DOSE ASSESSMENT OF NATURAL RADIOACTIVITY IN FLY ASH AND ENVIRONMENTAL MATERIALS FROM MORUPULE A COAL-FIRED POWER STATION IN BOTSWANA BY JOHN MUDIWA, 10435641 BSc BIOMEDICAL ENGINEERING, 2003 A THESIS SUBMITTED TO THE DEPARTMENT OF MEDICAL PHYSICS, UNIVERSITY OF GHANA, GRADUATE SCHOOL OF NUCLEAR AND ALLIED SCIENCES IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE AWARD OF MASTER OF PHILOSOPHY (MPhil) IN NUCLEAR SCIENCE AND TECHNOLOGY PROGRAM JULY, 2015 University of Ghana http://ugspace.ug.edu.gh i DECLARATION I hereby declare that this thesis submission is a result of research work undertaken by John Mudiwa under the Department of Medical Physics, Graduate School of Nuclear and Allied Sciences, University of Ghana, under the awesome supervision of Prof. Emmanuel Ofori Darko and Dr. Augustine Faanu. This work has never been submitted in whole or in part anywhere else for any sort of award. In parts of this submission where other sources of information have been used, such sources have been cited in this work and acknowledged under references. ……………………………………. ………………… JOHN MUDIWA, ID 10435641 DATE (STUDENT) …………………………………… ………………… PROF. EMMANUEL OFORI DARKO DATE (PRINCIPAL SUPERVISOR) …………………………………… ………………… DR. AUGUSTINE FAANU DATE (CO-SUPERVISOR) University of Ghana http://ugspace.ug.edu.gh ii DEDICATION First and foremost, I dedicate this work to my Lord and personal savior, Jesus Christ. I dedicate this research work to my father Mr. Ben Buyen Barnabas Mudiwa and especially my wife Neo Daphne Mudiwa for her wonderful support, encouragement and positive attitude towards my life. University of Ghana http://ugspace.ug.edu.gh iii ACKNOWLEDGEMENT I would like to show gratitude for God’s blessings and favour upon my life that have enabled me to complete this thesis work. I earnestly show my deepest appreciation to my supervisors Prof. Emmanuel Ofori Darko (Deputy Director, Radiation Protection Institute, GAEC) and Dr. Augustine Faanu (Head of Department at NSS, University of Ghana). I am extremely grateful to the Director of the Radiation Protection Institute (RPI), Prof. G. Emi-Reynolds and the Director of the Graduate School of Nuclear and Allied Sciences (SNAS) at the University of Ghana, Prof. Yaw Serfor-Armah. My deep gratitudes also go to the former and current supervisors of international students at SNAS, being Rev. Dr. A. Bamford and Dr. D. K. Adotey respectively. I am extremely thankful to all my lecturers at SNAS, including Prof. C. Schandorf, Prof. Akaho, Prof. J. Fletcher, Prof. Nana Ayensu, Dr. J. K. Amoako, Dr. J. Yeboah and Dr. Joseph Tandoh for all the knowledge they have equipped me with in preparation for this work. My heartfelt appreciation also goes to the GAEC Radiation Protection Institute laboratory staff who gave me so much support especially during sample preparation and analysis. I also sincerely give thanks to the technical staff and officials of Morupule Coal-Fired Power Station for all the assistance they offered me in availing samples and other useful information used in this study. I am grateful to my father Mr. Ben Buyen Barnabas Mudiwa and my wife Neo Daphne Mudiwa for their encouragement before and during my thesis work. I am also giving my heartfelt appreciation to the International Atomic Energy Agency for awarding me a full sponsorship to undertake the MPhil in Nuclear Science and Technology Program as well as this research work. University of Ghana http://ugspace.ug.edu.gh iv TABLE OF CONTENTS DECLARATION ................................................................................................................. i DEDICATION .................................................................................................................... ii ACKNOWLEDGEMENT ................................................................................................. iii TABLE OF CONTENTS ................................................................................................... iv LIST OF TABLES ............................................................................................................ vii LIST OF FIGURES ........................................................................................................... ix LIST OF PLATES ............................................................................................................. xi ABBREVIATIONS .......................................................................................................... xii ABSTRACT .........................................................................................................................1 CHAPTER ONE: INTRODUCTION ..................................................................................3 1.1 BACKGROUND TO THE STUDY ......................................................................... 3 1.2 STATEMENT OF PROBLEM ............................................................................ 5 1.3 OBJECTIVES OF THE STUDY .............................................................................. 6 1.4 RELEVANCE AND JUSTIFICATION ................................................................... 6 1.5 SCOPE AND LIMITATION .................................................................................... 8 1.6 THESIS STRUCTURE ............................................................................................. 9 CHAPTER TWO: LITERATURE REVIEW ....................................................................11 2.1 IONIZING RADIATION EXPOSURE DUE TO NATURAL SOURCES ........... 11 2.1.1 COSMIC RADIATION ............................................................................................12 2.1.2 TERRESTRIAL RADIATION .................................................................................14 2.1.3 RADIOACTIVITY IN SOIL, COAL, WATER AND FLY ASH............................18 2.2 EXPOSURE PATHWAYS ..................................................................................... 21 2.3 DOSE RECONSTRUCTION ................................................................................. 22 2.3.1 DOSE RECONSTRUCTION TECHNIQUES .........................................................24 2.4 INSTRUMENTATION TO MEASURE NATURAL RADIOACTIVITY............ 26 2.4.1 RESOLUTION AND EFFICIENCY ........................................................................28 CHAPTER THREE: MATERIALS AND METHODS ....................................................30 3.1 MATERIALS .......................................................................................................... 30 3.2 DESCRIPTION OF STUDY AREA ...................................................................... 30 University of Ghana http://ugspace.ug.edu.gh v 3.2.1 METEOROLOGY OF THE STUDY AREA ...........................................................36 3.2.2 GEOLOGY AND SOILS .........................................................................................36 3.2.3 HYDROGEOLOGY .................................................................................................37 3.2.4 VEGETATION .........................................................................................................38 3.3 METHOD ................................................................................................................ 39 3.3.1 SAMPLES COLLECTION ......................................................................................39 3.3.1.1 SOIL/COAL/FLY ASH SAMPLING ....................................................... 39 3.3.1.2 WATER SAMPLING ................................................................................ 40 3.3.2 SAMPLE PREPARATION FOR DIRECT GAMMA SPECTROMETRY .............40 3.3.2.1 SOIL/COAL/FLY ASH SAMPLE PRAPARATION ............................... 40 3.3.2.2 WATER SAMPLE PREPARATION ........................................................ 41 3.3.3 SAMPLE ANALYSIS USING DIRECT GAMMA SPECTROMETRY ................42 3.3.3.1 ENERGY CALIBRATION ....................................................................... 42 3.3.3.2 EFFICIENCY CALIBRATION ................................................................ 44 3.3.3.3 MINIMUM DETECTABLE ACTIVITY .................................................. 45 3.3.3.4 CALCULATION OF ANNUAL EFFECTIVE DOSE DUE TO THE RADIOACTIVITY IN SAMPLES ........................................................................ 46 3.3.3.5 ANNUAL EFFECTIVE DOSE CALCULATIONS FROM EXTERNAL GAMMA DOSE RATE MEASUREMENTS ....................................................... 48 3.3.4 RADIOLOGICAL HAZARD ASSESSMENT ........................................................48 3.3.5 DOSE RECONSTRUCTION ...................................................................................50 3.3.5.1 TAYLOR SERIES METHOD FOR NUMERICAL SOLUTIONS IN DOSE RECONSTRUCTION ................................................................................ 52 CHAPTER FOUR: RESULTS AND DISCUSSION ........................................................55 4.1 ENERGY AND EFFICIENCY CALIBRATION ................................................... 55 4.2 MINIMUM DETECTABLE ACTIVITY ............................................................... 57 4.3 ACTIVITY CONCENTRATIONS, ABSORBED DOSE RATES AND ANNUAL EFFECTIVE DOSES IN THE STUDY AREA ............................................................ 57 4.3.1 FLY ASH ..................................................................................................................57 4.3.2 COAL ........................................................................................................................61 4.3.3 SOIL ..........................................................................................................................64 University of Ghana http://ugspace.ug.edu.gh vi 4.3.4 WATER ....................................................................................................................67 4.4 COMPARISON OF ACTIVITY CONCENTRATION, GAMMA DOSE RATE AND ANNUAL EFFECTIVE DOSE TO SAMPLE TYPE ......................................... 70 4.5 RADIUM EQUIVALENT ACTIVITY, REPRESENTATIVE LEVEL INDEX, EXTERNAL AND INTERNAL HAZARD INDICES ................................................. 73 4.6 RECONSTRUCTED DOSES FROM THE STUDY AREA .................................. 80 4.7 ANNUAL EFFECTIVE DOSE MODEL OF THE FLY ASH STORAGE AREA 88 4.8 ANNUAL EFFECTIVE DOSE MODEL OF THE COAL STORAGE AREA ..... 89 4.9 ANNUAL EFFECTIVE DOSE MODEL FOR SOIL SAMPLES FROM THE STUDY AREA .............................................................................................................. 