks, and other waste rocks. Mining and beneficiation processes generate four categories of large-volume waste: 1. Mine waste 2. Tailings 3. Dump and heap leach waste 4. Mine water The volumes of NORM wastes produced could reach levels so high that existing low level radioactive waste (LLRW) facilities would readily be occupied by NORM if controlled disposal procedures are not adopted [Paschoa, 1998]. Uranium and Thorium are always present in association with a variety of elements in the geological formation especially in areas of high natural radioactivity. Different ore bodies produce different concentrations of uranium and thorium daughters in NORM wastes, depending not only on the extraction procedures, but also on the concentration and chemical forms of the NORM in the mineral matrices. NORM can also build-up especially in waste-piles with activity concentrations exceeding reference levels specified by regulatory authorities and international bodies responsible for setting-up standards. In many cases, some of the 22 University of Ghana http://ugspace.ug.edu.gh NORM are also concentrated by the process resulting in relatively high activity concentrations. The current concern over the regulation of NORM waste affects both Uranium/Thorium mining industries as well as other extracting industries throughout the world [CEA, 1992]. The potential environmental implications of NORM wastes need to be evaluated on a case by case basis due to the socio-political aspects and in respect of cost of reducing exposure to the public and workers. Some international and national organizations have already established Exempt Concentration Levels (ECL) for some naturally occurring radioactive materials [IAEA, 226 238 228 232 1992; UMTRCA, 1978]. Examples of ECLs for Ra, U, Ra and Th are shown in Table 2.2. Table 2.2: Exempt Concentration Levels in kBq/Kg for selected naturally occurring radionuclides for discharge in sanitary landfills [CEA, 1992; IAEA, 1992]. 226 238 228 232 Agency Ra U Ra Th IAEA 0.9 2.0 2.0 0.2 CEA 1.0 1.0 2.0 0.2 *IAEA– International Atomic Energy Agency, *CEA – Commissariat a l’Energie Atomique 23 University of Ghana http://ugspace.ug.edu.gh 2.5 Models of Radionuclide Transport in Water Bodies Partial Differential Equations are the basis of many mathematical models of physical, chemical and biological phenomena, and their use has also spread into economics, financial forecasting and other fields. Due to the complexity of the partial differential equations, exact analytical solutions cannot generally be found. It is often necessary to resort to numerical methods to find approximate solutions of these partial differential equations in order to investigate the predictions of the mathematical models. Some of these modelling methods have been reviewed in the 1980s [IAEA, 1985]. The further development of the computer technology during the last decade and the urgent need to increase the predictability of models in order to provide adequate information for making decision concerning the remedial measures in the most contaminated water bodies after the Chernobyl accident has led to the intensive development of river modelling. Mathematical models describing the radionuclide transport and dispersion in rivers, lakes and reservoirs can be classified according to two different approaches; 1. Spatial averaging of the variables and 2. The individual treatment of variables describing radionuclides in different physical-chemical forms. Variables averaged over compartments represent the highest level of averaging and, as a result, are used in models of the lowest spatial dimension. These box-type (zero- dimension) models treat the entire body of water (including the sediment layer, etc.) or a 24 University of Ghana http://ugspace.ug.edu.gh part of the entire body (e.g. one box for water and one for sediments) as a homogeneous compartment. Cross-sectionally averaged variables are often used in channel models and in models for narrow reservoirs. This one-dimensional (1-D) approach is used to simulate pollutant transport from the distances larger than tenths of river width downstream the point-source term (i.e. after full mixing of contaminant over cross section) up to the hundreds of kilometers. The time scale for river 1-D models is from minutes up to tens of years (e.g. for long term sedimentation studies). The two dimensional (2-D) vertical models operate with width averaged variables. These models are used to describe a current, a suspended sediment and a radionuclide transport in case of a significant variability with respect to the channel depth. Depth averaged variables are used in the lateral-longitudinal 2-D models which describe flow pattern and radionuclide dispersion in shallow reservoirs, parts of the river channels and flood plains. The lowest level of averaging takes place in the 3-D models solving primitive or basic governing equations. The real spatial averaging scale of these models is based on the width of the computational grid but not on a certain parameterization or averaging procedure. Modelling the fate of the radionuclides in all three different phases - radionuclides in solution, in suspension and deposited sediments is very important. Such an approach of the simulation of radionuclide dispersion has been considered by Onishi and Margvelashvili for one, two and three dimensional models [Onishi, 1977; Margvelashvili 25 University of Ghana http://ugspace.ug.edu.gh et al.1999]. Full-mixed box models have also been used by Booth and Monte [Booth, 1975; Monte, 1993]. 2.5.1 One -Dimensional Transport Model For the simulation of radionuclide transport in several United States rivers, the one- dimensional channel model TODAM has been used [Onishi et al., 1982]. The model describes the transport of radionuclides attached to three typical fractures of the suspended sediments - sand, silt and clay with the specific distribution coefficient (Kd) values for each of them. The Radionuclide transport model is supported by the comprehensive suspended sediment transport model that describes the transport of cohesive and non-cohesive sediments. TODAM does not include the river hydrodynamic model. It was used on the basis of river hydrodynamics calculated by specific codes (DKWAV or HEC-2 or CHARIMA). TODAM was used to simulate Pu-239 transport during flush-flood events in the Mortandad Canyon in New Mexico, USA to reconstruct bottom contamination of the Clinch-River and Tennessee River System due to releases from the Oak Ridge National Laboratory. It was also used to simulate Sr-90 and Cs-137 transport in Dnieper Reservoir after the Chernobyl accident [Zhelenznyak et al., 1995]. The 1-D model of SPA "TYPHOON" State Hydrometeorological Committee of USSR used empirical data on the sediment transport rate and flow [Borzilov et al., 1989]. The model includes more detailed descriptions of the transfer between different forms (oxidation states) of radionuclides. Model parameters have been identified on the basis of experimental data of the Pripyat River spring floods. 26 University of Ghana http://ugspace.ug.edu.gh The 1-D model by Smitz and Everbecq considers kinetics of radionuclide interaction with two size fractions of suspended solids [Smith and Everbecq, 1986]. The model was verified for migration of radionuclides in the Meuse River, and subsequently was extensively applied elsewhere. Several 1-D numerical models have been developed to simulate nonradioactive pollutant transport in rivers. These models do not take into consideration the specification of the radionuclide transport and radionuclide interaction with sediments, however some of them could be, in principle, modified for such purposes. One of the most well known European 1-D modelling system of the pollutant transport in rivers is MIKE11, developed by the Danish Hydraulic Institute [Havno et al., 1995]. MIKE11 is a modelling system for the simulation of flows, sediment transport and water quality in estuaries, rivers, irrigation systems and other water bodies. MIKE11 has been designed for integrated modular structure with basic computational models for hydrology, hydrodynamics, advection -dispersion, water quality and cohesive and non-cohesive sediment transport. It also includes models for the surface runoff. MIKE11 has a well developed graphical user interface integrated with the pre- and postprocessors that support the system interaction with the Geographic Information System (GIS) [Sorensen et al., 1996a]. One-dimensional model RIVTOX was also developed to simulate the radionuclide transport in the solute of suspended sediments and in the bottom depositions. After the Chernobyl accident it has been applied for the prediction of the radionuclide transport in river systems [Zheleznyak et al., 1992]. The model includes a submodel of the 27 University of Ghana http://ugspace.ug.edu.gh radionuclide transport and two submodels of the “driving forces”– a hydrodynamic (hydraulics) submodel and a sediment transport submodel. 2.5.2 Two- Dimensional Transport Model Two-dimensional models are widely used in modelling (simulation) the hydrodynamics and water quality of relatively shallow estuaries, reservoirs, floodplains and coastal areas and wind-driven lakes [Orlob, 1983]. The assumption of these models is the vertically well-mixed layer that allows for vertical integration of the continuity, momentum, and mass-transport equations. From the early 1980s, the 2-D lateral longitudinal models have been widely used as the efficient tool to simulate pollution of water bodies [Taylor and Pagenkopf 1981]. For radionuclide transport, the first comprehensive model (FETRA code) simulating the radionuclide transport in the solute and on the suspended sediments and taking into account the pollutant exchange with the bottom sediments has been developed by Yasuo Onishi [Onishi et al., 1981]. The FETRA code is based on the unsteady state two dimensional equations which simulate the transport, the deposition and the resuspension of sediments and contaminants together with their interactions [Onishi, 1981]. The model describes the transport of cohesive and noncohesive sediments by using the Du Boy formula. FETRA was validated on the basis of experimental data for the James River estuary, Virginia, USA. Recently, FETRA was applied to simulate Sr-90 washout from the Pripyat River floodplain [Onishi, 1981]. The COASTOX model was also developed at the Cybernetics Center, Kiev to simulate the transport and the dispersion of pollutants in the Dnieper reservoirs and in the Pripyat 28 University of Ghana http://ugspace.ug.edu.gh River [Zheleznyak et al., 1992]. It contains the radionuclide transport submodels similar to those used in FETRA. The model takes into account the sediment transport, the transport by the advection-diffusion, and the radionuclide-sediment interactions. It considers the dynamics of the bottom depositions and describes the rate of the sedimentation and the resuspension as a function of the difference between the actual and equilibrium concentration of the suspended matter depending on the transport capacity of the flow. The latter is calculated on the basis of the semi-empirical relationships. The Kd approach has been used for describing the adsorption/desorption and the diffusion transfer of the radionuclides in the systems "solution - suspended sediments" and "solution - bottom deposition". The exchange rates between the solution and the particles are taken into account to obtain the more realistic simulation of the kinetics of the processes. The adsorption and desorption rates are assumed not to be equal. The numerical approach which employs the finite-difference methods are used to solve the equations. The two main differences between FETRA and COASTOX are that the latter has the possibility to calculate non-reversible adsorption processes and that it contains the hydrodynamic submodel. In contrast, FETRA can be used only when coupled with some other hydrodynamical computer codes. COASTOX was applied and validated for the Kiev Reservoir, the Pripyat River floodplain, the Kralova Reservoir, and the Vakh River. 2.5.3 Three -Dimensional Transport Model It is reasonable to provide three-dimensional modelling of the transport of radionuclides in rivers and reservoirs in conditions of large vertical and lateral gradients of the hydrodynamical fields. Such conditions may occur close to the point of the release of 29 University of Ghana http://ugspace.ug.edu.gh radioactive material into water bodies, in the vicinity of heavily contaminated bottom areas, and in stratified water bodies. The FLESCOT model is an unsteady state, three-dimensional, finite difference model [Onishi and Trent, 1979]. It consists of submodels of hydrodynamics, turbulence, water temperature, salinity, sediments (both cohesive and noncohesive) and contaminants (both dissolved and sorbed on sediment). The FLESCOT model also simulates the behaviour of sediments and contaminants in the river bed, affected by erosion/deposition, direct adsorption/desorption between water and bottom sediments, and bioturbation. It can calculate wind-induced flow and wave-induced sediment transport, thus affecting radionuclide transport in shallow water. The model has been applied to the Hudson River estuary in New York for Cs-137 migration and accumulation, to Buzzards Bay/New Bedford Harbor in Massachusetts for Polychlorinated biphenyls (PCBs) and heavy metals to assess their transport and potential remediation activities using a hypothetical 3000m deep ocean for low-level radioactive waste disposal assessment. FLESCOT, like other models of lower dimensions such as TODAM, FETRA, and SERATRA uses multiple bed layers. The first layer (usually taken as a few cm thick) implicitly includes a very thin top layer (assigned as twice the bed sediment grown size) characterised by the chemical equilibrium between the attached and interstitial dissolved form of the radionuclide. Onishi's models also calculate sedimentation and erosion rates for different sediment size fractions taking into account the water flow and sediment characteristics. 