Ground Water Flow Model for Fractured Media Ernesto Da Silva Pitombeira University of New Hampshire, Durham

University of New Hampshire University of New Hampshire Scholars' Repository Doctoral Dissertations Student Scholarship Spring 1994 Ground water flow model for fractured media Ernesto da Silva Pitombeira University of New Hampshire, Durham Follow this and additional works at: https://scholars.unh.edu/dissertation Recommended Citation Pitombeira, Ernesto da Silva, "Ground water flow model for fractured media" (1994). Doctoral Dissertations. 1793. https://scholars.unh.edu/dissertation/1793 This Dissertation is brought to you for free and open access by the Student Scholarship at University of New Hampshire Scholars' Repository. It has been accepted for inclusion in Doctoral Dissertations by an authorized administrator of University of New Hampshire Scholars' Repository. For more information, please contact [email protected]. INFORMATION TO USERS This manuscript has been reproduced from the microfilm master. UMI films the text directly from the original or copy submitted. 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Further reproduction prohibited without permission. GROUND WATER FLOW MODEL FOR FRACTURED MEDIA BY ERNESTO DA S. PITOMBEIRA B.S. Universidade Federal do Ceard, 1968 M.S. Universidade Federal do Ceard, 1985 DISSERTATION Submitted to the University of New Hampshire in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy in Engineering May, 1994 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. This dissertation has been examined and approved. Dissert ion Director, Thomas F. Ballestero Associa rofessor of Civil Engineering : ,---------------------------------------------- Jean Benoit, Associate Professor of Civil Engineering eeker, Professor of Mathematics £ * J L - Pedro A. de Alba, Associate Professor of Civil Engineering nos H. Vernon, Ph.D., Structural Geologist ^nd Project Manager, Hydrosource Asssociates, Inc., New Hampshire Date Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. DEDICATION For all that he has represented to this work; For all that he represents to this work; for all that he has represented to myself as my friend, professor, and adviser; For all that he represents to myself as my friend, professor, and adviser; For all that he certainly will represent to myself as my friend, professor, and adviser; I dedicate this dissertation to DR. THOMAS P. BALLESTERO (QUEUAO), my friend, professor, and adviser. in Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. ACKNOWLEDGMENTS I would like to acknowledge my family (Suzy, Aline, and Glauber) for their patience and love, not only during my Ph.D. program but also during my lifetime. There were many people and institutions that helped me out in my program. In particular, I cannot forget: my dissertation committee — Dr. Thomas Ballestero, Dr. Jean Benoit, Dr. David Meeker, Dr. Pedro de Alba, and Dr. James Vernon — I am not able to find a word (or a thousand of them) to acknowledge them; CAPES - Brazil - I send to it my pride in being a CAPES fellow; my friends - Marilyn Ross, Frank "Chico" Smith, Karen Garrison, Ilson da Silveira, Marco Castro, and Clovis EspiTito Santo — even if I wrote a book, it would be impossible for me to express my debt to them; Dr. Wendell Brown -- for your support at the right time, I acknowledge you; my colleagues at UFC - Dr. Suetonio Mota, Dr. Walter Martins, Dr. FMvio Torres, and Dra. Jucineide Cavalcante — who helped out since the very beginning until the last minute of my stay in the United States. I also acknowledge HydroSource Associates, Inc., BCI Geonetics, Lockheed Engineering & Sciences Company, and the US-EPA for the data set used in this work. iv Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. TABLE OF CONTENTS DEDICATION........................................................................................................................iii ACKNOWLEDGMENTS.................................................................................................. iv LIST OF TABLES............................................................................................................... viii LIST OF FIGURES............................................................................................................ x ABSTRACT...........................................................................................................................xiv CHAPTER PAGE CHAPTER I INTRODUCTION.................................................................................. 1 CHAPTER II LITERATURE REVIEW....................................................................... 4 2.1 Introduction .................................................................................................... 4 2.2 Geometric Characteristics of Fractures in Rocks .................................... 5 2.3 Hydraulics of Fracture Flow ...................................................................... 14 2.4 Hydraulic Sink Capture Zone/Hydraulic Source Plume ........................ 21 2.5 Adjoint Sensitivity Analysis ....................................................................... 31 CHAPTER III MATHEMATICAL FORMULATION............................................... 35 3.1 Introduction .................................................................................................. 35 3.2 Fracture System Generation .......................................................................... 35 3.2.1 Location of the Fracture Centers ............................................................... 36 3.2.2 Fracture Orientation ........................ 38 3.2.3 Fracture Length............................................................................................. 41 3.2.3.1 Identification of the Fracture Intersections .............................................. 45 3.2.3.2 Elimination of the Isolated Fracture from the Flow Domain ................. 49 3.2.4 Fracture Aperture ........................................................................................ 53 3.2.5 Mesh Identification ....................................................................................... 54 3.3 Finite Element Model Using Line Elements ........................................... 57 3.3.1 The Parallel Plate Model and the Continuity Equation .......................... 59 3.3.1.1 The Parallel Plate Model ............................................................................. 59 v Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 3.3.1.2 Continuity Equation ..................................................................................... 59 3.3.2 Solution of the Continuity Equation .......................................................... 63 3.3.2.1 Galerkin Method ........................................................................................... 63 3.3.2.2 Assembly of Finite Elements...................................................................... 70 3.3.2.3 Boundary Conditions for a Specified System ........................................... 72 3.4 Capture Zone in a Fractured Medium ........................................................ 75 3.4.1 Concepts ........................................................................................................ 75 3.4.2 Number of Flow Paths ............................................................................... 77 3.4.3 Particle Backtracking and Travel Time ..................................................... 81 3.4.4 Capture Zone Shape ......................................................................................

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