90 4.10 ANNUAL EFFECTIVE DOSE MODEL FOR WATER SAMPLES FROM THE FLY ASH PONDS ........................................................................................................ 91 CHAPTER FIVE: CONCLUSION AND RECOMMENDATIONS ................................97 5.1 CONCLUSION ....................................................................................................... 97 5.2 RECOMMENDATIONS ...................................................................................... 100 5.2.1 MANAGEMENT OF MORUPULE A COAL-FIRED POWER STATION .........100 5.2.2 WORKERS OF MORUPULE A COAL-FIRED POWER STATION ............100 5.2.3 MEMBERS OF THE PUBLIC ...............................................................................101 5.2.4 THE REGULATORY AUTHORITY OF BOTSWANA.......................................101 5.2.5 RESEARCH SCIENTISTS ....................................................................................102 REFERENCES ................................................................................................................103 APPENDICES .................................................................................................................110 University of Ghana http://ugspace.ug.edu.gh vii LIST OF TABLES Table 2-1: Typical cosmogenic radionuclides Table 2-2: Thorium (4n) series Table 2-3: Neptunium (4n+1) series Table 2-4: Uranium (4n+2) series Table 2-5: Actinium (4n+3) series Table 2-6: Worldwide natural radionuclide concentration of coal Table 2-7: Natural radionuclide activity concentrations from fly ash and soil samples around Orji River Thermal Power Station Table 2-8: Radionuclide content of 20 fly ash samples from French coal-fired power stations Table 2-9: Average world activity concentration of 40K, 238U, 232Th and 226Ra in fly ash and coal in Bq/kg Table 3-1 Standard radionuclides used for the energy and efficiency calibration Table 4-1 Minimum detectable activities of K-40, Th-232 and U-238 Table 4-2 Experimental results for the average activity concentrations, absorbed dose rates and annual effective doses due to natural radionuclides in fly ash from the study area Table 4-3 Activity concentrations, absorbed dose rates and annual effective doses due to natural radionuclides in coal from the study area Table 4-4 Activity concentrations, absorbed dose rates and annual effective doses due to natural radionuclides in soil from the study area Table 4-5 Activity concentrations, absorbed dose rates and annual effective doses due to natural radionuclides in water from the fly ash ponds Table 4-6 Dose rate, annual effective dose, representative level index (I𝛾𝑟), radium equivalent activity (Ra𝑒𝑞), external hazard index (H𝑒𝑥𝑡) and internal hazard index (H𝑖𝑛𝑡) for fly ash samples University of Ghana http://ugspace.ug.edu.gh viii Table 4-7 Dose rate, annual effective dose, representative level index (I𝛾𝑟), radium equivalent activity (Ra𝑒𝑞), external hazard index (H𝑒𝑥𝑡) and internal hazard index (H𝑖𝑛𝑡) for coal samples Table 4-8 Dose rate, annual effective dose, representative level index (I𝛾𝑟), radium equivalent activity (Ra𝑒𝑞), external hazard index (H𝑒𝑥𝑡) and internal hazard index (H𝑖𝑛𝑡) for soil samples Table 4-9 Dose rate, annual effective dose, representative level index (I𝛾𝑟), radium equivalent activity (Ra𝑒𝑞), external hazard index (H𝑒𝑥𝑡) and internal hazard index (H𝑖𝑛𝑡) for water samples from the fly ash ponds Table 4-10 Reconstructed annual effective doses for fly ash samples Table 4-11 Reconstructed annual effective doses for coal samples Table 4-12 Reconstructed annual effective doses for soil samples Table 4-13 Reconstructed annual effective doses for water samples University of Ghana http://ugspace.ug.edu.gh ix LIST OF FIGURES Fig. 2-1 Worldwide exposure to natural radiation sources Fig. 2-2 Setup of the HPGe detector Fig. 3-1 General location of Morupule Coal-Fired Power Station in Botswana Fig. 3-2 Detailed location of Morupule Coal-Fired Power Station in Botswana Fig. 3-3 Aerial view showing part of the study area Fig. 3-4 Layout of Morupule Coal-Fired Power Station showing sampling points Fig. 3-5 3-D Satellite image showing positions of Lotsane and Morupule rivers Fig. 4-1 Energy calibration curve using mixed radionuclides standard Fig. 4-2 Efficiency calibration curve using mixed radionuclides standard Fig. 4-3 Plot of activity concentration for natural radionuclides Th-232, U-238 and K-40 in fly ash samples from the study area Fig. 4-4 Plot of activity concentration for natural radionuclides Th-232, U-238 and K-40 in coal samples from the study area Fig. 4-5 Plot of activity concentration for natural radionuclides Th-232, U-238 and K-40 in soil samples from the study area Fig. 4-6 Plot of activity concentration for natural radionuclides Th-232, U-238 and K-40 in water samples from the fly ash ponds Fig. 4-7 Activity concentration comparison for samples in the study area Fig. 4-8 Gamma dose rates comparison for samples in the study area Fig. 4-9 Annual effective dose comparison for samples in the study area Fig. 4-10 Comparison of hazard indices and radium equivalent values for all samples Fig. 4-11 Actual reconstructed annual effective dose for fly ash storage area Fig. 4-12 Actual reconstructed annual effective dose for coal storage area Fig. 4-13 Actual reconstructed annual effective dose for soil University of Ghana http://ugspace.ug.edu.gh x Fig. 4-14 Actual reconstructed annual effective dose for water Fig. 4-15 Graphical representation of the fly ash storage area model Fig. 4-16 Graphical representation of the coal storage area model Fig. 4-17 Graphical representation of the soil model for the study area Fig. 4-18 Graphical representation of the water model for the fly ash ponds University of Ghana http://ugspace.ug.edu.gh xi LIST OF PLATES Plate 1-1 Schematic of a Coal-Fired Power Station Plate 3-1 Two fly ash storage tanks Plate 3-2 Coal Storage Area University of Ghana http://ugspace.ug.edu.gh xii ABBREVIATIONS ALARA As low as reasonably archievable @ At λ Decay constant for the specific radionuclide 1L 1 liter µs Microsecond 1M HNO3 1 Molar nitric acid 𝞼 Standard deviation 3-D Three dimensional Ac-228 Actinium-228 𝑨𝒊 Initial radionuclide activity 𝑨𝒊𝒖 Initial radionuclide activity iAmount Total activity limit ANSI American National Standards Institute 7Be Berillium-7 Bi-214 Bismuth-214 Bq Becquerel Bq/kg Becquerel per kilogram Bq/l Becquerel per liter BSS Basic Safety Standards C Activity concentration for radionuclide at any time t 14C Carbon-14 𝑪𝒊𝒖 Initial activity concentration for radionuclide i Co-60 Cobalt-60 University of Ghana http://ugspace.ug.edu.gh xiii 𝑪𝒐 Initial activity concentration 𝑪𝒐𝒏𝒄𝒊 Activity concentration limit for radionuclide i dc Direct current 𝑫𝒐𝒔𝒆𝒊 Total dose due to the initial radionuclide activity 𝑫𝒐𝒔𝒆𝒍𝒊𝒎 Relevant dose limit in Sv/y 𝑫𝒐𝒔𝒆𝒊𝒖 Dose due to the initial activity of radionuclide i EC Electron capture Ecosurv Environmental consultancy company in Botswana eV Electron volt EIA Environmental Impact Assessment FWHM Full Width at Half Maximum FWTM Full Width at Tenth of Maximum g/kg Gram per kilogram GAEC Ghana Atomic Energy Commission GPS Global Positioning System 3H Tritium HPGe High Purity Germanium Detector IAEA International Atomic Energy Agency ICRP International Commission on Radiological Protection IEEE Institute of Electrical and Electronics Engineers ILO International Labor Organization 39K Pottaium-39 K-40 Potassium-40 41K Pottasium-41 University of Ghana http://ugspace.ug.edu.gh xiv K Kelvin keV Kiloelectrovolt mg/L Milligram per liter mm Millimeter mm/year Millimeter per year m/s Meter per second MCA Multi channel analyser MDA Minimum detectable activity MeV Megaelectronvolt mSv Milli Sievert nA Nano-Amperes 22Na Sodium-22 nGy/h Nano gray per hour NORM Naturally Occuring Radioactive Material 237Np Neptunium-237 NSS Nuclear Safety and Security ODE Ordinary Differential Equations Pb-214 Lead-214 ppm Parts per million 𝝆𝒃𝒅 Dry bulk density of the material 𝑸 Actual activity of radionuclide i 𝑸𝒊,𝒍 Activity limit for radionuclide i Raeq Radium equivalent activity concentration Ra-226 Radium-226 University of Ghana http://ugspace.ug.edu.gh xv RPI Radiation Protection Institute SNAS Graduate School of Nuclear and Allied Sciences STD Standard Sv Sievert Sv/y Sieverts per year Th-232 Thorium-232 Tl-208 Thallium-208 TLD Thermoluminiscence detector U-234 Uranium-234 U-235 Uranium-235 U-238 Uranium-238 UN United Nations UNSCEAR UN Scientific Committee on the Effects of Atomic Radiation UPS Uninterrupted Power Supply (UPS) USEPA United States Environmental Protection Agency USGS United States Geological Survey V Volt 𝑽𝒘 Volume of material that has a radiological impact in the scenario z z-score value University of Ghana http://ugspace.ug.edu.gh 1 ABSTRACT This study has been undertaken to estimate the occupational and public radiation doses due to natural radioactivity at Morupule A Coal-Fired Power Station and its environs. The radiation doses were reconstructed to include 60 year period from 1985 to 2045. Direct gamma ray spectroscopy was used to determine the natural radionuclides Th-232, U-238, and K-40 both qualitatively and quantitatively for fly ash, coal, soil and water (from the fly ash ponds) samples. The average activity concentrations for Th-232, U-238, and K-40 in fly ash samples were 64.54 Bq/kg, 49.37 Bq/kg and 40.08 Bq/kg respectively. In the case of coal, the corresponding average activity concentrations for Th-232, U-238, and K-40 were 27.43 Bq/kg, 18.10 Bq/kg and 17.38 Bq/kg respectively. For soil samples, the average activity concentrations for Th-232, U-238, and K-40 were 10.11 Bq/kg, 6.76 Bq/kg and 118.03 Bq/kg respectively. In water samples, the average activity concentrations for Th- 232, U-238, and K-40 were 0.79 Bq/l, 0.32 Bq/l and 1.01 Bq/l respectively. These average activity concentrations were generally comparable to the average world activity concentrations in the case of coal samples, but were generally lower than the average world activity concentrations in the case of fly ash, soil and water samples. The average annual effective doses for the study area were estimated as 0.320 mSv, 0.126 mSv, 0.069 mSv and 0.003 mSv for fly ash, coal, soil and water samples respectively. Dose reconstruction modelling estimated the average fly ash annual effective doses for the years 1985, 1995, 2005, 2015, 2025, 2035 and 2045 to be 0.182 mSv, 0.459 mSv, 0.756 mSv, 0.320 mSv, 0.183 mSv, 0.137 mSv and 0.124 mSv respectively. The reconstructed average coal annual effective doses for similar years were 0.070 mSv, 0.182 mSv, 0.303 mSv, 0.126 mSv, 0.070 mSv, 0.060 mSv and 0.046 mSv respectively. The dose reconstruction modelling also University of Ghana http://ugspace.ug.edu.gh 2 estimated the average soil annual effective doses for the same years as above to be 0.048 mSv, 0.091 mSv, 0.136 mSv, 0.070 mSv, 0.048 mSv, 0.041 mSv and 0.039 mSv respectively. Likewise, the reconstructed average annual effective doses for water were 0.0016 mSv, 0.0049 mSv, 0.0083 mSv, 0.0033 mSv, 0.0016 mSv, 0.0011 mSv and 0.0010 mSv respectively. All estimated and reconstructed average annual effective doses are within the recommended public and occupational dose limits of 1 mSv and 20 mSv respectively. The radium equivalent activity, representative level index, external and internal hazard indices for all samples are within recommended international values for their safe use as building materials. Results from this study reveal that there is no significant radiological impact to both the workers and the public within Morupule A Coal-Fired Power Station and its environs. University of Ghana http://ugspace.ug.edu.gh 3 CHAPTER ONE: INTRODUCTION The main aim of this chapter is to give a brief but rich introduction to the dose assessment of natural radioactivity from Morupule A Coal-Fired Power Station. This chapter includes a brief background to this study as well as the associated problem statement. The chapter also gives insight on the objectives, relevance and justification of this study. 