30 University of Ghana http://ugspace.ug.edu.gh The three dimensional model THREETOX was included into the Hydrological Dispersion Model (HDM). The specific importance of the code is coupling of hydrodynamic and radionuclide transport models [Zheleznyak and Margvelashvily, 1997]. 2.5.4 Zero-Dimensional Transport Model Box models (also known as compartment models or 0-D models) are widely used tools for ecological modelling in aquatic systems [Orlob, 1983]. Some of the models which were developed to simulate different kinds of pollutants can also be applied for the simulation of the transport of radionuclides in rivers - e.g. EXAMS and WASP4 [Felmy et al., 1983]. Early radionuclide transport models were constructed as box models and were applied mainly for lakes. Box models can be considered as the finite-difference approximation of 1-D river models. It is however mostly only applied on a coarse computational grid [Onishi, 1977]. The two-phase box model (radionuclides in bottom sediments and radionuclides in water) developed by the United States Nuclear Regulatory Commission (USNRC) is a simplification of the five-phase model proposed by Booth. The model has been used for Clinch and Tennessee Rivers case studies [USNRC, 1978]. The SMC model describes the transport of radionuclides in suspended and dissolved forms in river channels [Benes and Cernik, 1990]. It consists of hydrodynamic, sediment transport and radionuclide transport submodels. Distribution of the radionuclide between the water and the suspended solids is described by a kinetic equation for a two-step reversible reaction. The deposition of radionuclide in the bottom sediments depends on 31 University of Ghana http://ugspace.ug.edu.gh the exchange between suspended solids and bottom sediments characterized by an exchange coefficient. The model was used for modelling of migration of Cs-137 accidentally released into the Dudvakh River [Benes et al., 1992]. The sedimentation rate is a parameter of the model and can be tuned during the calculations. Monte's box-model is based on the subdivision of the water body in a set of sub-systems corresponding to the set of reservoirs [Monte, 1993]. In each sub-system the following processes are considered: radionuclide transport due to the horizontal movement of water and suspended matter; radionuclide interaction with suspended matter and with the top sediment layer; migration of radionuclides through the sediment; sedimentation and resuspension. The model accounts for three layers: a first thin top layer in which radionuclides are in chemical equilibrium with the overlying water; a second layer (just below the first) exchanging radionuclides with the overlying water through the top layer and/or with the deeper layer which acts as an ultimate radionuclide sink. The suspended sediment transport and sedimentation rate is not calculated in the model. These values are taken from measured data. The equations are solved using a set of first order differential equations. The model demonstrated reasonable good results in a validation study for the Dnieper reservoir cascade within the Vancouver Additional Matrix Program (VAMP). The WATOX model is a box-type model based on a set of first order differential equations that describes water, sediment and radionuclide transport [Zheleznyak et al.,1992]. Dissolved contamination, contamination on suspended sediment and the contamination of the bottom sediment are considered with a special treatment of the contamination-sediment interaction. The parametrisation of these processes is similar to those used by Schückler. However, some further processes are included. Additionally, a 32 University of Ghana http://ugspace.ug.edu.gh supplementary submodel to simulate the temporal variations of sedimentation- resuspension rates during flood events in reservoirs is included. As described for RIVTOX, COASTOX and THREETOX, WATOX takes into account different Kd values for suspended and bottom sediments, together with different exchange rate coefficients for adsorption and desorption. Model verification shows the high significance of this mechanism for the fate of Cs-137 in reservoirs. The model was tested and calibrated on the basis of post- Chernobyl data for the Dnieper reservoir cascade within the VAMP. The Hofer and Bayer model is a dynamic extension of the above mentioned steady state (static) model developed by Schükler [Hofer and Bayer, 1993]. The dynamics of radionuclide concentrations in filtered water, on suspended sediments and bottom sediments is described by the set of ordinary differential equations on the basis of two different Kd values for adsorption and desorption and exchange rate coefficients. The model coefficients were not calibrated on the basis of measurements. 2.5.5 Analytical Models The analytical models describe the radionuclide fate in rivers on the basis of analytical solution of the equations of box-model or 1-D models with respect to several simplifying assumption (e.g. flow parameters are constant within the river branch, water-bottom radionuclide exchange processes could be described only by one parameter and so on). Examples of this approach are presented by Coppe [Coppe, 1993]. The oversimplification in these approaches ends up in the fact, that the parameters of an analytical model calibrated for one water body cannot be used for other one without significant recalibration. The further development of the computer technique permits nowadays to use numerical models which describe the main significant processes in more detail based 33 University of Ghana http://ugspace.ug.edu.gh on physical characteristics of the site. Analytical model can be used only as a first estimation of the situation. An example is a conservative upper estimation of the radionuclide concentration after accidental releases. Therefore, they will not be considered in this study. 2.5.6 Modelling Radinuclide Exchanges in Water-Suspended Sediment and Bottom Deposition Konoplev has investigated the role of the physical-chemical forms of radionuclides and their transformation processes [Konoplev et al. 1990]. The dissolved fraction of a radionuclide can exist either as cations or as neutral species or as negatively charged complex compounds with dissolved organic substances, or as mineral component of the soil moisture. The cation form of a radionuclide in solution is in equilibrium with the fraction of the radionuclide adsorbed onto the solid particles. In the solid phase, radionuclides can be in exchangeable and non exchangeable form. In their exchangeable form, the radionuclide is sorbed by an ion exchange mechanism. The non-exchangeable form consists of radionuclides which originate from nuclear fuel or are radionuclides absorbed by a mechanism of irreversible sorption (i.e. incorporation into a mineral crystal lattice or formation of radionuclideorganic in soluble compounds, etc.) Benes described the sorption of the radionuclides by means of two parallel or consecutive reactions for ion exchange with two elements bounds at two different sites on the solid phase [Benes et al., 1992].The equation and parameters for all kinetic models were derived for general ion-exchange reactions. 34 University of Ghana http://ugspace.ug.edu.gh Comans studied caesium sorption on potassium and calcium saturated illite [Comans, 1990]. Applying the linearisation method developed by Jannasch to determine the number of processes, three consecutive reactions can be distinguished: one fast, instantaneous reaction and two distinct slow processes [Jannasch et al., 1988]. For investigating the sorption of caesium on time scales of days to weeks which is most relevant for natural systems, two-box and three- box models were suggested and the isotherm of Freundlich was assumed to describe the equilibrium. Intercomparison with experimental data for periods longer than two weeks showed that reversible reaction on calcium-illite was too slow, whereas the second process (irreversible reaction) was too fast. Therefore, a more complicated three- box model was used. This model assumed the existence of the easily accessible sorption sites, where the kinetically controlled processes are followed by irreversible sorption. There is no unified mathematical description of the sorption process governing the behaviour of metals and particulate radionuclides . Further detailed study of the sorption kinetics of radionuclides will be allowed to examine existing concepts in terms of a more fundamental description of the underlying processes. In general, models of radionuclide transport in the rivers/reservoirs do not include the above presented kinetics in their complete details. However, a reasonable level of model complexity which may reflect the main features of the exchange processes (radionuclides transfer in the system “water - suspended sediments - bottom depositions” - transition from a non-equilibrium to an equilibrium state, different Kd value for bottom deposition and suspended sediments, different rates of sorption and desorption) seems to be represented by a “Kd – exchange rate” approach which is used in practically all contemporary models. RIVTOX model used this approach as more complicated two-step 35 University of Ghana http://ugspace.ug.edu.gh 137 kinetic model, describing Cs transfer between exchangeable and non- exchangeable forms [Slavik et al., 1997]. 2.5.7 Modelling River Hydrodynamics and Sediment Transport To simulate the radionuclide transport in rivers, it is necessary to estimate beforehand the river flow and the suspended sediment transport driven by the river hydrodynamic processes. There are a lot of models to simulate river hydraulics and hydrodynamics. The Overviews of the methods are presented by Hoffa [Holly et al., 1990]. The one-dimensional models based on cross-sectionally averaged variables seem to be the most important for the determination of the river flow. There are also known computer codes such as HEC-6 and HEC- 2SR from the Hydrological Engineering Center, MIKE-11 from the Danish Hydraulics Institute and TELMAC from the Laboratory of Hydraulics, EDF, France [HEC, 1977]. The two last ones are commercially distributed modelling systems which include models of different dimensions. HEC-2SR, FLUVIAL 11, CHARIMA, MIKE-11, and TELMAC contain river hydraulic modules based on a numerical solution of the Saint-Venant equation. The possibility of an efficient estimation of river hydraulics on the basis of the numerical solution of the “diffusive wave” equation and the simplified version of the Saint-Venant equation were used. Suspended sediments act as a carrier of radionuclides in the river/reservoir flow. The amount of radionuclides transported by the sediments depends on the suspended sediment concentration in the river flow and the Kd value. After the Chernobyl accident, for 137 example, up to the half of CS transported by the Pripyat River from the vicinity of the 36 University of Ghana http://ugspace.ug.edu.gh Chernobyl Nuclear Power Plant (NPP) was bound on suspended sediments [Zheleznyak et al., 1992]. The sedimentation and bottom erosion processes play a key role in the flow self-purification and in the secondary contamination. For the steady state conditions, the sediment discharges are calculated by the empirical and semi-empirical formulae which connect the sediment discharge with the sediment parameters, the flow velocities and the river cross-section characteristics or shear stress acting on the bed. In case of the cohesive sediments (finest silt and clay) the cohesive bonds between the particles have to be taken into account [Mehta et al., 1989]. The variability of the streams and sediment parameters has resulted in several different formulae being used for the practical applications. It was demonstrated within model validation studies that several approaches show the most acceptable results for non- cohesive sediments over a wide range of flow and sediment conditions. However, for an individual river, the best result can also be obtained by the empirical formulae especially tuned for that river [Onishi, 1993]. The sediment transport models are based on the suspended sediment-mass conservation equation (advection-diffusion equation with the sink-source term describing sedimentation resuspension rate) and the equation of bottom deformation (Exner equation). The most important problem for modelling is the parametrisation of the sedimentation and resuspension rates. A physically based approach calculates these rates as a function of the difference between the actual and the equilibrium concentration of the suspended sediments. This is often titled “suspended sediment capacity” and can be derived on the basis of the above mentioned formulae. The most comprehensive models (e.g. CHARIMA) contain models of the river hydraulic computation and methods to 37 University of Ghana http://ugspace.ug.edu.gh simulate the bottom erosion dependent on the sediment grain distribution in the upper bottom layer (bottom armouring calculation) and to calculate the bottom friction dependent on the simulated dynamics of the bottom forms. Sousa studied the conditions that ensure stability for various finite difference schemes for the advection-diffusion equation, while Hindmarsh examined the stability criteria for the multidimensional advection-diffusion equation [Sousa, 2003]. Dehghan defined and calculated the stability conditions for several numerical methods [e.g. Forward in Time, Centre in Space (FTCS); Forward in Time, Backward in Space (FTBS); Lax-Wendroff; Backward in Time, Centre in Space (BTCS); and Crank-Nicolson methods] for the three- dimensional advection- diffusion equation and compared the numerical and analytical solutions [Dehghan, 2004 ]. Pepper and Okamoto solved the one-dimensional advection equation by using a spline interpolation technique that they called a quasi-Lagrangian cubic spline method [Pepper et al., 1997; Okamoto, 1998]. Ahmad & Kothyari also solved the one dimensional advection-diffusion equation by using cubic spline interpolation for the advection component and the Crank-Nicolson scheme for the diffusion component [Ahmad & Kothyari, 2001]. Sastry used a cubic spline technique to approximate the solution of the one-dimensional diffusion equation [Sastry, 1976]. In the Discontinuous Enrichment Method (DEM), the standard finite element polynomial field is “enriched” by the free-space solutions of the homogeneous partial differential equation (PDE) [Farhat et al., 2001]. Since the enrichment field is related to the underlying equation, it is more effective in resolving sharp gradients and rapid 38 University of Ghana http://ugspace.ug.edu.gh oscillations than piecewise polynomial basis functions. As continuity across element boundaries is no longer automatic, it must be enforced weakly using appropriate Lagrange Multipliers (LMs) [Farhat et al., 2001]. 