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Multi-Scale Modelling of Borehole Yields in Chalk Aquifers

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Multi-Scale Modelling of Borehole Yields in Chalk Aquifers Multi-scale modelling of borehole yields in chalk aquifers Kirsty Upton Department of Civil and Environmental Engineering Imperial College London A thesis submitted for the degree of Doctor of Philosophy Abstract A new multi-scale groundwater modelling methodology is presented to simulate pumped water levels in abstraction boreholes accurately within regional groundwater models. This provides a robust tool for assessing the sustainable yield of supply boreholes, thus improving our understanding of groundwater availability during drought. Under UK legislation water companies are required to quantify the reliable, or deployable, output (DO) of all groundwater and surface water sources under drought conditions. However, there is a current lack of appropriate tools for assessing groundwater DO, especially for hydrogeologically complex sources. This is a particular issue for sources in the Chalk aquifer, which is vertically heterogeneous and closely linked with the surface water system. The DO of an abstraction borehole is influenced by processes operating at different scales. The multi-scale model incorporates these processes, providing a new and unique method for simultaneously representing regional groundwater processes, local-scale processes, and features of a borehole. The 3D borehole-scale model solves the Darcy- Forchheimer equation in cylindrical co-ordinates to simulate both linear and non-linear radial flow to a borehole. It represents important features of the borehole itself and incorporates horizontal and vertical aquifer heterogeneity. The radial flow model is embedded within a Cartesian grid using a hybrid radial-Cartesian finite difference method which has not previously been applied in the field of groundwater modelling. A novel methodology is developed to couple this model to a regional groundwater model, ZOOMQ3D, using the OpenMI model linkage software. This provides a flexible and efficient tool for assessing the behaviour of a groundwater source within its regional hydrogeological context during historic droughts and under climate change. The advantages of the new method for calculating the sustainable yield of abstraction boreholes are demonstrated through application to a Chalk supply borehole in the Thames Basin. The multi-scale methodology has many potential applications beyond DO, but provides a valuable tool for water companies to produce a more reliable and robust assessment of groundwater availability, in line with the current water resources planning guidelines. 2 Statement of own work The contents of this thesis are the result of my own independent work, except where otherwise stated. Any quotation from, or description of, the work of others is fully acknowledged by reference to the original source, whether published or unpublished. Material from Chapters 4 and 5 was presented at the MODFLOW and More Conference in Colorado, 2013, and was published in the conference proceedings (Upton et al., 2013). The contents of Chapters 4-6 have also been presented at various other conferences and meetings, including the EGU conference in Vienna (2014), the UK Groundwater Modellers Forum meeting in Birmingham (2014), and the IAH Congress in Marrakech (2014). 3 Copyright declaration The copyright of this thesis rests with the author and is made available under a Creative Commons Attribution Non-Commercial No Derivatives licence. Researchers are free to copy, distribute or transmit the thesis on the condition that they attribute it, that they do not use it for commercial purposes and that they do not alter, transform or build upon it. For any reuse or redistribution, researchers must make clear to others the licence terms of this work. 4 Acknowledgements This research was primarily funded by the Engineering and Physical Sciences Research Council, with additional support from the British Geological Survey and Thames Water Utilities Ltd. I am extremely grateful to my supervisors, Adrian Butler and Chris Jackson, for giving me the opportunity to carry out this research, and for providing invaluable guidance, knowledge, and support at every stage of the project. There are many others at the British Geological Survey who have provided support and encouragement over the last 4 years. I would particularly like to thank Majdi Mansour for his expert guidance on radial flow modelling, other members of the Environmental Modelling Group for their input and assistance, and the groundwater team in Edinburgh for their support over the last nine months. Thanks to Mike Jones and the groundwater resources team at Thames Water for providing data and advice on the practical requirements and application of this work. I’d finally like to thank my family and friends and in particular my husband, Liam, for his unfaltering love and support throughout the many ups and downs of the last four years. 5 Contents Abstract......................................................................................................................................2 Statement of Own Work............................................................................................................3 Copyright Declaration...............................................................................................................4 Acknowledgements...................................................................................................................5 List of Figures..........................................................................................................................10 List of Tables...........................................................................................................................18 1 Introduction ...................................................................................................................... 19 1.1 The Chalk Aquifer as a Groundwater Resource........................................................ 19 1.2 Deployable Output .................................................................................................... 20 1.3 Aims of the Research ................................................................................................ 24 2 The Chalk Aquifer ............................................................................................................ 28 2.1 The Geology of the Chalk ......................................................................................... 28 2.2 Flow Processes within the Chalk .............................................................................. 29 2.3 Modelling the Chalk Aquifer .................................................................................... 31 2.3.1 The Importance of Groundwater Modelling ................................................................. 31 2.3.2 Modelling the Regional Chalk Aquifer ......................................................................... 32 2.3.3 Modelling Chalk Boreholes .......................................................................................... 33 2.3.4 Key Issues for Modelling the Chalk Aquifer ................................................................ 36 3 Multi-scale Modelling ...................................................................................................... 38 3.1 Introduction ............................................................................................................... 38 3.2 Groundwater Modelling at the Regional and Borehole Scale ................................... 39 3.2.1 Numerical Methods ....................................................................................................... 39 3.2.2 Regional Groundwater Modelling ................................................................................ 41 3.2.3 Modelling Flow to Boreholes ....................................................................................... 42 3.2.4 The Issue of Scale ......................................................................................................... 45 6 3.3 Multi-Scale Methods ................................................................................................. 46 3.3.1 Hybrid Radial-Cartesian Finite Difference Method ...................................................... 46 3.3.2 Finite Volume Two Point Flux Approximation Method ............................................... 47 3.3.3 Finite Volume Multi Point Flux Approximation Method ............................................. 49 3.4 Application to the Chalk ........................................................................................... 50 3.5 Conclusions ............................................................................................................... 53 4 The Darcy-Forchheimer Radial Flow Model ................................................................... 56 4.1 Introduction ............................................................................................................... 56 4.2 Development of the Radial Flow Model ................................................................... 56 4.3 Validation of the Radial Flow Model ........................................................................ 64 4.3.1 Confined Aquifer with Well Storage ............................................................................ 64 4.3.2 Confined Aquifer with Linear and Non-Linear Drawdown .......................................... 66 4.3.3 Unconfined Aquifer without Dewatering ...................................................................... 68 4.3.4 Unconfined Aquifer with
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