1.1 BACKGROUND TO THE STUDY NORM is mostly used in referring to all naturally occurring radioactive materials where the activities of humans have increased potential for radiation exposure. Natural radioactivity released into the environment in the generation of electricity from coal-fired power stations by coal combustion has been stated as possible causes of health, environmental, and technological problems associated with the use of coal [U.S. Geological Survey Fact Sheet FS-163-97, 1997]. Coal-fired power stations basically generate electricity through coal (a fossil fuel) combustion. The heat generated is used to create steam from water. This steam turns a turbine that is connected to a generator and the generator creates an electric current. The conditioned output current will then be sent out to the main electrical power grid. Plate 1- 1 below is a schematic of a typical coal-fired power station. University of Ghana http://ugspace.ug.edu.gh 4 Plate 1-1: Schematic of a Coal-Fired Power Station [en.wikipedia.org] Coal combustion takes place in the coal-fired power station and gaseous products are emitted through the stack gas pipe. Coal used in the combustion will contain some trace quantities of long-lived radionuclides giving rise to natural radioactivity such as U-238, K- 40, Th-232 and decay products like Ra-226 or Rn-222. During coal combustion, some mechanisms will enhance the concentrations of these long-lived radionuclides. By combusting coal, most non-combustible material remains in the fly-ash formed. This essentially means that most of the NORM will be transferred to the fly ash produced while some will leave through the stack gas pipe into the atmosphere. The fly ash has to be stored securely to prevent contamination of larger areas and this fly ash could be better utilized in making other products such as cement. The type of coal used and plant design has a very major effect on the activity discharged into the environment. Morupule A Coal-Fired Station uses the bituminous type of coal. Coal is grouped into four major categories being anthracite, bituminous, subbituminous University of Ghana http://ugspace.ug.edu.gh 5 and lignite. This categorization depends mainly on its percentage composition of carbon. The percentage compositions of carbon for anthracite, bituminous, subbituminous and lignite coal are 86%-97% C, 45%-86% C, 35%-45% C and 25%-35% C respectively [USEIA, 2010]. This research focuses on the dose assessment of natural radioactivity in fly ash and environmental materials from Morupule A Coal-Fired Power Station. Results obtained from this research were compared with the recommended IAEA and BSS values of natural radionuclide concentrations. 1.2 STATEMENT OF PROBLEM Generally, stochastic and deterministic health effects due to NORM exposure from coal- fired power stations is usually considered to be negligible. Natural radioactivity release by human activities such as coal combustion in coal-fired power stations into the environment is a major global issue. Fly ash waste generated through the coal combustion contains NORM and may release even more natural radioactivity into the environment [USEPA, 2006]. A NORM Environmental Impact Assessment was never performed prior to the commissioning of Morupule A Coal-Fired Power Station, which has been operating for almost 30 years now. The accumulated radiation doses and reference levels in the coal- fired power station and its surroundings due to these natural radionuclides are thus unknown. This implies that the NORM exposure to the coal-fired power station workers and members of the public in the vicinity is also unknown. There is therefore the need to establish natural radioactivity reference (baseline) data. There is generally lack of University of Ghana http://ugspace.ug.edu.gh 6 knowledge and awareness on natural radioactivity levels in the study area to both Morupule A Coal-Fired Power Station workers and surrounding public. 1.3 OBJECTIVES OF THE STUDY The main objective of this study is to assess the natural radioactivity impact of Morupule A Coal-Fired Power Station to both workers and the public living in the vicinity of the power station. This research has the following specific objectives: (a) To establish the activity concentration of the natural radionuclides U-238, Th-232 and K-40 in coal, fly ash, soil and water samples by gamma spectroscopy with the aid of high purity germanium detector (HPGe). (b) To estimate baseline data for these natural radionuclides through mathematical dose reconstruction modelling. (c) To provide suitable radiation protection recommendations to the regulatory authority, Morupule A Coal-Fired Power Station management and all other relevant stakeholders. 1.4 RELEVANCE AND JUSTIFICATION Electricity is very vital in our daily lives. It boosts the economy, vital life-saving equipment in hospitals and investor confidence. At the same time there is need to ensure the safety and protection of Morupule A Coal-Fired Power Station workers against the harmful effects of ionizing radiation. In so many countries worldwide inclusive of Botswana, NORMS from raw materials are not under adequate regulatory control. Documented University of Ghana http://ugspace.ug.edu.gh 7 information on natural radionuclide concentrations in raw materials and public exposures are minimal [Darko et al, 2005]. In this study, the annual effective dose from Morupule A Coal-Fired Power Station will be compared to the occupational annual effective worker dose limit of 20 mSv and the public effective annual dose limit of 1 mSv. This is meant to ensure compliance with ILO (International Labor Organization) and BSS (Basic Safety Standards). This study allows analysis of how much natural radionuclides the coal-fired power station releases into the environment. This work is justified because research on the NORM release from Morupule A Coal-Fired Power Station to the environment has never been carried out before. Scrubbers/ filters reduce the amount of radionuclides eventually emitted from the stack gas pipe into the atmosphere. These scrubbers/filters are normally a major component of the emission reduction technologies generally used in coal-fired power stations. The outcomes of this particular work will show the effectiveness of any emission reduction technology currently in place at Morupule A Coal-Fired Power Station. Study results will give an indication on the extent of radiological contamination around the power station due to the combustion of coal in the power station. Recommendations for improvement have been made based on the results. Results of this research may also unearth new ideas concerning natural radioactivity release from coal-fired power stations and may trigger other related research in years to come. The results will also contribute to preserve the environment and its natural resources like grasslands and vegetation for future University of Ghana http://ugspace.ug.edu.gh 8 generations. This work and other similar research will aid in the formulation of NORM regulations for Botswana. Of the overall importance is protection of the worker, environment and members of the public against the harmful effects of ionizing radiation. 1.5 SCOPE AND LIMITATION This research coverered the following steps: (a) The meteorological, vegetation, geological and hydrogeological data of the proposed study area were collected from relevant bodies such as the Ministry of Environment in Botswana. Meteorological data included factors such as precipitation, wind speed and wind direction. Online tools such as Google Earth were used to preview an aerial view of the study area and assess possible sampling points. (b) Fly ash, coal, soil and water samples were collected from the study area in the month of July, 2014. (c) Samples were analyzed by gamma spectroscopy at the Radiation Protection Institute laboratories of the Ghana Atomic Energy Commision in the period September 2014 to March 2015, after which the annual effective doses due to all the study area samples were estimated. MATLAB software was used to reconstruct the annual effective doses of the study area to include the sixty-year period 1985 ≤ Year ≤ 2045. (d) Due to thesis submission deadlines as well as expensive airline tickets constraints, sampling was done only during the winter season, which is also the driest season in Botswana. Sampling should have also been done in the wet/rainy season so as to cater for the seasonal variations of the results obtained. University of Ghana http://ugspace.ug.edu.gh 9 1.6 THESIS STRUCTURE This thesis consists of six major chapters as follows: (a) Chapter One This chapter gives a general introduction and background to the study. An important aspect of this chapter is that it clarifies the importance of this work as well as its relevance to a coal-fired power station. (b) Chapter Two This chapter gives an insight on what has so far been done on this topic from past and related work. It also shows the gaps in knowledge that need to be addressed, possibly through this research. Available theoretical approaches relevant to the dose assessment of natural radioactivity from coal-fired power stations are also discussed in this chapter. (c) Chapter Three Chapter three discusses the materials, equipment and methods used in this study as well as the calculations relevant to the research study. (d) Chapter Four Chapter four gives the results from this study in a clear and logical manner, aided by the use of tables or figures as required. The chapter also gives a discussion of results from the research study. It also emphasizes the significance of the results obtained. Any limitations of the experimental design of this research are elaborated in this chapter. University of Ghana http://ugspace.ug.edu.gh 10 (e) Chapter Five Chapter five concludes the study and gives an overall summary of the research, recommendations, lessons learned and any other relevant aspects based on the findings from this work. University of Ghana http://ugspace.ug.edu.gh 11 CHAPTER TWO: LITERATURE REVIEW The main aim of this chapter is to give an insight to the natural radioactivity sources as well as occupational and public exposure to these sources. It also focuses on natural radioactivity in samples of various matrices from Morupule A Coal-Fired Power Station and its surroundings. The detector resolution, detector efficiency, radiation exposure pathways, dose reconstruction and instrumentation used for measuring natural radioactivity are some key components of this section. 