2.6 Predictive Hydrologic Modelling Software Packages There exist numerous hydrologic modelling software packages. The most commonly employed include the U.S. Army Corps of Engineers (USACE) Hydrologic Engineering Center’s (HEC) series of programs. The most recent released, River Analysis System 9 (HEC-RAS), is an effective hydrodynamic model. HEC-RAS is able to simulate overbanking, construct flood-rating curves, predict bridge scour, and produce three- dimensional representations of river systems. HEC-RAS is a superb modelling tool for predicting near all aspects of a hydrologic event or simulating a typical river discharge [Dyhouse et al., 2003]. Despite the effective modelling capabilities of the HEC-RAS system, the Merrick Advance Remote Sensing (MARS) model does possess several advantages. The most glaring advantage of the MARS model over the HEC-RAS system is the comprehensive structure of its modelling packages that allows for consecutive simulations of hydrodynamics, sediment transport, chemical fate and transport, and remediation measures. While the effectiveness of the Corps’ model is undisputed, MARS’ ability to model contaminated sub-aqueous sediments from hydrodynamics to remediation renders it favorable for application to the Anacostia Active Capping Project (AACP). The HEC- RAS model was used, however, in the development of several of the required inputs for the MARS hydrodynamic model. The Tidal Anacostia Model (TAM) comprises the hydrodynamic component of the modelling framework developed for the Metropolitan 39 University of Ghana http://ugspace.ug.edu.gh Washington Council of Governments. The TAM model has been used effectively by the Interstate Commission on the Potomac River Basin (ICPRB) to predict various hydrologic aspects of the Anacostia River for input into the Water quality Simulation Program (WASP) model to determine sediment transport within the river system. As previously mentioned, the comprehensive modelling offered by the MARS model gives it a distinct advantage for use in the Anacostia Active Capping Project. Results from the TAM model has been used, however, to verify applicable MARS hydrodynamic model predictions [Schultz, 2001]. 2.7 Some study approaches to solving the Advection -Diffusion Equation Analytical solutions, numerical simulations, and experiment and field observations are used to address surface water flow and contaminant transport problems in coastal aquifers. Analytical methods basically provide solutions to governing equations of groundwater flow and contaminant transport with simplified boundary conditions and hydrogeological and chemical properties. Limitations for analytical solutions of surface water flow and contaminant transport in coastal aquifers include: assumptions of a uniform thickness of aquifer, a constant beach face angle, a uniform hydraulic conductivity and specific yield, a single inland boundary condition, and a single-phase homogeneous fluid, among others [Ataie-Ashtiani et al., 1999]. More complicated analytical solutions may take into consideration multiple aquifer layers and tidal fluctuations [Li et al., 1997; Nielson, 1990]. In analytical approach, much attention is given to surface water flow rather than to solute transport. It is extremely difficult or even impossible to derive analytical solutions to solute transport when a more complex system is considered, e.g., a system with one or 40 University of Ghana http://ugspace.ug.edu.gh more aspects among moving and periodic boundary conditions, variable-density flow, heterogeneity of geological settings, physical, chemical, and biological degradations, and multiple dimensions. Numerical modelling has been given more and more attention recently only with the aid of computers. It is more powerful than analytical analysis of a complex system. Unfortunately, even though numerical simulation has the potential to undertake the tasks, a comprehensive simulation model that can account for all the factors has not yet been constructed. Still, numerous numerical models have been developed dealing with one or more facets concerning surface water flow and contaminant transport in coastal aquifers. The major topics that are most frequently considered and intensively studied in numerical modelling include variable density flow and contaminant transport, tidally influenced water table fluctuation or periodic boundary conditions, saltwater-freshwater interface or saltwater intrusion, and sloping beaches and seepage dynamics [Simmons et al., 2001]. One of the most successful models is the saturated-unsaturated transport finite-element ground-water simulation model (SUTRA), developed by Voss which can be used to simulate variable-density flow with chemically reactive single species contaminant transport in saturated-unsaturated formations [Voss, 1984]. Later, Ataie-Ashtiani modified SUTRA such that it can account for periodic boundary conditions and sloping beach faces, in addition to variable density and variably saturated flow [Ataie-Ashtiani et al., 1999]. A potential problem embedded in the existing models is that the built-in boundary conditions are fixed. This boundary condition is not appropriate for the particular problem considered in this study. As a result, a numerical solution has been 41 University of Ghana http://ugspace.ug.edu.gh developed to solve the flow and transport equations directly, incorporating the correct boundary conditions pertinent to the coastal boundary. The widely used models for groundwater flow and solute transport, such as MODFLOW and SUTRA, or the others developed by various authors, do not account for tidal fluctuations. Even though SUTRA modified by Ataie-Ashtiani can incorporate tidal fluctuations, it is based on a boundary condition describing contaminant concentration or flux at the coastal boundary [Li et al., 1997]. Laboratory experimentation is another important and useful tool for the study of surface water flow and contaminant transport. Hydrologists have a long history of utilizing laboratory experiments in the study of surface water flow and contaminant transport. The laboratory experiments, known as Intermediate Scale Experiments (ISEs) have been able to investigate contaminant advection, diffusion, dispersion, and fluid flow in saturated and partially saturated systems, flow and transport in homogeneous and heterogeneous media, transport of contaminants under uniform- and variable-density flow fields, multiphase transport, chemical reactions, particle transport, and microbial interactions, as summarized by Silliman [Silliman et al., 1998]. The experimental study of the impact on flow and transport, however, has been barely conducted by investigators. The few studies include those done by Zhang and Volker [Zhang et al., 2001]. 2.8 The Numerical Approaches to Solving Partial Differential Equations 2.8.1 The Classical Random Walk Contaminant transport has long been modeled as a stochastic sequence of hop and rest periods leading to emergent properties after long time. Random walk and diffusion 42 University of Ghana http://ugspace.ug.edu.gh models are related. Specifically diffusion equations govern the stochastic processes that arise when the scaling limit of random walk is taken. Advection–dispersion equation can be approached from either Lagrangian or Eulerian point of view [Schumer et al., 2009]. 2.8.2 The Lagrangian Approach to the Advection–Diffusion Equation In general it is difficult to solve the advection diffusion equation analytically. Hence it is necessary to resort to numerical methods such as finite difference or finite element methods which are able to incorporate data only as boundary conditions or as calibration parameters [Tandon, 2000]. Based on experimental and theoretical results, the three-dimensional advection-diffusion equation has been solved by the Lagrange approach where the pollutant is represented by a predetermined large number of tracer particles. At any desired time interval, pollutant concentrations are calculated using a local mass balance [Lorin, 1999]. Despite other numerical methods that simulate the contaminant spreading by calculating concentration in a mesh nodes, the particle tracer model tracks several individual particles and then calculates the concentration. The main advantage of the Lagrangian technique over the other widely used numerical methods is the elimination of numerical diffusion but only when a high resolution scheme is used to solve the equations. Test results show that the traditional numerical methods frequently used to solve the particle trajectory equations does not give good solutions and therefore should be avoided [Garcia and Rodrriguez, 1998]. It should be noted that the Lagrangian approach does not solve the advective - diffusive transport equation directly. Rather it gives equivalent results. The discrepancy can be eliminated by adjusting the calibration parameters [Garcia and Rodrriguez, 1998]. 43 University of Ghana http://ugspace.ug.edu.gh 2.8.3 The Eulerian Approach to the Advection-Diffusion Equation In this study, the Eulerian approach to Advection-Diffusion Equation has been employed. The approach is well adapted to transport problems. It preserves the performance of characteristic methods and treats general boundary conditions naturally in their formulations. The approach chooses a particle in a specific location in space and describes particle motion through that location with time. A conservative particle mass equation that relates the rate of mass change at that location with the difference between the mass of particles entering and leaving the location is employed [Schumer et al., 2009]. (2.1) Where, n is the effective porosity (n = 1 for transport at the surface). Particle concentration (C) is mass per unit volume, and flux (F) is the mass per unit area per unit time. If particle flux is assumed by advection and Fickian dispersion, (2.2) Where, v is average particle velocity, λ is the decay constant of the radionuclide and D is the dispersion coefficient. From (2.1) and (2.2) the advection diffusion in one dimension can be written as (2.3) 2.9 The Present Model The fate of radionuclides dispersed in surface water depends on many complex factors. The hydrodynamic, geochemical and biochemical factors all interact in establishing the rate of radionuclide transport. Though a lot of work has been done in this area in other 44 University of Ghana http://ugspace.ug.edu.gh countries, much attention has not been given to it in Ghana. Using the Eulerian method, a finite difference scheme has been employed to find the solution to the advection-diffusion equation derived. The solution has been implemented in MATLAB computer programme to estimate the concentration of NORM isotopes in the Taamang River in order to determine the impact on the public and the environment. 45 University of Ghana http://ugspace.ug.edu.gh CHAPTER THREE 3.0 MATERIALS AND METHODS In this chapter, a theoretical model for the assessment of NORM discharges at the Aboso goldmines in Damang is presented. A conceptual model for surface water flow and contaminant transport is formulated. The model considers surface water flow without tributary or lateral inflow. Initial conditions, boundary conditions and contaminant input are also described, and the solution of the equation is found using the finite difference method. A computer programme is written in MATLAB to implement the solution. A brief description of the study area is also presented. 3.1 Description of the Study Area The study area is the Goldfields Company Limited in Damang, Tarkwa. The Goldfields Company Limited was selected for the study for the following reasons: 1. It is one of the largest gold mining Companies in Ghana with an annual production in excess of 900,000 ounces from its operations in Damang and Tarkwa [Faanu, 2011]. 2. The greater part of the population is distributed around the mines. 3. The major source of water used for drinking, household purposes, irrigation, and livestock watering is considered to be from surface water into which is discharged liquid effluents from the processing plant. 3.1.1 Location and Size Damang Gold Mine is owned and operated by Aboso Goldfields Limited (AGL), a Ghanaian registered company [Gold Fields, 2011]. It is located in South Western Ghana near the Southern end of what is commonly referred to as the Tarkwa Basin, 300 46 University of Ghana http://ugspace.ug.edu.gh kilometres by road West of Accra, the capital of Ghana at latitude of 5° 11’ N and longitude of 1° 57’ W. The Damang concession lies to the North and joins the Tarkwa concession, which is located near the town of Tarkwa. The total population of the Tarkwa Township is about 80,000 [Ofori A, 2008]. The estimated population of the District is 236,000 [Kumah, 2007]. The area is served with good access roads and an established infrastructure. The mine is further served by a main road connected to the port of Takoradi, some 90 kilometres to the South-East. The Damang ore body is hosted by a North-Easterly plunging antiform developed within Tarkwaian sediments. The main Damang pit is located close to the closure of the antiform, and all other known palaeoplacer mineralisation is located on the East and West limbs of the Damang anticline. The Damang concession covers a total area of 25,454 hectares [Gold Fields, 2011]. Damang Fig 3.1 Location of Damang in Ghana 47 University of Ghana http://ugspace.ug.edu.gh 3.1.2 Climate and Vegetation Damang lies within the South-Western Equatorial Zone [Tarkwa Nsuaem Municipal Assembly, 2006]. A tropical climate, with average monthly temperatures between 21°C and 32°C and is characterized by two distinct rainy seasons from March to July and September to November. Average annual rainfall of the site is 2,030 millimetres. The Wassa West District experiences the highest rainfall in Ghana [Tarkwa Nsuaem Municipal Assembly, 2006]. Although there may be minor disruptions to operations during the wet season, there is no operating or long-term constraint on production due to climate [Gold Fields, 2011]. Sunshine duration for most part of the year averages 7 hours per day. Relative humidity is generally high throughout the year between 70 – 80 percent in the dry season and 75 – 80 percent in the wet season. This has an important effect on the environment in creating watersheds, large expanses of stagnant water bodies, deep trenches and gullies as well as leaching the nutrient content of the soil. The forest is full of climbers and lianas, which are able to reach into the upper tree layer. Economic trees include mahogany, wawa, odum, sapele among others. In recent times, most part of the rich forest has been reduced to secondary forest through increased human activity. Human activities like, excessive opening cast mining, farming activities and indiscriminate lumbering, have impacted negatively on the natural vegetation [IFC, 2003]. 3.1.3 Geology and Soil The Damang ore bodies are located within the Tarkwaian sediments, which form a significant portion of the stratigraphy of the Ashanti Belt in South-West Ghana. The Ashanti Belt is a North-Easterly striking, broadly synclinal structure made up of Lower 48 University of Ghana http://ugspace.ug.edu.gh Proterozoic sediments and volcanics underlain by the metavolcanics and metasediments of the Birimian system. The Tarkwaian unconformably overlies the Birimian, and is characterised by lower intensity metamorphism and the predominance of coarse-grained, immature sedimentary units. The Damang Gold Mine exploits oxide and fresh hydrothermal mineralisation in addition to palaeoplacer mineralisation. The hydrothermal mineralisation is located in Tarkwaian sediments and is the only deposit of its kind located on the Eastern side of the Ashanti Belt in South-West Ghana [Gold Fields, 2011]. Fig 3.2: Geology of Ghana showing Damang 49 University of Ghana http://ugspace.ug.edu.gh Fig 3.3: Local geology plan of Damang lease area [Source: Gold Fields, 2011] 3.1.4 Topography and Drainage Damang falls within the forest dissected plateaus physiographic region. Pre-cambrain rocks of Birimian and Tarkwaian formations underlie the forest-disserted plateau. The land rises from about 240 meters to about 300 meters above sea level. The area is generally undulating with few scarps ranging between 150 meters to 300 meters above sea level. The Bonsa, Ankobra and Huni rivers and their numerous tributaries including Buri, Anoni, Sumin, Ayiasu drain the area depicting a dendritics pattern [Tarkwa Nsuaem Municipal Assembly, 2006]. 3.2 Conceptual Model of the Research Problem Effluents discharged into the Taamang River undergo hydrodynamic flow and reach a receptor location. The effluents may contain radionuclides that may be concentrated due to the processing activities of the mines. As the river flows, the contaminant is carried 50 University of Ghana http://ugspace.ug.edu.gh downstream where the river serves as the major source of water for drinking, recreation, household purposes, fishing, irrigation and livestock. The discharge of effluents into the Taamang River and the river flow regime to the receptor location can be represented by a river stream scheme shown below. Inflow boundary Cross sections, Calculation points Outflow boundary Fig 3.4: River stream scheme 3.2.1 Basic river characteristics of the Taamang River The model has been developed to allow the radionuclide concentration in the Taamang River to be calculated at different points along the river. It has been designed to require a minimum input of site specific data. For a discharge into the Taamang River, the hypothetical critical group lives at a distance of about 500 m downstream from the discharged point and on the same side of the river. Other river dimensions obtained were that, the river is 187.47 m wide with an average -1 depth of 2.65 m and velocity of 1.03 ms . According to IAEA Safety Reports Series No. 51 University of Ghana http://ugspace.ug.edu.gh 3 -1 19, these dimensions are compatible with river flow rate of approximately 500.0 m s 2 -1 and dispersion coefficient of 4617 m s [IAEA, 2001]. 3.2.2 Assumptions made in the Model In this model, equation for transport of radionuclides in surface water was used [IAEA, 2001]. The following assumptions were made; 1. No radionuclide was initially present in the river before the discharge occurs. 2. Surface water geometry (e.g. river cross-section, shoreline, etc.) does not change greatly with distance. 3. The river flow characteristics (e.g. river flow velocity, river flow rate, river depth, river width, etc.) do not change significantly with distance and time. 4. Values for flow rates, current velocity and water depth are representative of the lowest annual average conditions occurring over a period of 30 years. The 30 year low annual river flow rate is one third of the mean annual river flow rate. 5. Radionuclides in water and sediment, under the conditions of a routine, long term release can be considered to be in equilibrium. 6. Radionuclides adsorbed onto sediments in water, reducing the dissolved radionuclide concentration in the water column are neglected. 7. Chemical processes such as radionuclide volatisation are neglected. 3.3 Surface Water Flow Equations Radionuclides discharged into surface waters are subjected to a series of physical and chemical processes that affect their transport from the source point. These processes include [IAEA, 2001]; 52 University of Ghana http://ugspace.ug.edu.gh 1. Flow processes, such as downcurrent transport (advection) and mixing processes (turbulent dispersion); 2. Sediment processes, such as adsorption/desorption on suspended, shore/beach and bottom sediments, and downcurrent transport, deposition and resuspension of sediment, which adsorbs radionuclides; 3. Other processes, including radionuclide decay and other mechanisms that will reduce concentrations in water, such as radionuclide volatilization. In general, radionuclide transport and fate in surface water may be expressed as an Advection-Diffusion/Dispersion Equation. The mass balance in this case can be written in the following form: (Change of mass in the control volume in time interval ∆t) = (Mass entering the control volume in ∆t) – (Mass leaving the control volume in ∆t) Mass entering Mass leaving the control volume the control volume ∆X Positive x direction Fig 3.5: Mass balance of the pollutant transport in x-direction Thus, (Rate of Accumulation -Rate of Production) = (Rate of Input-Rate of Output) 53 University of Ghana http://ugspace.ug.edu.gh Mathematically, (3.1) Where, Kx, Ky and Kz are hydraulic conductivities in the x, y and z directions respectively, h is the hydraulic head and R is the source term t is time m is mass in the control volume If represents the flux of the particular dissolved constituent (in this case the radionuclide) into and out of a given volume element of the river, then from (3.1), (3.2) As the effluents are released into the water body, they are transported by advection, diffusion and/or dispersion (turbulence) processes. The concentration patterns are largely controlled by turbulent diffusion. This process depends on how turbulent the water body is at a given time and space. The advective flux ( ) is described by the product of velocity and concentration as follows; (3.3) Where, are the mean water velocities in the x, y and z directions respectively, ε is the fraction of space called the porosity and C is the concentration of the radionuclide. Note that, (3.4) 54 University of Ghana http://ugspace.ug.edu.gh From Fick’s law of diffusion, the number of particles passing from one medium into another in a unit time per unit area (flux) is proportional to the concentration gradient. Hence (3.5) Where, is the constant of proportionality. D is called the effective molecular diffusion coefficient in the porous medium. Therefore, , (3.6) Where, Dx, Dy and Dz are diffusion/dispersion coefficients in the x, y and z directions respectively and is the porosity. Now combining advection and diffusion in equations (3.3) and (3.6) respectively, (3.7) Substituting (3.7) into (3.2) in 1D gives, (3.8) Where, Hence, (3.9) Assume that there is uniformity in the porosity, thus is constant in all directions. Dividing through by and re-arranging gives, 55 University of Ghana http://ugspace.ug.edu.gh (3.10) But, (3.11) Where, N is the number of radionuclides present. Also, , Hence, (3.12) From equation (3.12), (3.13) Substituting (3.13) into (3.10) and rearranging gives a resulting constituent transport equation in one direction for a continuous release as (3.14) Where, 3 C - Radionuclide concentration (Bq/m ) Vx - Component of flow velocity in x direction (m/s) x - Longitudinal direction (m) 2 Dx -Turbulent Diffusivity in x direction (m /s) -1 λ - Radionuclide decay constant (s ) t -Time (s) The Partial Differential Equation (PDE) in (3.14) describes the rate of change of radionuclide concentration with time and distance. The one dimensional simplification is accomplished by averaging over the river cross-section. Equation (3.14) is similar to the 56 University of Ghana http://ugspace.ug.edu.gh one dimensional advective-dispersive contaminant-transport equation describing the time rate of change of contaminant concentration subject to variable flow velocity and dispersion coefficient proposed by Euler [Schumer et al., 2009]. (3.15) Rearranging (3.15) gives, , Note, (3.16) Where, 2 A - Main channel cross-sectional area of the river [L ] -3 C - Main channel solute concentration of the river [ML ] 2 -1 D - Dispersion coefficient [L T ] 3 -1 Q - Volumetric flow rate of the river [L T ] t - Time [T] x - Distance from the discharged point [L] -1 λ - Decay rate of radioactive nuclide [T ] 3.3.1 Initial Conditions The initial conditions considered are 0 The value zero shows that no contaminant was discharged. Commonly used initial conditions include a constant value representing a uniform initial distribution of contaminant over the entire river, a function f(x) of the location along the flow system, or an exponentially increasing or decreasing function for a more realistic distribution after a certain period of time since the first release of contamination. In the current study, the 57 University of Ghana http://ugspace.ug.edu.gh initial condition is chosen to be zero contaminant concentration over the entire river. This is used in conjunction with an appropriate boundary condition to simulate pollution release at any time and consequent movement along the river corridor. 3.3.2 Boundary Conditions Three types of boundary conditions are generally associated with the contaminant- transport equation: the Dirichlet (or first-type), Neumann (or second-type), and Cauchy (or third-type) boundary conditions. For a one-dimensional problem, they can be described as follows [Yuan Ding and Yong Peng, 2009]. 1. The first-type boundary condition specifies the value of the concentration along a cross-section of the flow and transport boundary as Where, g(t) is the measured concentration in the effluent water as a function of time. 2. The second-type boundary condition specifies the gradient in solute concentration along a cross-section of the boundary as Where, p(t) is the measured concentration gradient in the effluent water as a function of time. 3. The third-type boundary condition specifies the flux of solute across the boundary as 58 University of Ghana http://ugspace.ug.edu.gh Where, f (t) is the measured concentration in the flow as a function of time [Yuan Ding and Yong Peng, 2009]. These three types of boundary conditions are used to describe the conditions at the effluent ends of a flow system. In this study, the effluent boundary is generally assigned with the second-type boundary condition to specify a constant or variant effluent of contaminant source. Application of the first-type boundary condition presumes that the concentration gradient across the boundary equals zero as soon as flow begins, which may lead to overestimation of the mass of contaminant in the system at early times. The second and third-type boundary conditions allow for contaminant concentration at the effluent boundary to be lower than the effluent concentration initially, and then to increase as more contaminant enters the system. Over time, the concentration gradient across the boundary decreases as the concentration at the effluent boundary approaches the effluent concentration, which eventually reaches the case of the first type boundary condition [Yuan Ding and Yong Peng, 2009]. 