2.1 IONIZING RADIATION EXPOSURE DUE TO NATURAL SOURCES There is a continuous exposure of all living organisms to ionizing radiation emanating from natural sources [UNSCEAR, 2000]. The levels of such exposures differ with respect to altitude and location. Irradiation coming externally from radionuclides that are present naturally within the environment or anthropogenic practices is an important aspect when dealing with human populations. Estimates by the United Nations Scientific Committee on the Effects of Atomic Radiation (UNSCEAR) have revealed that exposure due to natural sources accounts for over 98% of the total radiation dose on the population, excluding medical exposure [UNSCEAR, 2000]. The major sources of exposure due to natural radiation are: i. Cosmic rays from outer space ii. Terrestrial radionuclides Figure 2-1 is a graphical illustration of worldwide exposure to natural radiation sources. These sources include cosmic rays, indoor/outdoor gamma ray exposure as well as radon gas. University of Ghana http://ugspace.ug.edu.gh 12 Fig. 2-1: Worldwide exposure to natural radiation sources [world-nuclear.org] 2.1.1 COSMIC RADIATION The primary cosmic radiation sources are outer space galaxies, while the sun is the secondary source. Cosmic radiation sources from outer space are normally referred to as galactic cosmic radiation. Galactic cosmic radiation comprises of about 2% electrons and 98% baryons [Reitz, 1993]. Protons constitute about 87% of the baryons. They are particles with very high energy. The Austrian physicist Victor Hess received a Nobel Prize for his discovery of cosmic rays in 1936 [Cember, 2009]. The continuous interaction between cosmic rays with atmospheric nitrogen results in cosmic radiation. The resulting radionuclides are referred to as cosmogenic radionuclides. Cosmogenic radionuclides include 3H, 14C, 22Na and 7Be as depicted in Table 2-1. University of Ghana http://ugspace.ug.edu.gh 13 Table 2-1: Typical cosmogenic radionuclides [Cooper, Randle and Sochi, 2003] Radionuclide Half life (years) Mode of decay 3H 12.26 Beta 7Be 0.15 EC 10Be 1.6E6 Beta 14C 5.73E3 Beta 22Na 2.6 EC 26Al 7.4E5 EC 32Si 280 Beta 32P 0.04 Beta 33P 0.07 Beta 35S 0.24 Beta 36Cl 3.01E5 Beta 39Ar 269 Beta 81Kr 2.29E5 EC With the exception of 14C, 3H and 22Na, the three of which have human body metabolic functions, cosmogenic radionuclides generally have a minimal contribution to radiation doses [UNSCEAR, 2000]. Most shielding from cosmic radiation is provided by the atmosphere of the earth. Therefore at lower altitudes, the additional shielding provided by the atmosphere of the earth reduces cosmic radiation dose. In general, the exposure to cosmic radiation mostly depends on altitude and has a weak dependence on latitude. Cosmic radiation adds to the earth’s background radiation. University of Ghana http://ugspace.ug.edu.gh 14 2.1.2 TERRESTRIAL RADIATION Primordial radionuclides are those naturally occurring radionuclides originating on earth such that their half lives are comparable to planet earth’s age [UNSCEAR, 2008]. The primordial radionuclides are found in almost all environmental materials, the human body inclusive. Examples of primordial radionuclides are 232Th, 40K, 235U, 238U and 87Rb with half lives of 1.41 x 1010 years, 1.28 x 109 years, 7.04 x 108 years, 4.47 x 109 years and 4.70 x 1010 years respectively. Natural uranium is a mixture of three isotopes being 99.3% 238U, 0.7% 235U and 0.005% 234U. 234U and 238U isotopes are part of a decay series known as the uranium series (4n+2). The 235U isotope is part of the actinium series (4n + 3). 232Th is part of a decay series known as the thorium series (4n). 232Th is actually the most abundant of these naturally occurring primordial radionuclides. 237Np is part of the neptunium series (4n+1). In all the four above-mentioned radioactive decay series, the first radionuclide in the decay series is long lived. The terminal radionuclides for the 4n, 4n+1, 4n+2 and 4n+3 series are 208Th, 209Bi, 206Pb and 207Pb respectively [Cember, 2009]. Tables 2-2 to 2-5 show the 4n, 4n+1, 4n+2 and 4n+3 series respectively. University of Ghana http://ugspace.ug.edu.gh 15 Table 2-2: Thorium (4n) series [Cember, 2009] Table 2-3: Neptunium (4n+1) series [Cember, 2009] University of Ghana http://ugspace.ug.edu.gh 16 Table 2-4: Uranium (4n+2) series [Cember, 2009] University of Ghana http://ugspace.ug.edu.gh 17 Table 2-5: Actinium (4n+3) series [Cember, 2009] 40K is a naturally occurring radionuclide with a low atomic number and widespread environmental distribution. Crystal rocks, oceans, plants and animals have been found to contain an average 40K concentration of 27 g/kg, 380 mg/L, 1.7 g/kg and 1.7 g/kg respectively [Cember, 2009]. Potassium in nature comprises of the three isotopes 39K, 40K and 41K such that 40K is the only radioactive of the three. The natural isotopic abundance of 40K is 0.0118%. Potassium is also found in rocks and is soluble, therefore it dissolves in wet conditions [Xhixha, 2012]. Homeostatis control normally keeps the 40K concentration at a constant level in the body, therefore environmental concentration changes of 40K do University of Ghana http://ugspace.ug.edu.gh 18 not normally significantly affect the total 40K dose that is delivered to humans [IAEA, 2007]. 2.1.3 RADIOACTIVITY IN SOIL, COAL, WATER AND FLY ASH As mentioned in Section 2.1.2 above, primordial radionuclides are found in almost all environmental materials. Such environmental materials include soil, coal and the fly ash generated in the combustion of coal. In coal-fired power stations, the fly ash is collected by means of an electronic precipitator as a dry powder or it may be discharged into the fly ash pond as slurry in a semi-wet condition [Shamshad, Fulekar and Bhawana, 2012]. The fly ash slurry may be transported to the open fly ash pond or disposal site using either the open or closed water cycle systems [Paschoa and Steinhausler, 2010]. Thus, the fly ash water from the fly ash disposal sites or the fly ash ponds also constitutes these environmental materials. Radionuclides released into the environment will undergo radioactive decay, or they may undergo wet or dry deposition [UNSCEAR, 2000]. Previous work done on natural radioactivity from certain coal-fired power stations around the world is available. Table 2-6 shows natural radinuclide concentrations in coal from various parts of the world. University of Ghana http://ugspace.ug.edu.gh 19 Table 2-6: Worldwide natural radionuclide concentration of coal [Uslu and Gökmeşe, 2010] Table 2-6 shows that the concentrations of natural radionuclides vary with different types of coal and generally depend on the ash content and caloric value [Uslu and Gökmeşe, 2010]. Human activities like mining and the combustion of natural resources like coal may result in enhancing of NORMS such that they may cause elevated natural radioactivity exposure to humans as well as the environment [UNSCEAR, 2000]. Table 2-7 shows the natural radionuclide activity concentrations from fly ash and soil samples around Orji River Coal-Fired Thermal Power Station in Nigeria [Ademola and Onyema, 2014]. University of Ghana http://ugspace.ug.edu.gh 20 Table 2-7: Natural radionuclide activity concentrations from fly ash and soil samples around Orji River Thermal Power Station [Ademola and Onyema, 2014] Sample No. 226Ra (Bq/kg) 232Th (Bq/kg) 40K (Bq/kg) Mean±𝞼 Range Mean±𝞼 Range Mean±𝞼 Range Fly ash 10 28.2±8.3 18.1-38.8 37.6±5.0 31.6-44.7 335±32 287-385 Soil (10m) 10 32.7±4.3 26.3-38.4 40.0±4.2 32.1-46.6 298±15 278-324 Soil (100m) 10 39.1±11.2 14.6-52.4 34.1±5.2 25.2-40.2 257±19 223-286 Fly ash radioactivity is mostly due to 40K, 238U and 232Th decay series [Degrange, Lepicard; 2004]. A study was conducted on the radionuclide content of 20 samples from French coal- fired power stations and the results are shown in Table 2-8. Table 2-8: Radionuclide content of 20 fly ash samples from French coal-fired power stations [Degrange and Lepicard, 2004] University of Ghana http://ugspace.ug.edu.gh 21 Average world activity concentration shows that the NORM content of coal is less than that of fly ash as depicted in Table 2-9 [UNSCEAR, 1982]. Table 2-9: Average world activity concentration of 40K, 238U, 232Th and 226Ra in fly ash and coal in Bq/kg [UNSCEAR, 1982] Nuclides Coal Fly Ash 40K 50 265 238U 20 200 226Ra 20 240 232Th 20 70 2.2 EXPOSURE PATHWAYS Exposure pathways are the various ways through which individuals may be exposed to ionizing radiation. Therefore the following are all the relevant and applicable exposure pathways in this natural radioactivity research: (a) External exposure to gamma rays (b) Internal exposure by inhalation (c) Internal exposure by ingestion (d) Contamination of the skin by radioactive material directly deposited on the skin Close and prolonged contact of workers with material containing NORMs results in occupational exposure. Inhalation of radioactive dust as a result of work also results in occupational exposure. The most common exposure pathway for natural radionuclides is external gamma radiation [IAEA, 2005]. Due to the low specic activity of NORM material, skin contamination is normally considered irrelevant in NORM dose assessments. University of Ghana http://ugspace.ug.edu.gh 22 Public exposure may result due to products from an industrial process such as liquid or atmospheric discharges of radionuclides. The use of industrial products such as fly ash for making cement or concrete will also result in public exposure. The most significant radiation exposure pathways for the public are normally external gamma rays, ingestion and inhalation [European Commission, 2001]. 