3.3.3 Contaminant Input For the effluent end of the river, the first or the second-type boundary condition is generally used to specify a constant input of contaminant source. For example, a continuous contaminant input at the effluent boundary at a constant rate may be simply represented by the equation below, assuming it is well-mixed instantly over the entire vertical section, And, a pulse-type input can be represented by 59 University of Ghana http://ugspace.ug.edu.gh Where, is the time span of the contaminant release (assuming release starts at time zero). When considering the contamination release and discharge problem in industrial sites, this situation is realistic in the sense that generally industries or waste sites release pollution in a finite time period, either because industrial firms have a finite life or the pollution problem is controlled after a certain time with the awareness of the contamination or government regulation. Contaminant concentration at the boundary can be set to vary over period as a result of a variable discharge rate, but it would be more convenient to set it as a constant to simplify the problem without resulting in significant detriment to this study [Yuan Ding and Yong Peng, 2009]. 3.4 Development of the Finite Difference Solution Finite difference method has been employed to obtain a solution to the partial differential equation in (3.14) above. The main idea behind the use of the finite difference method was to approximate the derivatives appearing in the equation by a set of values of the function at a selected number of points. The time and distance have been discretised and using Euler’s forward and backward difference, a matrix has been generated to determine the concentration of natural radionuclides in the Taamang River. To apply the finite difference method to the partial differential equation, the following steps are involved: 1. Derive a Partial Differential Equation 60 University of Ghana http://ugspace.ug.edu.gh 2. Employ a finite difference mesh of uniformly spaced grid lines for the independent variables 3. Discretise the independent variables into specific intervals 4. Develop finite difference equations by minimizing errors caused by the approximation. 5. Solve the resulting set of equations by applying the initial and boundary conditions. 3.4.1 Euler’s Method From Eulerian approach, equation (3.14) can be written as (3.17) Employing a finite difference mesh to equation (3.17) and discretising the distance and time axes into intervals of ∆x and ∆t respectively. A mesh of uniformly spaced grid-lines are introduced as Where, M denotes the total number of spatial grid-spacing and N denotes the total number of temporal grid-spacing. Applying the finite difference approximation, these formulations are obtained as; (3.18) Where, is the mean diffusive coefficient between the grids 61 University of Ghana http://ugspace.ug.edu.gh (3.19) Where, is the mean diffusive coefficient between the grids t i, j+1 O Dip/qip i-1, j i, j i+1, j j ∆t i, j-1 ∆t x ∆x i ∆x Dim/qim Fig 3.6: One-Dimensional Discretisation of the Model Domain Now approximating the derivatives using Euler’s forward difference in time and backward difference in space at point O (Fig 3.7), we have the following [Everstine, 2010] (3.20) 62 University of Ghana http://ugspace.ug.edu.gh (3.21) With the central finite difference as (3.22) Inserting (3.20), (3.21) and (3.22) into (3.17) gives (3.23) Multiplying through by ∆t and rearranging gives, (3.24) Hence, (concentration at next step) given (concentration at current time step) can be computed as follows; (3.25) For simplicity, let (3.26) (3.27) Substituting (3.26) and (3.27) into (3.25) gives, (3.28) Expanding (3.28) gives, (3.29) 63 University of Ghana http://ugspace.ug.edu.gh Collecting terms involving + ) + 1)+ , +1, (3.30) Rearranging (3.30) gives, + ) + + (3.31) Simplifying further gives, + + (3.32) Where, + From (3.32), when + + (3.33) When , + + (3.34) Also for all j, (3.35) Applying the Neumann boundary condition at , we have (3.36) Equation (3.36) above implies that for all t, (3.37) 64 University of Ghana http://ugspace.ug.edu.gh Substituting (3.37) into (3.34) for all t gives + + (3.38) Hence, + (3.39) This system of equations for n nodes can be written in matrix notation by applying the initial and boundary conditions as, = (3.40) The numerical solution to the matrix above is implemented in MATLAB which is used to determine the concentration of the natural radionuclides in the river. 3.5 Model Implementation using MATLAB MATLAB (matrix laboratory) is a numerical computing environment and fourth- generation programming language. Developed by MathWorks, MATLAB allows matrix manipulations, plotting of functions and data, implementation of algorithms, creation of user interfaces, and interfacing with programs written in other languages, including C, C++, Java, and Fortran. An additional package, Simulink, adds graphical multi-domain simulation and Model-Based Design for dynamic and embedded systems [Moler, 2006]. MATLAB code transport.m has been used to solve equation (3.39) with appropriate initial and boundary conditions. Transport .m is for implicit flow and decay model of the 65 University of Ghana http://ugspace.ug.edu.gh polluted river. The application of the MATLAB code determines the radioisotope concentration with respect to space and time. The implementation of the above model to determine the concentration depends on both space and time and will have nested loops where the outer loop is for discrete time and the inner loop is for discrete space. In the MATLAB code transport.m, these nested loops are given in lines 50-58 and in lines 65-75. Lines 1-14 contain the input data. Lines 79- 103 contain the output data in the form of a surface plot for the concentration. The results of the implementation of the finite difference solution in equation (3.39) in MATLAB has been presented and discussed in the next chapter. 3.6 Committed Effective Dose Estimation from Radioactive Effluent Discharges The ingestion doses for infants and adults are calculated using the following general equation, (3.41) Where, is the annual effective dose from consumption of radionuclide (Sv/y) is the concentration of radionuclide i in drinking water at the time of consumption 3 (Bq/m ) 3 is the consumption rate for drinking water (m /y) is the dose coefficient for ingestion of radionuclide i (Sv/Bq) 66 University of Ghana http://ugspace.ug.edu.gh The dose coefficient values given are those recommended in the BSS for all unspecified compounds for the purpose of calculating doses [IAEA, 2001]. 67 University of Ghana http://ugspace.ug.edu.gh CHAPTER FOUR 4.0 RESULTS AND DISCUSSIONS This chapter provides the results obtained from modelling natural radionuclides in the Taamang River from liquid effluents discharges from the gold processing plant of the Aboso gold mines in Damang. Implementation of the numerical solution to the Advection-Diffusion Equation in MATLAB code transport.m, has been used to estimate the concentrations of the natural radionuclides in the river. Considering a river that has been polluted upstream, the concentration (amount per volume) will reduce and disperse downstream. It is possible to predict at any point in time and space the concentration of the pollutant. The results of the simulation are grouped into two categories depending on the half-life of the radionuclides considered in this study: 1. Simulation of Short-Lived Natural Radionuclides, and 2. Simulation of Long-Lived Natural Radionuclides. A default amount of the radioanuclide was kept constant at the point of discharge in the river for all the simulations over the entire period. In the present study, the concentration of the pollutant and annual committed effective dose were estimated at distances of 100 m, 200 m, 300 m, 400 m and 500 m from the point of release in order to determine the fate of the radionuclide. At 500 m from the released point, the Taamang river water is used by the public for drinking, cooking, etc. Hence the public are likely to receive the maximum dose at 500 m from the released point. The results of the simulation are shown in Figures 4.1- 4.10. 68 University of Ghana http://ugspace.ug.edu.gh 4.1 Distribution of Short-Lived Natural Radionuclides For short-lived radionuclides, the maximum concentration is built up at the point of release. As soon as it is mixed with the river water, the radionuclide concentration reduction process initiates and the dilution of pollutant in the river water starts. Radionuclides considered under this category are Radium-224 and Polonium -210 with half-lives of 3.66 days and 138 days respectively. 4.1.1 Simulation of Radium-224 Figure 4.1 is a 3-D plot of the variation of the concentration of Radium-224 with distance and time. Figure 4.2 is a 2-D plot of the variation of concentration of Radium-224 with distance and time. 8 6 4 2 0 500 450 400 350 4000 300 3500 250 3000 200 2500 150 2000 100 1500 50 1000 0 500 Distance from Release Point (m) 0 Time since Release (h) Fig 4.1: 3-D Plot of Variation of the Concentration of Radium-224 with time and distance from discharge point 69 Concentration of Ra-224 (Bq/m3) University of Ghana http://ugspace.ug.edu.gh 1 t=1000h 0.9 t=1050h t=1100h 0.8 t=1150h t=1200h 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0 50 100 150 200 250 300 350 400 450 500 Distance from Release Point (m) Fig 4.2: 2-D Plot of Variation of the Concentration of Radium-224 with time and distance from discharge point The results shown in Figures 4.1 and 4.2 demonstrate that the radioisotope is rapidly diluted in the river at a distance of approximately 100 m and eventually disappears at a distance of about 300 m from the release point. This is due to reduction processes such as radioactive decay and other processes including diffusion of the discharged radionuclide in the river. The concentration decreases as distance increases from the point of release and eventually approaches zero. The concentration approaches zero at 300 m from the release point. This means that the radionuclide decays completely while being transported by the river before reaching the receptor location. 70 Concentration of Ra-224 (Bq/m3) University of Ghana http://ugspace.ug.edu.gh 4.1.2 Simulation of Polonium -210 Figures 4.3 and 4.4 show results of the simulations performed for Polonium-210 radinuclide over a specific time interval. Figure 4.3 is a 3-D plot of the variation of concentration of Polonium–210 with respect to distance and time from the discharged point. Figure 4.4 is a 2-D plot of the variation of the concentration of Polonium-210 with respect to distance and time from the discharged point. 8 6 4 2 0 500 450 400 350 3500 4000300 250 3000 200 2500 150 2000 100 1500 50 1000 0 0 500 Distance from Release Point (m) Time since Release (h) Fig 4.3: 3-D Plot of the Variation of the Concentration of Polonium-210 with time and distance from discharge point 71 Concentration of Po-210 (Bq/m3) University of Ghana http://ugspace.ug.edu.gh 1 t=1000h 0.9 t=1050h 0.8 t=1100h t=1150h 0.7 t=1200h 0.6 0.5 0.4 0.3 0.2 0.1 0 0 50 100 150 200 250 300 350 400 450 500 Distance from Release Point (m) Fig 4.4: 2-D Plot of Variation of the Concentration of Polonium-210 with time and distance from discharge point The results in Fig 4.3 and Fig 4.4 show that the concentration remains constant until the radionuclide travels about 100 m from the release point. The concentration of the radionuclide then reduces due to radioactive decay and other processes and eventually approaches zero at about 300 m from the release point as it is mixed with the river water and subsequently moves away from the discharged point. A significant fraction of the total concentration released can thus be stored in the bottom sediments over the course of the river flow from the release point. It can be inferred that about 95% of the discharged pollutant is diluted at a distance of 300 m. Hence the impact of the radionuclide may not be felt by the users of the river at about 300 m and beyond from the discharged point. 72 Concentration of Po-210 (Bq/m3) University of Ghana http://ugspace.ug.edu.gh 4.2 Distribution of Long-Lived Natural Radionuclides Results of the simulation of long-lived radioisotopes with half-lives of several years show an accumulation of the radionuclide as the discharge commences and gradually decreases in concentration with time. Even though these radionuclides have longer half-lives, the reduction in the concentration may be attributed not only to decay but to diffusion of the radionuclide as well as adsorption by aquatic plant, sediments, etc. However, some amount of the radioisotope is present at the receptor location. This is illustrated in Figures 4.5 to 4.10 for Radium-226, Uranium-238 and Thorium-232. 