2.3 DOSE RECONSTRUCTION Assessment of likely radiological doses to members of the public are to be done with reference to the critical group. The critical group is the individuals being exposed to the highest radiation dose. In cases where radiation exposure mechanisms result in future doses, the critical group concept may not be ideal since there is a possibility of significant human habitat change over a small time period [IAEA, 2003]. Radiation from environmental radionuclides could be calculated from radionuclide deposition on plants or soil during a liquid or atmospheric release. It could also be calculated from a residual radionuclides exposure in the environment some time after the end of this release. The calculated radiation doses are actually accumulated radiation doses due to continuous chronic exposure. The committed effective dose for the first year is also calculated. Another important aspect is the calculation of an integrated dose for a specified number of years. Internal radiation doses are calculated using equations from the International Commission on Radiological Protection (ICRP). Calculations for doses due to external exposure from contaminated water and soil are based on the assumption that the contaminated medium is big enough to be treated like an infinite plane or volume with respect to the range of radiation released [Napier, Kennedy Jr. and Soldat, 1980]. University of Ghana http://ugspace.ug.edu.gh 23 Normal exposure refers to radiation exposure which would be reasonably expected to occur, with a probability of unity [ICRP, 1993]. In case of normal exposures, individual doses are expressed as annual effective doses due to external radiation. Annual effective committed dose is used in the case of radionuclides intake. The sum of external annual effective dose and annual effective committed dose is normally compared with the established dose constraint. Potential exposures should be included in the overall safety analysis of a facility. A potential exposure is one that is not certain to happen, but has the potential to happen [IAEA, 2003]. Risk control due to potential exposure is attained by increasing protection to reduce the probability of occurrence of events. This risk control is also attained by mitigation, which simply means increasing protection such that the consequenses will be reduced. Protection against potential exposures must have similar objective levels as protection against normal exposure since both normal and potential exposure have a similar risk of health effects [ICRP, 1997]. Dose reconstruction is necessary for defining dose levels in public exposures. Doses due to external and internal radiation sources can be reconstructed for internal organs and tissue. In dose reconstruction, organ doses may be used for evaluating the stochastic detriment and defining radiation threshold values in order to prevent deterministic effects [IAEA, 2004]. University of Ghana http://ugspace.ug.edu.gh 24 The Basic Safety Standards contains some dose limits and dose constraints for workers and the public [IAEA, 2003]. According to the Basic Safety Standards, the occupational exposure limits for all workers are: (a) 20 mSv effective dose per year, averaged over a consecutive 5 year period, or [IAEA, 2003]. (b) 50 mSv total effective dose in any single year [IAEA, 2003]. The Basic Safety Standards further states that dose limits to members of the public are: (c) 1 mSv effective dose in a year [IAEA, 2003]. 2.3.1 DOSE RECONSTRUCTION TECHNIQUES Theoretical models may be used for generating radiation doses to public members within the critical group. A mathematical model may be used in the form of algebraic and differential equations. The solutions to these mathematical models can be analytical or numerical and can be simulated by means of a computer programming language. Analytical methods are restricted to solving simple mathematical problems, while numerical methods can solve even the more complicated polynomials of order five and above [Stroud, 2003]. Field measurements will normally provide the relevant input parameters for the computer programming used. An analytical solution is generally an exact solution to a mathematical equation, while, a numerical solution is an approximation [Ye Zhang, 2011]. The activity concentration, C, for a radionuclide at any time t is calculated by Equation 2.4: t- .e  oCC  (2.4) Where, 𝐶𝑜 represents the initial activity concentration and λ represents the decay constant for the specific radionuclide [IAEA, 2003]. The actual activity concentration limit for a University of Ghana http://ugspace.ug.edu.gh 25 given radionuclide is computed through Equation 2.5 below: iu iu i Dose CDose Conc .lim (2.5) Where, 𝐶𝑜𝑛𝑐𝑖 represents the activity concentration limit (Bq/kg) for radionuclide i in the scenario, 𝐷𝑜𝑠𝑒𝑙𝑖𝑚 represents the scenario relevant dose limit in Sv/y, 𝐶𝑖𝑢 represents the initial activity concentration (Bq/kg) for radionuclide i that has a radiological impact in the area, while 𝐷𝑜𝑠𝑒𝑖𝑢 represents the dose due to the initial activity of radionuclide i in Sv/y [IAEA, 2003]. 𝐶𝑖𝑢 represents the initial activity concentration (Bq/kg) for radionuclide i that has a radiological impact in the scenario and is defined by Equation 2.6: wbd iu iu V A C   (2.6) Where, 𝐴𝑖𝑢 represents the initial radionuclide activity (Bq) that has a radiological impact in the scenario, 𝜌𝑏𝑑 represents the dry bulk density of the material in kg/m3 and 𝑉𝑤 represents the volume (m3) of material that has a radiological impact in the scenario [IAEA, 2003]. For each radionuclide in the material, the total activity limit (Bq) is given by Equation 2.7: i i i Dose ADose Amount .lim (2.7) Where, 𝐷𝑜𝑠𝑒𝑙𝑖𝑚 represents the applicable dose limit in Sv/y, 𝐴𝑖 represents the initial radionuclide activity (Bq) in the total amount of material and 𝐷𝑜𝑠𝑒𝑖 represents the total dose (Sv/y) due to the initial radionuclide activity [IAEA, 2003]. As soon as the required radionuclide activity limits are established in the material, it should be ensured that the combined doses from all radionuclides remain below the relevant public or worker dose limit. This can be attained by the summation rule from Equation 2.8: University of Ghana http://ugspace.ug.edu.gh 26 1 ,  lii Q Q (2.8) Where, 𝑄 represents the actual activity (Bq or Bq/kg) of radionuclide i that will be disposed and 𝑄𝑖,𝑙 represents the activity limit (Bq or Bq/kg) for radionuclide i from the available samples, based on the assumption that only radionuclide i will be disposed [IAEA, 2003]. Our calculation end points are the radionuclide activity concentration limits as well as the total activity limit that corresponds to an annual effective dose limit of 1 mSv/y and 20 mSv/y to members of the public and occupationally exposed workers respectively. 2.4 INSTRUMENTATION TO MEASURE NATURAL RADIOACTIVITY Various instruments can be used to measure the ionizing radiation emitted by samples. Typical instruments used are scintillation counters, gas filled detectors and solid state detectors. Examples of scintillation counters are the liquid scintillation counter [Abdellah, 2013]. Ionization chambers, proportional counters and Geiger-Muller counters are examples of gas filled detectors that are widely used [Faanu, 2011]. Solid state detectors are basically semiconductor detectors [Saha, 2006]. The basic requirement for each of these instruments is that the incoming ionizing radiation should interact with the detector such that the magnitude of the response of the instrument is proportional to the radiation effect that is being measured [Cember, 2009; Faanu, 2011]. To get a response from the detector, the radiation should have undergone either the Photoelectric Effect, Compton Scattering or Pair Production. The result of interaction in a detector is the appearance of a given amount of electric charge within the detector’s active volume [Cember, 2009; Faanu, 2011]. Ionizing gamma rays University of Ghana http://ugspace.ug.edu.gh http://link.springer.com/search?facet-author=%22Gopal+B.+Saha+Ph.D.%22 27 interact with atoms in the sensitive detector volume and this produces electrons by the ionization process. Collection of these electrons results in an output pulse. Figure 2-2 below shows the basic HPGe experimental setup required to achieve the output pulse. Fig. 2-2: Setup of the HPGe detector [Hossain, Sharip and Viswanathan, 2011] The energy required to produce ionization event in semi conductor detectors is 3.5 eV in contrast to the gas filled detectors which require mean high energy of 30-35 eV [Cember, 2009; Faanu, 2011]. Being neither good insulators nor conductors, semiconductors have electrical conduction properties midway between insulators and conductors, such that the most widely used semiconductors are germanium and silicon [Winn, 2010]. Semiconductors are members of group IV in the periodic table. Each member of this group has four valence electrons and will form a crystal lattice of covalently bonded atoms. These covalent bonds could be disrupted by the absorption of energy. An energy of 1.12 eV is needed for knocking out one valence electron from silicon. This would then result in a free electron and “hole” in the position that was previously occupied by the valence electron [Faanu, 2011]. The resulting hole and free electron are able to move about in the lattice University of Ghana http://ugspace.ug.edu.gh 28 structure. An electron that is adjacent to the hole can jump into the hole, thus leaving another hole behind. This property of semicondutors implies that current will flow through them if they are connected in a closed electrical circuit [Cember, 2009]. Therefore, the operation of a semiconductor detector is dependent on the excess holes or excess electrons present. An n-type semiconductor has excess electrons, while the p-type semiconductor has excess holes [Winn, 2010]. 