4.2.1 Simulation of Radium-226 Figures 4.5 and 4.6 show the results of the simulation of Radium-226 with distance and time. Figure 4.5 shows a 3-D plot of the variation of Radium-226 with distance and time. 8 6 4 2 0 500 450 400 350 4000 300 3500 250 3000 200 2500 150 2000 100 1500 50 1000 0 5000 Distance from Release Point (m) Time since Release (y) Fig 4.5: 3-D Plot of Variation of the Concentration of Radium-226 with time and distance from discharge point 73 Concentration of Ra-226 (Bq/m3) University of Ghana http://ugspace.ug.edu.gh 1 t=1000y t=1050y 0.8 t=1100y t=1150y t=1200y 0.6 0.4 0.2 0 0 50 100 150 200 250 300 350 400 450 500 Distance from Release Point (m) Fig 4.6: 2-D Plot of Variation of the Concentration of Radium-226 with time and distance from discharge point The results in Fig 4.5 and Fig 4.6 show a gradual decrease in the concentration of the radioisotope with some amount downstream. After the discharge, the concentration is found to range between approximately 0.02 Bq/L and 0.1 Bq/L at a distance of 500 m from the discharge point. This means that a fraction of the radionuclide concentration has not been reduced. In case of decreasing dispersion in an accelerated flow field, the concentration will reach the danger level in a region away from the source of the pollution, in the longest time. 74 Concentration of Ra-226 (Bq/m3) University of Ghana http://ugspace.ug.edu.gh Hence, some amount of the radionuclide is expected at the receptor location. It may therefore not be advisable for users residing 500 m from the discharged point (critical group) to use water from the river depending on the discharge rate. 4.2.2 Simulation of Uranium-238 The results from the simulation of Uranium-238 show that some amount of the radionuclide is present at the receptor location. Figures 4.5 and 4.6 show the variation of the concentration of Uranium-238 with respect to time and distance. A similar trend as seen in the simulation of Radium-226 is observed. 8 6 4 2 0 500 450 400 350 4000 300 3000 3500250 200 2000 2500150 100 150050 1000 0 0 500 Time since Release (y) Distance from Discharge Point (m) Fig 4.7: 3-D Plot of Variation of the Concentration of Uranium-238 with time and distance from discharge point 75 Concentration of U-238 (Bq/m3) University of Ghana http://ugspace.ug.edu.gh 1.1 t=1000y 1 t=1050y t=1100y 0.9 t=1150y t=1200y 0.8 0.7 0.6 0.5 0.4 0 50 100 150 200 250 300 350 400 450 500 Distance from Release Point (m) Fig 4.8: 2-D Plot of Variation of concentration of Uranium-238 with time and distance from discharge point The results indicate that the concentration of Uranium-238 remains constant until it is transported up to a distance of 200 m from the release point and consequently reduces slightly. The concentration varies between 0.38 Bq/L, and 0.70 Bq/L. This shows that some amount of the radionuclide would be present at 500 m from the release point where the river is used by the public. Users of the river at this location may be exposed to some amount of the naturally occurring radionuclide, Uranium-238. 76 Concentration of Uranium-238 (Bq/m3) University of Ghana http://ugspace.ug.edu.gh 4.2.3 Simulation of Thorium-232 Figures 4.9 and 4.10 illustrate the variation of Thorium-232 with time and distance from the discharge point. The results indicate that the concentration of the radionuclide is accumulated at the discharge point. However, as the radionuclide travels downstream, its concentration decreases slightly, 300 m from the discharged point and beyond. 8 6 4 2 0 500 450 400 350 3500 4000300 250 3000 200 150 2000 2500 100 1500 50 1000 0 0 500 Distance from Release Point (m) Times since Release (y) Fig 4.9: 3-D Plot of Variation of the Concentration of Thorium-232 with time and distance from discharge point 77 Concentration of Th-232 (Bq/m3) University of Ghana http://ugspace.ug.edu.gh 1.05 t=1000y t=1050y 1 t=1100y t=1150y 0.95 t=1200y 0.9 0.85 0.8 0.75 0.7 0.65 0 50 100 150 200 250 300 350 400 450 500 Distance from Release Point (m) Fig 4.10: 2-D Plot of Variation of the Concentration of Thorium-232 with time and distance from discharge point It should be noted that due to the long half-life of Thorium-232, a significant amount of the radionuclide could be found at 500 m from the release point. At the receptor location, the concentration varies approximately between 0.66 Bq/L and 0.90 Bq/L. This shows that users of the river living as far as 500 m from the discharged point may receive some radiation doses. 78 Concentration of Th-232 (Bq/m3) University of Ghana http://ugspace.ug.edu.gh 4.3 Comparison of Results with Published Data Since field data were not available in the study area, the results obtained from the model were compared with the results of the radiological studies carried out on some surface water in the Tarkwa mining area by Faanu et al (2011) and other publications. Table 4.1: Comparison of results from current study with data from other Publications. Location Type of Distance Activity Reference Surface from Concentration (Bq/L) Water Discharge 238 232 Point (m) U Th * Damang Taamang 500 0.54 0.78 This Work Ghana River (2013) *HuniValley Huniso N/A 0.76±0.03 0.41±0.02 Faanu et al Ghana River (2011) *Bonsaso Bonsa 30 000 0.11±0.09 0.52±0.04 Faanu et al Ghana River (2011) Kota Tinggi Lebam, (1.81±0.01) (1.03±0.01) Ahmad et al -3 -3 district, Johor, N/A x10 x 10 (2004) Malaysia Lukah -3 -3 Kinta Tumbor N/A 0.24x10 0.21x10 Ahmad et al District, River to to (2009) -3 -3 Malaysia 31.9x10 5.69x10 Likuyu, Mkuju 54000 2.5 ± 0.4 1.9 ± 0.2 Najat et al Tanzania River (2013) Kilowelo 2.2 ± 0.3 1.8 ± 0.1 River * Within the Tarkwa Municipality in the Western Region of Ghana N/A- Not Available Table 4.1 shows comparison of the results from this study with data from other 238 publications. According to Faanu et al (2011), the average activity concentrations of U 79 University of Ghana http://ugspace.ug.edu.gh 232 and Th were respectively 0.11±0.09 Bq/L and 0.52±0.04 Bq/L for river Bonsaso at a distance of 30 km at a remote location from the discharge point. Similarly, the average 238 232 concentrations of U and Th in samples from the Huniso River were 0.76±0.03 Bq/L and 0.41±0.03 Bq/L respectively. Also, a study carried out in some rivers in the Kota Tinggi district in Malaysia revealed that, the average activity concentration of Uranium-238 and Thorium-232 in the water samples were 1.8±0.01 mBq/L and 1.03±0.01 mBq/L respectively [Ahmad et al., 2004]. Similarly, in the Tumbor River in the Kinta district, the activity concentrations varied 238 232 from 0.24 mBq/L to 31.96 mBq/L and 0.21 mBq/L to 5.69 mBq/L for U and Th respectively [Ahmad et al., 2009]. The low concentrations may be attributed to the fact that the study was not done close to a mining site. In the study of Natural Radioactivity in water from Likuyu Village in the neighborhood 238 of Mkuju uranium deposit in Tanzania, the average activity concentration of U and 232 Th were 2.5±0.4 Bq/L and 1.9±0.2 Bq/L respectively for samples from the Mkuju River. For the Kilowelo River, the average concentrations were 2.2±0.3 Bq/L and 1.8±0.1 3 238 232 Bq/m for U and Th respectively. The highest mean values of the radionuclides were found in samples from northern and southern parts of Lukuyu village, which might be influenced by the flow of rivers Mkuju and Kilowero from the Mkuju uranium deposit to the village[Najat et al.,2013], . Additionally, the current model has been compared with similar work done by Malik (2001). He used the HydroTrack model to simulate the transport of radioactive pollutants in a sewage system by the application of Lagrangian random-walk methods to model the 80 University of Ghana http://ugspace.ug.edu.gh turbulent dispersion. Preliminary results revealed that the concentration of pollutant increases with time at a point of release and decreases due to concentration reduction processes. The concentration decreases rapidly as the distance increases from the point of release [Malik, 2001]. 4.4 Activity Concentration and Annual Committed Effective Dose from Ingestion of water from the Taamang River at various Receptor Locations The ICRP philosophy of radiological protection aims at preventing deterministic effects and also reducing the occurrence of stochastic effects of cancer and hereditary diseases to acceptable levels. This is achieved by a system of protection that requires justification of practice to ensure it produces a net benefit, optimisation of protection to keep exposures as low as reasonably achievable (ALARA) and the protection of individuals by imposing either dose limits or controls on the risks from potential exposures [ICRP, 2007]. As a result, the potential exposure of the population in the study area was assessed by estimating the annual committed effective doses from the activity concentration at various receptor locations for purposes of comparison with recommended dose limits. In the current study, the activity concentrations and corresponding annual committed effective doses are high at distances closer to the discharged point. The average activity concentrations were 0.06 Bq/L, 0.54 Bq/L and 0.78 Bq/L with corresponding committed 226 238 232 effective doses of 0.01 μSv/y, 0.06 μ Sv/y, and 0.011 μSv/y for Ra, U and Th respectively at a distance of 500 m from the discharged point where the critical group resides. Table 4.2 shows the activity concentrations and the annual committed effective doses for various receptor locations. 81 University of Ghana http://ugspace.ug.edu.gh Table 4.2: Activity Concentration and Annual Committed Effective Dose from 226 238 232 consumption of Ra, U and Th in the Taamang River at various Receptor Locations Radionuclide Distance from Average Activity Average Annual Discharged Point Concentration Committed (m) (Bq/L) Effective Dose (μSv/y) 226 Ra 100 1.00 0.17 238 U 1.00 0.03 232 Th 1.00 0.14 226 Ra 200 0.93 0.16 238 U 1.00 0.03 232 Th 1.00 0.14 226 Ra 300 0.54 0.09 238 U 0.96 0.02 232 Th 0.99 0.14 226 Ra 400 0.19 0.03 238 U 0.81 0.02 232 Th 0.92 0.13 226 Ra 500 0.06 0.01 238 U 0.54 0.06 232 Th 0.78 0.11 82 University of Ghana http://ugspace.ug.edu.gh CHAPTER FIVE 5.0 CONCLUSIONS AND RECOMMENDATIONS This chapter provides the major conclusions and relevant recommendations made to stake holders about how radiological health and safety policies of gold mining companies in Ghana can be improved. 5.1 Conclusions The release of radioactive materials into the environment during normal operations or under emergency conditions may lead to adverse health effects. The concentrations received by the public from natural radiation are important since they constitute the largest dose received by the world’s population. The present study describes the use of a mathematical model to simulate transport of Natural Radionuclides that decay in time. The simulated distribution of the radionuclide is able to trace the concentration of the radioisotopes from the point of contamination to the receptor location. At the receptor locations, the concentrations were approximately 224 210 zero for both Ra and Po. However, for long-lived radionuclides, the average activity concentrations were 0.06 Bq/L, 0.54 Bq/L and 0.78 Bq/L at 500 m from the discharged 226 238 232 point where the water is used by the public for Ra, U and Th respectively. The average annual committed effective doses estimated were 0.01 μSv/y, 0.06 μSv/y, and 226 238 232 0.11 μSv/y for Ra, U and Th respectively. It can be inferred from the fact that the concentrations of pollutants in the surface water decrease downstream of the mine waste discharge point and that there is a large dilution due to dispersion and decay in the water body. The possibility also exists that part of the 83 University of Ghana http://ugspace.ug.edu.gh pollutants are absorbed on cave clays that are present in the river channels. However, long-lived natural radionuclides were present at the receptor location because of their long half-lives. The results of the study show that the water body in the study area may have higher concentration of natural radionuclides at the point of discharge compared to the receptor location. The activity concentrations measured are far below the ICRP recommended level of 1000 Bq/L for which remedial action is needed. The annual committed effective doses are also lower than the 1 mSv per year dose limit recommended by the ICRP for public radiation exposure control [WHO, 2004; ICRP, 1990; 2007]. The results indicate insignificant levels of the natural radionuclides, implying that the mining activities do not pose any significant radiological hazard to the communities in this area. Even though the activity concentrations and the annual committed effective doses are far below recommended levels, studies have shown that long term accumulation of NORM may call for health concern [Von et. al., 2012]. The study has proven to be capable and comprehensive means of modelling the river and the associated natural radionuclide transport. With future revisions, it is hoped that the findings from the use of the model can aid in developing strategies for mitigating the consequences of discharges when they exceed authorized limits. 5.2 Recommendations Recommendations made in this study have been put into three categories: 1. Recommendations for future study 2. Recommendations to Gold mining Companies and 84 University of Ghana http://ugspace.ug.edu.gh 3. Recommendations to the Radiation Protection Board (RPB) and the Environmental Protection Agency (EPA). 5.2.1 Recommendations for future study 1. It is recommended that simulation of radionuclides continues in other sewage outfalls situated in other mining sites. 2. It is also recommended that water velocity at different pollutant locations and other parameters be studied to establish the direction of flow of pollutant particles at a particular location. 3. There is also a need for field measurements to be conducted in order to ascertain the validity of the model. 5.2.2 Recommendations to Gold mining Companies 5.2.2.1 Water Management Planning Site-specific surface water management plan should be developed and implemented by mining companies. The plan should include: 1. The identification of the mine property subwatersheds, including those for mine waste areas, drainage flow paths, and receiving water bodies; 2. Analysis of the local groundwater regime, including flow direction and rates, recharge and discharge areas, and relationship with the local surface water regime; 3. Descriptions of measures to be implemented to manage water; 4. The identification and assessment of opportunities for diverting natural runoff away from the mine site to prevent pollution of water bodies; 85 University of Ghana http://ugspace.ug.edu.gh 5. Indication of the locations of mine water and seepage sampling stations and mine waste areas; 6. Monitoring of water quality and level in retention facilities, such as tailings management facilities, sedimentation ponds and polishing ponds; and 7. Inspection of drainage ditches and dikes for sediment accumulation and bank erosion and damage. 5.2.2.2 Water Use and Recycling Ore processing facilities should be designed to: 1. Minimize the volume of fresh water that is used for ore processing by: i. Using ore processing methods that require less water; and ii. Maximizing the recycling of water to reduce requirements for freshwater intake; and 2. Avoid or minimize the use of reagents that require treatment prior to effluent discharge. 5.2.2.3 Diversion of Clean Runoff and Consolidation of Wastewater Streams In planning the site layout, consideration to be given should include: 1. Consolidating to the degree practicable all facilities that are potential sources of wastewater with similar characteristics and treatment requirements; 2. Diverting all clean streams and drainage runoff away from areas of possible contamination by constructing ditches or dikes; and 3. Locating effluent discharge points away from environmentally sensitive areas. 86 University of Ghana http://ugspace.ug.edu.gh 5.2.3 Recommendation to the Radiation Protection Board (RPB) and the Environmental Protection Agency (EPA) 5.2.3.1 Safe Drinking Water Act Under the provision of the Safe Drinking Water Act (SDWA), the EPA should issue drinking water standards for NORM. These standards for the protection of both underground water and surface water will prohibit the disposal of NORM that could jeopardize drinking water quality. The RPB should also regulate the discharge of radioactive materials into surface water. Also, specific effluent limits should be established for low-level NORM discharges. Regulatory requirements are needed in order to predict doses to the critical group. There is the need to set levels of annual doses for (i) exemption/exclusion (ii) authorization by licensing and (iii) authorization by registration 5.2.3.2 Environmental Auditing Periodic environmental audits should be conducted to determine: 1. Whether the site is operating in compliance with applicable regulatory requirements and appropriate non-regulatory and corporate requirements. For authorization by licensing, specific conditions will be required for: (i) Discharge limits (ii) Effluent and environmental monitoring (iii) Reporting of monitoring to the regulatory body (RPB); and 2. Whether the Environmental Management Systems (EMS) and other environmental plans have been properly implemented and maintained. 87 University of Ghana http://ugspace.ug.edu.gh REFERENCES  Abraham J.P., Whicker, F.W., Hinton T. G., Rowan D.J. (2000): Inventory and 137 spatial pattern of Cs in a pond: a comparison of two survey methods. Journal of Environmental Radioactivity, 51(2): 157–171.  Addy Samuel N. (1998):‘Ghana: revival of the mineral sector’, Resource policy, vol. 24(4): 229-239.  Ahmad Z., Kothyari U.C. (2001): Time-line cubic spline interpolation scheme for solution of advection equation. Computer & Fluids, 30(6): 737-752.  Ahmad T. R. (2009): Health Risk Implications of High Background Radiation Dose Rate in Kampung Sungai Durian, Kinta District, Perak, Malaysia. Global Journal of Health Science, 1(2):140-149  Akosa A.B., Adimado A.A., Amegbey N.A., Nignpense B.E., Carboo, D., Gyasi S. (2002): Report submitted by Cyanide investigation committee, Ministry of Environment and Science, Ghana.  Akabzaa T., Darimani A. (2001): Impact of mining sector investment in Ghana; a study of the Tarkwa mining region. Pp 43.  Aryee B.N.A. (2001): ‘Ghana’s mining sector: its contribution to the national economy’, Resource Policy, 27(2): 61-75.  Ataie-Ashtiani B., Volker R.E., Lockington D.A. (1999): Numerical and experimental study of seepage in unconfined aquifers with a periodic boundary condition. Journal of Hydrology, 222(1-4): 165-184. th  Austin G. T. (1984): Shreves chemical process industry 5 Edition, Mc-Graw Hill, Inc., Singapore, pp. 529-553.  Avotri T.S.M., Amegbey N.A., Sandow M.A., Forson S.A.K. (2002): The health impact of cyanide spillage at Gold Fields Ghana Ltd., Tarkwa. (Funded by Goldfields Ghana Limited, GFGL)  Benes P., Cernik M. (1990): Model Calculations and Experimental Analysis of Transport of Radiocesium in the System Wastewater Channel - Dudvah. Report of the Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University, Prague. 88 University of Ghana http://ugspace.ug.edu.gh  Benes P., Picat P., Cernik M., Quinalt J.M. (1992): Kinetics of radionuclide interaction with suspended solids in modelling the migration of radionuclides in river. Parameters for two-step kinetics. J. Radioanalitical and Nuclear Chemistry, 159(2): 175-186  Booth R.S. (1975): A system analysis model for calculating radionuclide transport between receiving water and bottom sediments, Oak Ridge National Lab., ORNL-TM-4751, 37p.  Borzilov V.A., Sedunov Y.S., Novittsky, M.A. (1989): Forecasting of secondary radioactive contamination of the rivers in 30-th kilometers zone of the Chernobyl NPP, Meteorologia, Gidrologia, 2, 5-13.  Burrough P.A., Van der Perk M., Howard B.J., Prister B.S., Sansone U., Voitsekohovitch O.V. (1999): Environmental mobility of radiocaesium in the Pripyat catchment, Ukraine &Belarus. Water, Air, & Soil Pollution 110(1–2): 35–55.  CEA (1992): Determination des valeurs de radioactivité dites valecurs de minimis, permetant ľevacuation sans condition, CEA, ISPN, SERGD No. 92/22. Commissariat á ľ Energy Atomique.  Cember, H., Johnson, T.E (2009): Introduction to Health Physics. Fourth Edition. Pp 85  Comans R.N.J. (1990): Sorption of cadmium and cesium at mineral/water interfaces. Ph.D. thesis, Rijksuniversiteit Utrecht.  Coppe, P. (1993): Estimated models of impact used by Electricité de France within the framework of the french and european regulations, Radioprotection, Special issue, Proc. of the joint seminary from September 15th to 18th 1992, Fribourg, Switzerland, 185-189  Darko E. O., Tetteh G. K., Akaho, E. H. K. (2005): Occupational radiation exposure to norms in a gold mine, Journal of Radiation Protection Dosimetry, Vol. 114.  Dehghan M. (2004): Numerical solution of the three-dimensional advection- diffusion equation. Applied Mathematics and Computation, 150(1): 5-19.  Dyhouse J., Hatchett J., (2003): Floodplain Modelling Using HECRAS. Waterbury, CT: Haestad Methods. 89 University of Ghana http://ugspace.ug.edu.gh  Everstine Gordon C. (2010): Numerical solution of Partial Differential Equations. Gaithersburg, Maryland. Pp 24.  Faanu A. (2011): Assessment of public exposure to naturally occurring radioactive materials from mining and mineral processing activities of Tarkwa Goldmine in Ghana, PhD. Thesis, Kwame Nkrumah University of Science and Technology, Kumasi.  Farhat C., Harari I., Franca L. P. (2001): The discontinuous enrichment method. Computer. Methods Appl. Mech. Engrg., 190(48):6455-6479.  Felmy A.R., Brown S.M., Onishi Y., Argo R.S., Yabusaki S.B. (1983): MEXAMS – the metals exposure analysis modelling system. Prepared for the U.S. Environmental Protection Agency by Battelle, Pacific Northwest Laboratories, Richland, Washington. - 295p.  Garćia R., Rodrŕiguez J. (1998): A visual tool to simulate hydrodynamics, pollutant and suspended sediment transport in rivers and coastal regions, J. Hydraulic Research, 35(5): 583 – 589.  Gold Fields Ghana Limited (2004): An Independent Technical Report on the Damang Gold Mine, Ghana. Report Prepared for Gold Fields Limited and IAMGold Corporation under the Guidelines of National Instrument 43-101 and accompanying documents 43-101.F1 and 43-101.CP. Pp 13  Gold Fields Ghana Limited (2011): Damang Gold Mine Technical Short Form Report. Pp 2.  Havno K., Madsen M.N., Dorge J. (1995): MIKE 11 -a generalized river modeling package.- Computer Models of Watershed Hydrology (Ed. V.P. Singh), Water Resources Publications, USA.- p.p.733-782 .  Heling R., Raskob W., Popov A., Zheleznyak M. (1999): Overview of Hydrological Dispersion Module –HDM of RODOS. RODOS Report. RODOS- WG4-TN (99)18.  Hilson, G. (2002a): ‘Harvesting mineral riches: 1000 years of gold mining in Ghana’, Resource Policy. 28(1): 13-26.  Hilson, G. (2002b): ‘Promoting sustainable development in Ghanaian small- 90 University of Ghana http://ugspace.ug.edu.gh scale gold mining operations’, The Environmentalist. 22 (1):51-57.  Hofer H., Bayer A. (1993) : Calculation of radionuclide dispersion in flowing waters with a dynamic model, Kerntechnik, 58(3):164-169  Holly F.M., Yang J.C., Schwarz P., Schaefer J., Hsu S.H., Charima E. R. (1990): numerical simulation on unsteady water and sediment movement in multiply connected networks of mobile-bed channels. IIHR Report No. 343, Iowa Institute of Hydraulic Research, University of Iowa, Iowa City, Iowa. - 327 p.  HEC (1977): HEC-6 scour and deposition in rivers and reservoirs. Hydrologic Engineering Center. U.S. Army Corps of Engineering, Davis, California. – 295 p.  HPS. (1996). Radiation Risk in Perspective: Position statement of the Health Physics Society.  IAEA (1985): Hydrological Dispersion of Radioactive Material in Relation to Nuclear Power Plant Siting. Safety Series N50-SG-S6, Vienna, 116p  IAEA (1992): Principles for the exemption of radiation and practices from regulatory control, safety series No.89. International Atomic Energy Agency, Vienna  IAEA (2001): Generic models for use in Assessing the Impact of Discharges of Radioactive Substances to the Environment, Safety Report Series. NO. 19,Vienna  IAEA (2002): Radionuclide transport dynamics in freshwater resources, Final results of Co-ordinated Research Project (1997-2000) TECDOC-1314  IAEA, (2003a): Extent of environmental contamination by naturally occurring radioactive material (norm) and technological options for mitigation. IAEA technical reports series no. 419  IAEA. (2003b): Post Graduate Educational Course in Radiation Protection and Safety of Radiation Sources. Biological Effects of Ionizing Radiation Effects of Radiation at the Molecular and Cellular Level.  IAEA (2010): Setting Authorized Limits for Radioactive Discharges: Practical Issues to Consider, TECDOC-1638, VIENNA. 91 University of Ghana http://ugspace.ug.edu.gh  IAEA (2011): International Basic Safety Standards for Protection against Ionizing Radiation and for the Safety of Radiation Sources (BSS), Safety Series No. GSR Part 3 (Interim),Vienna.  ICRP (1991): 1990 recommendations of the International Commission on Radiological Protection, ICRP Publication 60, Pergamon Press, Oxford.  ICRP. (2007): Recommendations of the International Commission on Radiological Protection, ICRP Publication 103, Pergamon Press, Oxford.  IFC (2003): Socio-Economic Baseline and Impact Assessment Report, Community Development Plan, International Finance Corporation, Iduapriem and Teberebie Goldmines, Ghana.  Jannasch H.W., Honeyman B.D., Balistrieri L.S., Murray J.W. (1988): Kinetics of trace element uptake by marine particles. Geochim. Cosmochim. Acta 52(2): 567-577.  Konoplev A.V., Bulgakov A.A., Shcuratova I.T. (1990): Migration in soil and surface flow of the some radioactive products in the zone of Chernobyl NPP, Meteorologia and Gidrologia, 6 (1): 119-121.  Kortatsi B.K. (2004): Hydrochemistry of groundwater in the mining area of Tarkwa-Prestea, Ghana, PhD thesis, University of Ghana, Legon-Accra, Ghana.  Ku T. L., Luo S., Leslie B. W., Hammond D. E. (1992): Decay series disequilibria applied to the study of rock-water interaction and geothermal systems. In: Uranium Series Disequilibrium: Applications to Earth, Marine and Environmental Sciences (eds. M. Ivanovich and R. S. Harmon) pp. 631–668. Clarendon Press, Oxford.  Kuma J.S., Younger P.L. (2001): Pedological characteristics related to groundwater occurrence in the Tarkwa area, Ghana, Journal of African Earth Sciences, vol. 33(2):363-376.  Kumah J. S. (2007): Hydrogeological Studies on the Tarkwa Gold Mining District, Ghana, Bulletin of Engineering Geology and the Environment, (Bull Eng Geol Env), 66(1):1512-1522.  Li L., Barry D.A., Pattiaratchi C.B. (1997): Numerical modelling of tide-induced 92 University of Ghana http://ugspace.ug.edu.gh beach water table fluctuations. Coastal Engineering, 30(1-2): 105-123.  Lorin R. D. (1999): Fundamentals of Environmental Discharge Modelling, CRT Press: LLC USA.  Luyben W.L (1995): Process Modelling, simulation and control for chemical nd engineers”; 2 edition; Mc-Graw Hill, Singapore. Pp. 17-124  Malik A. Q. (2001): Computation of the Dispersion of Decaying Pollutants Discharged at Sea. University of Brunei Darussalam, Department of Physics, Jalan Tungku Link, Gadong BE1410, Brunei Darussalam.  Malmgren L., Jansson M. (1995): The fate of Chernobyl radiocesium in the River Oere catchment, northern Sweden. Aquatic Sciences 57(2): 144–160.  Margvelashvili N., Maderich V., Zheleznyak M. (1999): Simulation of radionuclide flux from Dnieper-Bug Estuary into the Black sea. J. Environmental Radioactivity, 43(2): 157 171.  Matsunaga T., T. Ueno H., Amano Y., Tkatchenko A., Kovalyov M., Watanabe Y. (1999): Characteristics of Chernobyl derived radionuclides in particulate form in surface waters in the exclusion zone around the Chernobyl Nuclear Power Plant. Journal of Contaminant Hydrology, 35(1–3): 101–113.  Mehta J., Hayter P., Parker W., Krone R., Teeter A. (1989): Cohesive sediment transport. I: Process description. J.Hydraul.Eng.,115(8):1076-1093  Moler C. (2006): The Growth of MATLAB and the MathWorks over Two Decades.  