2.4.1 RESOLUTION AND EFFICIENCY Resolution refers to the ability of the detector to distinguish between two energy peaks that are very close to each other. This implies that two sharp energy peaks must be produced by the detector in order for them to be clearly distinguished. The resolution is given by Equation 2.9 below: Energy FWHM solution Re (2.9) Where, Full Width at Half Maximum is represented by ‘FWHM’. Resolution decreases with energy. Detector efficiency is the quotient that relates the source activity to the number of counts observed. Various types of efficiency such as Absolute efficiency, Intrinsic efficiency and Full energy photo peak efficiency may be used for gamma-ray detectors [Akkurt, Gunoglu and Arda, 2014]. Absolute efficiency is the ratio of counts recorded on the detector to the number of gamma rays emitted. The detector’s absolute efficiency is necessary in radioactivity measurements and is given by Equation 2.10 below: S C abs N N  (2.10) University of Ghana http://ugspace.ug.edu.gh http://www.hindawi.com/46401767/ http://www.hindawi.com/37850621/ http://www.hindawi.com/60247506/ 29 Where, Ɛ𝑎𝑏𝑠 is the absolute efficiency of the detector, 𝑁𝐶 is the number of counts the detector records and 𝑁𝑆 is the number of gamma rays the source emits. Intrinsic efficiency is the ratio of the total number of pulses recorded on the detector to the number of gamma- rays arriving at the detector. Full energy photo peak efficiency refers to the efficiency for making only the full energy peaks [Akkurt, Gunoglu and Arda, 2014]. University of Ghana http://ugspace.ug.edu.gh http://www.hindawi.com/46401767/ http://www.hindawi.com/37850621/ http://www.hindawi.com/60247506/ 30 CHAPTER THREE: MATERIALS AND METHODS This chapter gives insight on the geology as well as the location of the study area. The type of samples collected, sampling procedure, sample preparation and analysis method are also described in this section. Mathematical functions or details to be used for natural radionuclide activity concentration calculations are also explained. Sampling was conducted in the study area from 01/07/2014 to 18/07/2014. Details pertaining to the radiation dose reconstruction are thoroughly presented. 3.1 MATERIALS Several materials and equipment were used to successfully carry out this research. Polythene bags, clean 1L polythene containers, 0.45 µm filter paper and 1M HNO3 are some of the materials that were crucial for this study. A gamma spectroscopy system that comprised of Genie 2000 software, a High Purity Germanium Detector (HPGe) and multi channel analyzer (MCA) were very important for this research. 1 liter Marinelli beakers, analytical balance, gloves, sample drying trays, sample grinder, sample drying oven, 500 µm sample wire mesh sieve and Global Positioning System device (GPS) with model number 6195us, serial number 584037-001 and version 001 were excellent resources for the success of this study. MATLAB R2011b and Microsoft Excel software were also used for this project. 3.2 DESCRIPTION OF STUDY AREA The study area is Morupule A Coal-Fired Power Station, located in Morupule (Botswana) at GPS coordinates 22.520˚S 27.037˚E and comprising of four turbo generators, each with an output of 33 MW. The power station uses 560, 000 to 630, 000 tonnes of bituminous coal each year and has been in operation since 1986. Basically, Morupule A Coal-fired University of Ghana http://ugspace.ug.edu.gh 31 Power Station was the first major power station built in Botswana. The coal-fired power station is located 300 km to the north of Botswana’s capital city, Gaborone. Road networks giving access to the power station are the A14 (connecting Palapye village and Serowe village) and the A1 (connecting Francistown city to Gaborone city via Palapye). Figure 3- 1 is a map of Botswana showing the general positional location (C) of Morupule A Coal- Fired Power Station. Figure 3-2 is another map showing the location (C) Morupule A Coal- Fired Station in Botswana with more details like nearby urban or rural locations. Fig. 3-1: General location of Morupule A Coal-Fired Power Station in Botswana University of Ghana http://ugspace.ug.edu.gh 32 Fig. 3-2: Detailed location of Morupule Coal-Fired Power Station in Botswana A small primary school (Kgaswe Primary School) is located approximately adjacent to the A14 road described above and about 800m to the south of Morupule Coal-Fired Power Station. The GPS coordinates of the school are 22.530˚S 27.038˚E. Palapye village is the nearest village and is located approximately 6 km to the east of Morupule A Coal-Fired Power Station. The land surrounding Morupule A Coal-Fired Power Station is mostly used as a communal grazing area for livestock such as cattle, sheep and goats. The fly-ash storage is just adjacent to the electrical power generation units, outside of the main building. There is a vast expanse of open space around the power station with vegetation such as trees and grass. Figure 3-3 shows an aerial view representing part of the study area. It shows the positions of the two fly ash storage tanks that are adjacent to the electrical University of Ghana http://ugspace.ug.edu.gh 33 power generation units (turbo generators), the coal storage area, the fly ash pond, the main power station gate, Kgaswe Primary School and all other features are shown. Figure 3-4 shows the points where samples were collected in and around Morupule A Coal-Fired Power Station, including those sampling points from just outside of Palapye village and at the new Bus Rank in Palapye. Plates 3-1 to 3-2 are actual on-site photographs that show some of the points where sampling was done within Morupule A Coal-Fired Power Station and its surroundings. Fig. 3-3: Aerial view showing part of the study area [Google Earth] University of Ghana http://ugspace.ug.edu.gh 34 Fig. 3-4: Layout of Morupule Coal-Fired Power Station showing sampling points University of Ghana http://ugspace.ug.edu.gh 35 Plate 3-1: Two fly ash storage tanks Plate 3-2: Coal Storage Area University of Ghana http://ugspace.ug.edu.gh 36 3.2.1 METEOROLOGY OF THE STUDY AREA Botswana generally has a predominantly subtropical climate that makes the whole country to be mostly semi-arid to arid. This therefore applies to the climate of Morupule. The rainy season lies in the summer months between October to March. January normally presents the peak of the rainy season. The winter season normally lies between the months of May to August. Winter is usually dry with peak winds in August. The transition months are usually April and September. The Morupule area has a potential evapotranspiration rate of 900 mm/year to 1200 mm/year, receives a mean annual precipitation of 371 mm and has average annual temperatures that lie between 30°C and 14°C [Ecosurv Environmental Consultants, 2008]. The north easterly winds are dominant in the area and have an average wind speed of 3 m/s. The evapotranspiration rate is thus about two or three times the average annual rainfall [Ecosurv Environmental Consultants, 2008]. 3.2.2 GEOLOGY AND SOILS The location of the area is on the Karoo Supergroup and the Palapye Group [Ecosurv Environmental Consultants, 2008]. Assemblages on the lower main seam Karoo at Morupule in Botswana are similar to the Striatopodocarpites fusus Biozone in the Collie Basin of Western Australia and to the 3a Microfloral Biozone in the Northern Karoo Basin of South Africa: An Aktastinian age for the Morupule strata is indicated by this [Stephenson and McLean, 2004]. Geology of the area comprises of mudstones and shales (Lotsane formation) covered by relatively thin Kalahari Beds. Tswapong formation fractured quartzites are found outcroping the western slope on the Tswapong Hills while black shales consisting of the Karoo Supergroup sediment siltstones and mudstones are University of Ghana http://ugspace.ug.edu.gh http://sajg.geoscienceworld.org/search?author1=M.+H.+Stephenson&sortspec=date&submit=Submit http://sajg.geoscienceworld.org/search?author1=D.+McLean&sortspec=date&submit=Submit 37 found covering the Lotsane formation [Ecosurv Environmental Consultants and GIBB Botswana, 2007]. The eastern edge is made up of these rocks, as well as successive shales, sandstones and conglomerates. The coal seams providing fuel for Morupule A Coal-Fired Power Station are found within all these sequences [Ecosurv Environmental Consultants and GIBB Botswana, 2007]. The study area has soils that are of orange color, sandy silt loam texture and fine grain size. The soils are wind blown, and were formed by the weathering of the Ntane Sandstone Formation that outcrops the Serowe escarpment. Ferralic Arenosols is the main soil type in the Morupule A Coal-Fired Power Station Area, whereas Calcaric Cambisols and Orthic Luvisols soil types predominate southwards, while clay soil is found in the lower soil profile [Ecosurv Environmental Consultants and GIBB Botswana, 2007]. 3.2.3 HYDROGEOLOGY The area is approximately 950 m above the mean sea level and there generally is a gentle slope falling away towards the south east of the area. Lotsane and Morupule rivers are each located within 10 km of Morupule A Coal-Fired Power Station and are both ephemeral, meaning that they only flow at certain times during the year. Morupule river runs north- southwards and actually pours into Lotsane river, which in turn flows eastwards towards Palapye. Figure 3-5 shows the locations of Lotsane and Morupule rivers in relation to Morupule A Coal-Fired Power Station and other nearby topographical features [Water Surveys Botswana, 2007], all in 3-D (three dimensions). University of Ghana http://ugspace.ug.edu.gh 38 Fig. 3-5: 3-D Satellite image showing positions of Lotsane and Morupule rivers Lotsane river then feeds the Limpopo river at the Botswana-South Africa border. Below the Lotsane formation mentioned in Section 3.1.3 above lies the Palapye fractured quartzitic which may be considered to be a very minor aquifer. The Lotsane formation as well as the shales and mudstones from the Karoo sequence mentioned in Section 3.1.3 above do not have usable groundwater quantities [Ecosurv Environmental Consultants and GIBB Botswana, 2007]. 3.2.4 VEGETATION Acacia/Burkea/Ochna Savannah and Acacia Savannah are the two main vegetation types that are found in the area. The rocky hill outcrops is an additional vegetation type that is also found within the area. Invasive species of Argemone Mexicana and Dichrostachys University of Ghana http://ugspace.ug.edu.gh 39 cineria also exist in this area [Ecosurv Environmental Consultants, 2008]. Nicotiana sp is the most common bushy plant species that is found on the walls of the fly ash ponds [Ecosurv Environmental Consultants and GIBB Botswana, 2007]. 3.3 METHOD 3.3.1 SAMPLES COLLECTION Thirty (30) samples of various matrices were collected in and around Morupule A Coal- Fired Power Station. These comprised of: (a) Nine (9) soil samples from the power station, its surroundings and the nearby village of Palapye (about 5 km away). (b) Seven (7) bituminous coal samples from within the power station. (c) Eight (8) fly ash samples from the fly ash storage area. (d) Six (6) water samples from the fly ash ponds. Random sampling was performed over a large area to ensure that each sample was a true representative of the whole and suitable to use in the study. All sample collection equipment, sample preparation areas and containers were kept clean to avoid contamination. Any sample with relatively high levels of activity was kept separated from other samples to avoid cross contamination. 3.3.1.1 SOIL/COAL/FLY ASH SAMPLING Soil samples from different and undisturbed areas were collected to a depth of 25-50 cm with a coring tool into clearly labelled polythene bags. Bituminous coal and fly ash samples from different locations were collected by means of a scooping tool into clearly labelled polythene bags. Visible objects like grass and roots were removed manually from the soil and bituminous coal samples. All labelled samples were tightly sealed in their polythene University of Ghana http://ugspace.ug.edu.gh 40 bags. The labelled samples were then transferred to GAEC laboratory to be prepared for analysis. As a precaution for ensuring that representative samples were collected for analysis from the area, a survey was first done with the sole aim of determining the sampling points. All soil sampling points were marked by means of a Global Positioning System device (GPS) with model 6195us, serial number 584037-001 and version 001. Appendix 3 shows all soil sampling points within Morupule A Coal-Fired Power Station and its surroundings. Appendices 4 and 5 show all fly ash and bituminous coal sampling points respectively within Morupule A Coal-Fired Power Station. 3.3.1.2 WATER SAMPLING Clean and clearly labelled 1L polythene containers were used to collect water samples from regions of interest within the fly ash pond. Visible coarse material or suspended sediments were first removed by filtering the water samples using 0.45 µm filter paper, after which the collected water samples were immediately spiked with 1M HNO3 before the respective container lids were sealed in place. The 1M HNO3 was meant to prevent the adsorption of radionuclides onto the internal surface of the polythene container walls [Martin, Hancock; 1992]. All water sampling points were marked by means of a Global Positioning System device (GPS) with model 6195us, serial number 584037-001 and version 001. All labelled and sealed water samples were then transferred to GAEC laboratory to be prepared for analysis. Appendix 6 shows all water sampling points from the fly ash ponds. 3.3.2 SAMPLE PREPARATION FOR DIRECT GAMMA SPECTROMETRY 3.3.2.1 SOIL/COAL/FLY ASH SAMPLE PRAPARATION At GAEC laboratory, the soil, bituminous coal and fly ash samples were spread onto clean aluminium trays and air dried in the laboratory for several days as required. They were then University of Ghana http://ugspace.ug.edu.gh 41 dried to a constant weight in an oven for 3 hours at 105 °C [Faanu, 2011]. The soil and coal samples were crushed into a fine powdery state by means of a grinder, after which they were sieved into previously weighed 1 liter marinelli beakers using a 500 µm wire mesh sieve. The dry fly ash samples were added into previously weighed 1 liter marinelli beakers without first being crushed since they were already in a fine powder state. All these marinelli beakers with samples were then tightly sealed with their respective lids and paper tape, after which the sealed marinelli beakers were weighed again to obtain the actual weight of the samples. The tightly sealed 1 liter marinelli beakers were then kept for 30 days to achieve secular equilibrium between the parent and daughter radionuclide of the enclosed contents [Faanu, 2011; Agalga, Darko and Schandorf, 2013; Ademola and Onyema, 2014]. After this period of 30 days, the contents of the sealed marineli beakers underwent radionuclide detection and measurement by a gamma spectrometry system using HPGe detector (High Purity Germanium Detector) for 10 hours. The resulting radionuclide activity concentrations were in the units Bq/kg [Faanu, 2011]. 3.3.2.2 WATER SAMPLE PREPARATION The collected 1 liter water samples were filtered into their respective previously weighed 1 liter Marinelli beakers. The respective Marinelli beakers with samples were then tightly sealed with their respective lids and paper tape, after which the sealed marinelli beakers were weighed again to obtain the actual weight of the water samples. The sealed Marineli beakers then underwent radionuclide detection and measurement by a gamma spectrometry system using HPGe detector (High Purity Germanium Detector) for 10 hours. The resulting radionuclide activity concentrations were in the units Bq/l [Faanu, 2011]. University of Ghana http://ugspace.ug.edu.gh 42 3.3.3 SAMPLE ANALYSIS USING DIRECT GAMMA SPECTROMETRY A computerized gamma ray spectrometry system was used for this study. The system comprises of n-type High Purity Germanium Detector (HPGe) coupled with a Multi Channel Analyzer (MCA) [Faanu, Ephraim and Darko, 2010]. The computer system used is loaded with the software Genie 2000. Liquid nitrogen is used for cooling the HPGe detector to a temperature of 77 K [Reguigui, 2006]. The computerized gamma spectrometry system is powered by an uninterrupted power supply (UPS) unit. HPGe detector relative efficiency is 25% and its energy resolution is 1.8 keV at a Co-60 gamma energy of 1332 keV [Faanu et al., 2013]. Qualitative identification of radionuclides was done with the aid of their photopeak energies, while their quantification was done using the software Genie 2000. HPGe detector energy and efficiency calibrations were perfomed before analysis of the collected samples. The energy and efficiency calibrations were performed to allow the qualitative identification and quantification of the natural radionuclides of interest. HPGe detector calibration was performed by means of a reference standard solution. The reference standard solution was measured into a 1 liter marinelli beaker and counted for 10 hours. 3.3.3.1 ENERGY CALIBRATION The HPGe detector energy daily calibration was performed through the matching of gamma energy peaks in the spectrum of the reference standard to the spectrometer channel number [Çetiner, 2008]. The centroid channels and corresponding radionuclide energy peaks were recorded and used to make a calibration curve of Energy vs. Channel Number. University of Ghana http://ugspace.ug.edu.gh 43 A least square curve fitting was done to obtain the calibration curve in polynomial form, represented by Equation 3.1 below:  N n i aE 0 inC (3.1) Where, 𝐸𝑖 is the calibration energy for the ith channel number, 𝐶𝑖 is the ith channel number, the summation is from n = 0 to n = N, while 𝑎𝑛 gives the calibration constant [Çetiner, 2008]. The calibration was performed through the counting of standard radionuclides with known activities and gamma energy peaks from 60 keV to 2000 keV [Faanu, 2011]. The HPGe detector was used to count the standard for 10 hours. Table 3-1 gives the standard radionuclides used in the energy calibration as well as their activities, emission rates and gamma energies. Table 3-1: Standard radionuclides used for the energy and efficiency calibration University of Ghana http://ugspace.ug.edu.gh 44 3.3.3.2 EFFICIENCY CALIBRATION Detector efficiency was defined earlier in Section 2.4.1. Efficiency calibration of the system was performed accurately to ensure proper quantification of the radionuclides that were present in the samples [Faanu, 2011]. During efficiency calibration, the peak search algorithm was necessary to locate as well as quantify peaks before associating them with decay-corrected emission rates for each line. Thus, an efficiency curve and equation were determined in the process, such that the efficiency curve may go to as high as the 9th order polynomial [Çetiner, 2008]. For this particular work, a 4th order polynomial was used. It is imperative that all detector system adjustments and settings be carried out prior to determining the efficiencies and this should be maintained until a new calibration is undertaken [Faanu, 2011; IAEA, 1989]. The efficiency calibration of the HPGe detector generally shows that efficiency decreases as the energy increases [Rahman, Naher, Ghosh and Islam, 2014]. The same mixed radionuclides standard was used for both the energy and efficiency calibration of the HPGe detector, with the standard being counted for 10 hours at a number of calibration points between 60 keV to 2000 keV [Faanu, 2011]. To determine efficiencies, Equation 3.2 was used [Darko et al., 2007; Faanu, 2011]: 𝜂(𝐸) = 𝑁𝑇−𝑁𝐵 𝑃𝐸. 𝐴𝑆𝑇𝐷 𝑇𝑆𝑇𝐷 (3.2) Where, 𝑁𝑇 represents the total counts under a photopeak, 𝑁𝐵 denotes the background count, 𝑃𝐸 is the gamma ray yield, 𝐴𝑆𝑇𝐷 represents the activity of calibration standard during the time of measurement in Becquerels (Bq), while 𝑇𝑆𝑇𝐷 represents the counting time of the University of Ghana http://ugspace.ug.edu.gh 45 standard. Table 3-1 gives the standard radionuclides used in the efficiency calibration as well as their activities, emission rates and gamma energies. 3.3.3.3 MINIMUM DETECTABLE ACTIVITY The minimum detectable activity (MDA) is the lowest radioactivity quantity that can be measured at specific conditions. Thus, the MDA becomes particularly important for environmental level systems in which the sample count rate is almost similar to the background reading [Faanu, 2011]. The main factor affecting MDA is the background value, such that this background value can be reduced by better resolution. MDA values become lower at better resolution and higher efficiency of the detector [Abraham, Pelled and German, 2002]. In the determination of MDA, the the background is counted with a blank such as a sample holder. For this research, a distilled water-filled 1L Marinelli beaker was counted for 10 hours such that the average background peaks were used to determine the MDA. In the case of Ra-226, the MDA was determined by utilizing the average peaks of the daughter gamma lines 295.2 keV and 351.9 keV of Pb-214 as well as 609.31 keV and 1764.5 keV of Bi-214. For determining the MDA of Th-232, the daughter gamma lines 238.63 keV of Pb-212, 583.2 keV and 2614.53 keV of Tl-208, 1460.8 keV of K-40, as well as 911.21 keV of Ac-228 were utilized [Faanu, 2011]. Equation 3.3 was used to determine the MDA: MDA = 𝐾𝛼√𝑁𝐵 𝑃𝐸.𝜂(𝐸)𝑇𝑐𝑀 (3.3) Where, MDA denotes the minimum detectable activity in Bq/kg, 𝐾𝛼 represents the statistical coverage factor of 1.645 at 95% confidence level, 𝑁𝐵 represents the background University of Ghana http://ugspace.ug.edu.gh 46 counts in the region of interest for a particular radionuclide, 𝑃𝐸 represents the gamma emission probability, 𝑇𝑐 is the time of counting, 𝜂(𝐸) is the photopeak efficiency while M is the dry weight of the sample [Khandaker et al., 2012]. 