Monte L. (1993): A predictive model for the behavior of radionucledes in lakes system. Health Physics 65(3):288-294  NAS. (1990): Health Effects of exposure to low levels of ionizing radiation, BEIR V, National Academy of Sciences, National Research Council, Academy Press, Washington DC.  NAS. (2006): Health risks from exposure to low levels of ionizing radiation, BEIR VII, National Academy of Sciences National Research Council, Academy Press, Washington DC. 93 University of Ghana http://ugspace.ug.edu.gh  Najat K. M., Mohamed S. M. (2013): Natural Radioactivity in Soil and Water from Likuyu Village in the Neighborhood of Mkuju Uranium Deposit. International Journal of Analytical Chemistry, 2013; 2013:501856. doi: 10.1155/2013/501856. Epub 2013 May 28.  Nielson P. (1990): Tidal dynamics of the water table in beaches. Water Resources Research, 26(9): 2127-2134.  NRC. (1999): Evaluation of Guidelines for exposures to Technologically Enhanced Naturally Occurring Radioactive Materials, National Research Council , Washington, DC.  Ntibery B.K., Atorkui E., Aryee B.N.A. (2003): ‘Trends in small-scale mining of precious minerals in Ghana: a perspective on its environmental impact’ Journal of Cleaner production, vol. 11(2): 131-140. 137 Nylen T. H. G. (1997): The origin and dynamics of Cs discharge from a coniferous forest catchment. Journal of Hydrology, 192(1/4): 338–354.  Ofori A. (2008): Corporate Social Responsibility of Mining Companies in Ghana, MA Thesis, Clark University, USA.  Okamoto S. K., Sakai K., Matsumoto K., KobayashiK (1998): Development and application of a three-Dimensional Taylor-Galerkin numerical model for air quality simulation near roadway tunnel portals. J. Appl. Meteor., 37(2) 1010- 1025.  Onishi Y. (1993): Sediment transport models and their testing. - In NATO Advanced Studies Institute Lecture Series, Pullman, WA.  Onishi Y., Trent D. (1979): Mathematical Simulation of Sediment and Radionuclide Transport in Surface Waters, NUREG/CR-1034, Washington D.C.  Onishi Y. ( 1977): Mathematical simulation of sediment and radionuclide transport in the Columbia River, Battelle Pacific Northwest Lab., Richland, Washington D.C., Rep. BNWL-2228.  Onishi Y., Wheelan, G., Skaggs, R.L. (1982): Development of a Multi-media 94 University of Ghana http://ugspace.ug.edu.gh Radionuclide Exposure Assessment Methodology for Low-Level Waste Management, PNL-3370, Pacific Northwest Laboratory, Richland, Washington D.C.  Onishi, Y. (1981): Sediment and Contaminant Transport Model, Journal of Hydraulic Division, American Society of Civil Engineers, 107 (HY9): 1089- 1107  Orlob G.T (Ed.) (1983): Mathematical Modelling of Water Quality: Streams, Lakes and Reservoirs, International Series on Applied Systems Analysis, IIASA, Pitman Press, 12 -518p.  Paschoa A. S. (1998): Potential Environmental and Regulatory Implications of Naturally Occurring Radioactive Materials (NORM). Applied Radiation and Isotope. 49 (3):189-196. Elsevier Science, Britain.  Pepper D.W., Kern C.D., Long Jr P.E. (1979): Modelling the dispersion of atmospheric pollution using cubic splines and chapeau functions. Atmos. Environ., 13(2): 223-237  Sanchez-Cabeza, J.A., L. Pujol, J. Merino, J.M. Bruach, J. Molero (2000): Artificial radionuclides in waters of the lower section of the river Ebro (Northeast Spain). Water, Air, & Soil Pollution, 118(3– 4): 339–35.  Sastry S.S. (1976): Finite difference approximations to one-dimensional parabolic equations using a cubic spline technique. J. Comp. Appl. Math., 2.  Schultz C.L. (2001): Calibration of the TAM/WASP Sediment Transport Model- Draft Report. Rockville, MD: Interstate Commission on the Potomac River Basin  Schumer R., Meershaert M., Baeumer B. (2009): Fractional advection-dispersion equation for modeling transport at the earth surface, Journal of Geophysics. Research vol 114, F00A07, doi: 10.1029/2008JF00 1246.  Silliman, S.E., Zheng L., Conwell P. (1998): The use of laboratory experiments for the study of conservative contaminant transport in heterogeneous porous media. Hydrogeology Journal, 6(1): 166-177. 95 University of Ghana http://ugspace.ug.edu.gh  Simmons, C.T., Fenstemaker T.R., Sharp Jr. J.M. (2001): Variable-density groundwater flow and contaminant transport in heterogeneous porous media: 293 approaches, resolutions and future challenges. Journal of Contaminant Hydrology, 52(1-4): 245-275.  Slavik O., Zheleznyak M., Dzuba N., Marinets A., Lyashenko G., Papush L., Shepeleva T., Mihaly B. (1997): Implementation of the decision support system for the river-reservoir network affected by releases from the Bohunice NPP, Slovakia - Radiation Protection Dosimetry,73(1-4):171-175  Smith-Asante E. (2011): Mining activities in Obuasi and Tarkwa Pollute 262 rivers, Ghana Business News, 15/08/2011.  Smitz Y., Everbecq E. (1986): Modelling the Behaviour of Radionuclides in Aquatic Ecosystems, Paper presented at CEC Seminar on Cycling of Long-Lived Radionuclides in the Biosphere: Observations and Models, Madrid.  Sousa E. (2003): The controversial stability analysis. Applied Mathematics and Computation, 145(2): 777-794.  Sørensen H.R., Kjelds J., Deckers F., Waardenburg F. (1996a): Application of GIS in hydrological and hydraulic modelling: DLIS and MIKE11-GIS. HydroGIS 96: Application of Geographic Information Systems in Hydrology and Water Resources Management. Proc. Vienna, April 1996, (IAHS Publ. no. 235, 1996).  Tandon P. N. (2000): Mathematical and Computer Models for the disposal of Liquid effluents in deep Sea, In: A. P. Dwivedi (edi.), Mathematical modeling of Non-linear Systems: Proceedings of the International Conference India, pp. 224 – 241.  Tarkwa Nsuaem Municipal Assembly (2006): Technical Report of the Tarkwa Nsuaem Municipal Assembly.  Taylor G. I., Pagenkopf J. R., (1981): TRANQUAL- Two-dimensional modelling of transport water quality processes. Proceedings, EPA storm water and water quality management modelling group meeting, Niagara Falls, Canada.  UMTRCA (1978): Uranium mill tailings radiation control act. As awarded 96 University of Ghana http://ugspace.ug.edu.gh Public Law 92-604 [H. R. 13650] U. S. Department of Energy (DOE).  UNSCEAR (2000): Sources and Effects of Ionizing Radiation, 2000 Report to the General Assembly with Scientific Annexes, United Nations, New York.  USNRC (1978): Liquid pathway generic study. Impact of accidental radioactivity releases to hydrosphere from floating and land-based nuclear power plants. United States Nuclear Regulatory Commission. USNRC, NUREG-0440. - 212 p.  Von Neubeck C., Shankaran H., Karin N.J., Kauer P.M., Chrisler W.B., Xihai W., Robinson R.J., Waters K.M., Tilton S.C., Sowa M.B (2012): Cell Type- Dependent Gene Transcription Profile in a Three-Dimensional Human Skin Tissue Model Exposed to Low Doses of Ionizing Radiation: Implications for Medical Exposures. Environmental and Molecular Mutagenesis 53(4):247-259. DOI:10.1002/em.21682.  Voss C.I. (1984): SUTRA- a finite element simulation model for saturated unsaturated, fluid density dependent groundwater flow with energy transport or 294 chemically reactive single species contaminant transport. U.S. Geological Survey, National Center, Reston, Virginia.  WHO. (2004): Guidelines drinking-water quality, 3rd Ed. Recommendations, Vol. 1. World Health Organization, Geneva.  Yuan D., Yong P. (2009): Contaminant transport in coastal aquifers. Department of Civil and Environmental Engineering. New Jersey Institute of Technology, Newark, New Jersey.  Zhang Q., Volker R.E., Lockington D.A. (2001): Influence of seaward boundary condition on contaminant transport in unconfined coastal aquifers. Journal of Contaminant Hydrology, 49(1-4): 201-215.  Zheleznyak M., Blaylock G., Gontier G., Konoplev A. (1995): Modelling of radionuclide transfer in rivers and reservoirs: validation study within the IAEA\CEC VAMP Programme. International Symposium on Environmental Impact of Radioactive Releases, IAEA, Vienna, 8, IAEA-SM- 339, p.330-331  Zheleznyak M., Demchenko R., Khursin S., Kuzmenko Yu., Tkalich P., Vitjuk N. (1992): Mathematical modelling of radionuclide dispersion in the Pripyat- 97 University of Ghana http://ugspace.ug.edu.gh Dnieper aquatic system after the Chernobyl accident. -The Science of the Total Environment. 112(1):89-114  Zheleznyak M., Margvelashvily N. (1997): Numerical modelling of three- dimensional radionuclide fields in Kiev Reservoir. - Dopovidi (Proceedings) of National Academy of Sciences of Ukraine, No.12. 98 University of Ghana http://ugspace.ug.edu.gh APPENDIX A Table A: Radionuclide Half-Life and Decay Constants 99 University of Ghana http://ugspace.ug.edu.gh 100 University of Ghana http://ugspace.ug.edu.gh 101 University of Ghana http://ugspace.ug.edu.gh APPENDIX B Table B: Relationship between River flow rate, River width and River depth using Linear Interpolation between values 102 University of Ghana http://ugspace.ug.edu.gh APPENDIX C Table C: Examples of Longitudinal Dispersion Coefficients in Rivers 103 University of Ghana http://ugspace.ug.edu.gh APPENDIX D Table D: Examples of Lateral Dispersion Coefficients in Rivers 104 University of Ghana http://ugspace.ug.edu.gh APPENDIX E Table E: Chemical symbols and Characteristics of Uranium- 238 Series, Thorium- 232 Series and K-40 Decay Series NORM Symbol Half-Life Major Emissions NORM Symbol Half-Life Major Emissions 238 9 232 10 Uranium 238 U 4.5 × 10 y α Thorium 232 Th 1.4 × 10 y α 234 228 Thorium 234 Th 24.0 d β, γ Radium 228 Ra 5.7 y β 234m 228 Protactinium 234m Pa 1.2 m β, γ Actinium 228 Ac 6.1 h β, γ 234 5 228 Uranium 234 U 2.5 × 10 y α, γ Thorium 228 Th 1.9 y α, γ 230 4 224 Thorium 230 Th 7.7 ×10 y α, γ Radium 224 Ra 3.7 d α, γ 226 3 220 Radium 226 Ra 1.6 × 10 y α, γ Radon 220 Rn 55.6 s α 222 216 Radon 222 Rn 3.83 d α Polonium 216 Po 0.15 s α 218 212 Polonium 218 Po 3.1 m α Lead 212 Pb 10.6 h β, γ 214 212 Lead 214 Pb 27 m β, γ Bismuth 212 Bi 61 m α, β, γ 105 University of Ghana http://ugspace.ug.edu.gh 214 212 - 7 Bismuth 214 Bi 20 m β, γ Polonium 212 Po 3 × 10 s α 214 4 – 208 Polonium 214 Po 1.6 × 10 s α, γ Thallium 208 Tl 3.1 m β, γ 210 208 Lead 210 Pb 22.3 y β, γ Lead 208 Pb Stable none 210 Bismuth 210 Bi 5.01 d β 210 Polonium 210 Po 138 d α POTASSIUM-40 206 9 Lead 206 Pb Stable none Potassium 40 40K 1.3 × 10 y β, γ 106 University of Ghana http://ugspace.ug.edu.gh APPENDIX F Table F: Default values of intake per person for various critical groups in the world (Adults) 107 University of Ghana http://ugspace.ug.edu.gh APPENDIX G Table G: Committed Effective dose coefficients for ingestion (Sv/Bq) 108 University of Ghana http://ugspace.ug.edu.gh 109 University of Ghana http://ugspace.ug.edu.gh 110 University of Ghana http://ugspace.ug.edu.gh APPENDIX H BASIC RIVER CHARACTERISTICS OF THE TAAMANG RIVER RIVER DEPTH (D) = 2.6 m RIVER WIDTH (B) = 187 m 3 -1 These dimensions correspond to a river flow rate (qr) of 500 m s [IAEA, 2001]. Given that the River Velocity , Where, qr = River flow rate B = River width D = River depth The horizontal dispersion coefficient (Dx) is given by [IAEA, 2001]; Where, U = River Velocity D = River Mean Depth U* = River Shear Velocity = 0.1U 111 University of Ghana http://ugspace.ug.edu.gh APPENDIX I MATLAB CODE TRANSPORT.M %Advection-Dispersion-reaction solved with implicit format long clear all clc file=input(' enter radionuclide = ','s'); Tfinal = input(' input Tfinal T = ') ; % final time c0= input(' enter C0 = ') ; U= input(' enter velocity U = ') ; D = input(' enter Diffusive mean D = ') ; k = input(' enter decay constant k = ') ; L= input(' input length of domain L= ') ; disp('-------------------------------------------') disp('-------------------------------------------') disp('the constant values you have defined are') D L U c0 k delx=10 %should be less than 2*D/U for stability delt = 50 %should be less than (delx^2)/(2*D+k*delx^2) CIN = c0; %input concentration %first node and last node are fictitious TN=ceil(L/delx)+3; %Total nodes (see above comment) TT=ceil(Tfinal/delt); %total time periods in the simulation A = zeros(TN,TN); b = zeros(TN,1); x = zeros(TT,TN); %flops(0); term1= (-D*delt/delx^2)+(-U*delt/(2*delx)); term2=1+(2*D*delt/delx^2)+k*delt; term3=(-D*delt/delx^2)+(U*delt/(2*delx)); %first equation is from applying the left %boundary condition A(1,1)=1; A(1,2)=2*delx*U/D; A(1,3)=-1; b(1,1)=2*delx*U*CIN/D; %now for nodes 2 (first actual node!) to Last %actual node %which corresponds here to node=TN-1; for i=2:TN-1 112 University of Ghana http://ugspace.ug.edu.gh A(i,i-1)=term1; A(i,i)=term2; A(i,i+1)=term3; %b(i,1)=x(timeindex-1,i); %because this is the only one that changes %in the AX=b equation for each time will place %this in time stepping loop later. end %the last equation is from applying the right %boundary condition A(TN,TN-1)=1; A(TN,TN)=-1; for timeindex=2:TT for i=2:TN-1 b(i,1)=x(timeindex-1,i); %rhs that changes every time step end %now solve the Ax=b to get the solution x(timeindex,:) = (A\b)'; %you can use LU to make this step efficient end %of time loop save -ASCII -TABS x.xls x %flops figure(1) plot(1/c0*x(:,2:TN-1)') title('Progression of Concentration Profiles') xlabel('x(X10m)') legend('t=1000s','t=1050s','t=1100s','t=1150s','t=1200s'); ylabel('Concentration ') grid on figure(2) plot([0:delx:L]',1/c0*x(20,2:TN-1)',[0:delx:L]',1/c0*x(21,2:TN- 1)',[0:delx:L]',1/c0*x(22,2:TN-1)',[0:delx:L]',1/c0*x(23,2:TN- 1)',[0:delx:L]',1/c0*x(24,2:TN-1)') title('Progression of Concentration Profiles') xlabel('x(m)') ylabel('Concentration ') legend('t=1000s','t=1050s','t=1100s','t=1150s','t=1200s'); grid on figure(3) plot([1:delt:Tfinal]',1/c0*x(:,20),[1:delt:Tfinal]',1/c0*x(:,30),[1:del t:Tfinal]',1/c0*x(:,40),[1:delt:Tfinal]',1/c0*x(:,50)) xlabel('t(s)') legend('x=200','x=300','x=400','x=500'); ylabel('Concentration ') grid on figure(4) X=[0:delx:L]; T=[1:delt:Tfinal]; mesh(T,X,x(:,2:TN-1)') 113