3.3.3.4 CALCULATION OF ANNUAL EFFECTIVE DOSE DUE TO THE RADIOACTIVITY IN SAMPLES For soil/coal/fly-ash/water samples, the activity concentration of U-238 was calculated from the average peak energies of 295.21 keV and 351.92 keV for Pb-214 and 609.31 keV as well as 1764.49 for Bi-214. In the same way, activity concentration for Th-232 was calculated from the peak Pb-212 energy of 238.63 keV, Ac-228 peak energy of 911.21 keV, as well as the average peak energies for Tl-208 being 583.19 keV and 2614.53 keV. Activity concentration for K-40 was calculated by utilizing its peak energy of 1460.83 keV. Bi-214, with a peak energy of 609.31 keV, was used to determine Ra-226. Activity concentration for soil, coal and fly ash samples are in the units Bq.kg-1. Water sample activity concentration is in the units Bq.l-1. Equation 3.4 below was used to calculate activity concentrations of K-40, Th-232, U-238 and Ra-226 for the soil, coal, fly ash and water samples in this study: 𝐴𝑠𝑝 = 𝑁𝐷𝑒𝜆𝑃𝑡𝑑 𝑝.𝑇𝑐.𝜂(𝐸).𝑚 (3.4) Where, 𝑁𝐷 represents the radionuclide net count in samples, exp (𝜆𝑃𝑡𝑑) represents the decay correction factor for delay between time of sampling and counting, 𝑡𝑑 represents the time delay between the sampling and counting, P represents the gamma-ray yield, η(E) represents the detector system’s absolute counting efficiency, 𝑇𝑐 represents the counting University of Ghana http://ugspace.ug.edu.gh 47 time of sample, m represents the sample mass in kilograms or volume in liters, while 𝜆𝑃 represents the decay constant associated with the parent radionuclide. At 1.0 m above the ground for soil/coal/water/fly-ash samples, the external gamma dose rate, 𝐷𝛾, was calculated from the activity concentrations using Equation (3.5) below [Faanu, Ephraim and Darko, 2010; Faanu et al., 2013; Zeevaert, Sweeck and Vanmarcke, 2005]: 𝐷𝛾(𝑛𝐺𝑦ℎ−1) = 𝐷𝐶𝐹𝐾 × 𝐴𝐾 + 𝐷𝐶𝐹𝑈 × 𝐴𝑈 + 𝐷𝐶𝐹𝑇ℎ × 𝐴𝑇ℎ (3.5) Where, 𝐷𝐶𝐹𝐾, 𝐷𝐶𝐹𝑈 and 𝐷𝐶𝐹𝑇ℎ are dose conversion factors for K-40, U-238 and Th-232 respectively in nSv.h-1/Bqkg such that 𝐴𝐾, 𝐴𝑇ℎ and 𝐴𝑈 are the activity concentrations for K-40, Th-232 and U -238 and respectively. 𝐷𝐶𝐹𝐾, 𝐷𝐶𝐹𝑈 and 𝐷𝐶𝐹𝑇ℎ values are listed below [UNSCEAR, 2000; Faanu, 2011]: 𝐷𝐶𝐹𝐾 = 0.0417 nSv.h-1.Bq-1kg-1 𝐷𝐶𝐹𝑈 = 0.462 nSv.h-1.Bq-1kg-1 𝐷𝐶𝐹𝑇ℎ = 0.604 nSv.h-1.Bq-1kg-1 The average annual effective dose was calculated from the absorbed dose rate by using a dose conversion factor of 0.7 Sv.Gy-1 as well as the outdoor occupancy factor of 0.2 [UNSCEAR, 2000]. Equation 3.6 below was used to calculate the average annual effective dose: Eγ = Dγ × 0.2 × 8760 × 0.7 (3.6) Where, Eγ represents the average annual effective dose, Dγ represents the absorbed dose rate in air [Faanu, Ephraim and Darko, 2010; UNSCEAR, 2000]. University of Ghana http://ugspace.ug.edu.gh 48 3.3.3.5 ANNUAL EFFECTIVE DOSE CALCULATIONS FROM EXTERNAL GAMMA DOSE RATE MEASUREMENTS At every sampling point, several external gamma dose rate measurements were made at 1m above the ground with a suitable and calibrated Thermo survey meter (serial number 21535 and model FH40G-L10) and the average dose rate was computed. The annual effective dose (𝐸𝛾,𝑒𝑥𝑡) was then estimated from this measured average external gamma dose rate using Equation 3.7a below: 𝐸𝛾,𝑒𝑥𝑡 = 𝐷𝛾,𝑒𝑥𝑡. 𝑇𝑒𝑥𝑝. 𝐷𝐶𝐹𝑒𝑥𝑡 (3.7a) Where, 𝐷𝛾,𝑒𝑥𝑡 represents the average external (outdoor) gamma dose rate in μGy.h-1, 𝑇𝑒𝑥𝑝 represents the exposure duration per year of 8760 hours (365 days x 24 hours) and using the outdoor occupancy factor of 0.2, 𝐷𝐶𝐹𝑒𝑥𝑡 represents the effective dose to absorbed dose conversion factor of 0.7 Sv.Gy-1 for the environmental exposure to gamma rays [Faanu, Ephraim and Darko, 2010; UNSCEAR, 2000, Faanu, 2011]. For the indoor case, Equation 3.7b was used to estimate the annual effective dose: 𝐸𝛾,𝑖𝑛𝑑 = 𝐷𝛾,𝑖𝑛𝑑. 𝑇𝑒𝑥𝑝. 𝐷𝐶𝐹𝑖𝑛𝑑 (3.7b) Where, 𝐷𝛾,𝑖𝑛𝑑 denotes the calculated dose rate in nGy.h-1, 𝑇𝑒𝑥𝑝 denotes the indoor occupancy time (0.8 × 24 h × 365 days = 7008 h.y-1), and 𝐷𝐶𝐹𝑖𝑛𝑑 is the conversion factor of 0.7 Sv.Gy-1 [Allam, Ramadan and Taha, 2014]. 3.3.4 RADIOLOGICAL HAZARD ASSESSMENT Soil and fly ash from the study area may be used as building materials. Fly ash is an excellent substitute for concrete, cement and clay [Ademola and Onyema, 2014]. The University of Ghana http://ugspace.ug.edu.gh http://www.rpe.org.in/searchresult.asp?search=&author=Kh+A+Allam&journal=Y&but_search=Search&entries=10&pg=1&s=0 http://www.rpe.org.in/searchresult.asp?search=&author=AbouBakr+A+Ramadan&journal=Y&but_search=Search&entries=10&pg=1&s=0 http://www.rpe.org.in/searchresult.asp?search=&author=Amal+Taha&journal=Y&but_search=Search&entries=10&pg=1&s=0 49 radium equivalent activity concentration (Raeq), external hazard (Hext ) and internal hazard (Hint ) indices were used to assess the radiological hazard due to natural radioactivity from the fly ash, coal, soil and water which may be used as building/construction material. The only natural radionuclides considered in this radiological assessment are 40K, 226Ra and 232Th. Calculations of Raeq, Hext and Hint were done by means of equations (3.8) to (3.10) respectively: Raeq=ARa+1.43ATh+0.077AK (3.8) Hext=ARa/370+ATh/259+AK/4810≤1 (3.9) Hint=ARa/185+ATh/259+AK/4810≤1 (3.10) Where, ARa, ATh and AK are activity concentrations for the natural radionuclides 226Ra, 232Th and 40K in Bq/kg respectively. Raeq index basis is on the estimation that the same gamma dose rate is produced by 1 Bq/kg of 226Ra, 0.7 Bq/kg of 232Th and 13 Bq/kg of 40K. In order to ensure that bulding materials are safe to use with respect to radiation, the maximum Raeq for these materials must not exceed 370 Bq/kg. The maximum allowed values for Hext and Hint are unity and dimensionless [Ademola and Onyema, 2014]. The representative level index (Iγr) is a radiation index hazard that is used to estimate the level of γ radiation hazard [Harb et al., 2008; NEA-OECD, 1979] due to natural radionuclides in samples and is represented by Equation 3.11 below: Iγr=ARa/150+ATh/100+AK/1500 (3.11) Where, ARa, ATh and AK are activity concentrations for natural radionuclides 226Ra, 232Th and 40K in Bq/kg respectively. In order for the radiation hazard to be negligible, the value of the representative level index Iγr must be less than unity [Harb et al., 2008]. University of Ghana http://ugspace.ug.edu.gh 50 3.3.5 DOSE RECONSTRUCTION Radioactive decay is a random process, therefore we cannot predict if a single nucleus in a sample will undergo radioactive decay in a given time period. What can be predicted is the average decay behaviour for a very large number of similar radionuclides N in a sample. During a small interval of time Δt, ΔN of the atoms undergo radioactive decay [Shultis and Faw, 2007]. The probability for any radionuclide in the sample to decay in time interval Δt is therefore given by ΔN/N. The value of the statistically averaged decay probability per unit time (considering the limit of infinitely small time interval Δt) approaches λ, which is the decay constant: λ= lim Δt→0 ( ΔN/N Δt ) (3.12) Every radionuclide has its own unique decay constant. Decay constant is basically the probability that a radionuclide decays in unit time for an infinitesimal interval of time. The radionuclide decays more slowly for smaller values of the decay constant λ. The decay constant is zero (λ = 0) for stable radionuclides. For radionuclides, λ only depends on nuclear forces and is not dependent on empirical factors like pressure or temperature [Shultis and Faw, 2007]. In the case of a sample consisting of a large number of similar radionuclides (N > > > 1), continuous mathematics is used to define an inherently discrete process. Therefore, at time t, N(t) is the average number of radionuclides present in the sample. The probability for any radionuclide in the sample to decay in a time interval dt is λdt. Therefore in dt and at a time t, λdtN(t) decays are expected in the sample. This should equal the decrease –dN in the number of radionuclides from the sample as shown below: -dN=λN(t)dt (3.13a) University of Ghana http://ugspace.ug.edu.gh https://www.google.com.gh/search?tbo=p&tbm=bks&q=inauthor:%22J.+Kenneth+Shultis%22 https://www.google.com.gh/search?tbo=p&tbm=bks&q=inauthor:%22Richard+E.+Faw%22 https://www.google.com.gh/search?tbo=p&tbm=bks&q=inauthor:%22Richard+E.+Faw%22 https://www.google.com.gh/search?tbo=p&tbm=bks&q=inauthor:%22J.+Kenneth+Shultis%22 https://www.google.com.gh/search?tbo=p&tbm=bks&q=inauthor:%22Richard+E.+Faw%22 51 The above expression simplifies to Equation 3.13b below: dN(t) dt = −λ N(t) (3.13b) The solution of the differential Equation 3.13b above is given as Equation 3.14 below: N(t)=No𝑒−λt (3.14) Where, No represents the number of radionuclides present in the sample when t = 0. Equation 3.14 is thus known as the radioactive decay law, with a unique property known as the half - life [Shultis and Faw, 2007]. The half - life denotes the time required for the activity to reduce to half of its value by a radioactive decay process [McNaught and Wilkinson, 1997]. The half life is a constant represented by 𝑇1/2 and is independent of time. Using the concept of half life and substituting into Equation 3.14 will yield expression 3.15 below: N(𝑇1/2)≡ No 2 = No𝑒−λ𝑇1/2 (3.15) Solving Equation 3.15 gives Equation 3.16 for 𝑇1/2 below: 𝑇1/2= ln 2 λ (3.16) Some useful averages and probabilities are determined using the exponential decay law. Considering No similar radionuclides at an initial time t = 0, it is expected that the number of atoms will be No𝑒−λ𝑡 at a later time t. Equation 3.17 represents the probability 𝑃 that any one of the atoms does not undergo radioactive decay in the time interval t: 𝑃(𝑡) = N(t) N(0) = 𝑒−λt (3.17) Equation 3.18 below represents the probability P(t) of radionuclide decay in the time interval t [Mayin, 2014]: P(t)=1-𝑃(𝑡)=1- 𝑒−λt (3.18) University of Ghana http://ugspace.ug.edu.gh https://www.google.com.gh/search?tbo=p&tbm=bks&q=inauthor:%22J.+Kenneth+Shultis%22 https://www.google.com.gh/search?tbo=p&tbm=bks&q=inauthor:%22Richard+E.+Faw%22 52 As t becomes very small (t Δt < < 1), Taylor series approximation shows that: P(Δt)=1-𝑒−λΔt=1–[1-λΔt+ 1 2! (λΔt)2-…]≈λΔ𝑡 (3.19) 3.3.5.1 TAYLOR SERIES METHOD FOR NUMERICAL SOLUTIONS IN DOSE RECONSTRUCTION The Taylor Series method with numerical derivatives was used to approximate numerical solutions to ordinary differential equations. This Taylor Series method was one of the earliest analytic-numeric algorithms used in the approximation of solutions to ordinary differential equations [Miletics and Moln´arka, 2014]. The exponential term (decay factor) fro