Scholars' Mine Masters Theses Student Theses and Dissertations Summer 2016 Characterization of fracture initiation in non-cylindrical buckle folds using 3D finite element analysis Eli Jacob Steinbeck Follow this and additional works at: https://scholarsmine.mst.edu/masters_theses Part of the Geology Commons, and the Petroleum Engineering Commons Department: Recommended Citation Steinbeck, Eli Jacob, "Characterization of fracture initiation in non-cylindrical buckle folds using 3D finite element analysis" (2016). Masters Theses. 7570. https://scholarsmine.mst.edu/masters_theses/7570 This thesis is brought to you by Scholars' Mine, a service of the Missouri S&T Library and Learning Resources. This work is protected by U. S. Copyright Law. Unauthorized use including reproduction for redistribution requires the permission of the copyright holder. For more information, please contact [email protected]. CHARACTERIZATION OF FRACTURE INITIATION IN NON-CYLINDRICAL BUCKLE FOLDS USING 3D FINITE ELEMENT ANALYSIS by ELI JACOB STEINBECK A THESIS Presented to the Faculty of the Graduate School of the MISSOURI UNIVERSITY OF SCIENCE AND TECHNOLOGY In Partial Fulfillment of the Requirements for the Degree MASTER OF SCIENCE IN PETROLEUM ENGINEERING 2016 Approved by Dr. Andreas Eckert, Advisor Dr. John Hogan Dr. Runar Nygaard 2016 Eli Jacob Steinbeck All Rights Reserved iii ABSTRACT The spatial distribution of fracture sets associated with buckle folds has been well documented in field studies. There are difficulties, however, in placing accurate constraints on the timing of the initiation of individual fracture sets during the deformation history of the fold under in-situ conditions. This study investigates specific conditions that give rise to the initiation of various fracture sets in the hinge and limb of a pericline, based on an analysis of the effective stress evolution during the processes of buckling and erosional unloading. A 3D finite element modeling approach is used to simulate the effective stress evolution in single-layer folds with a Maxwell viscoelastic rheology, while including the influence of overburden stress, pore pressure, and a geologic strain rate. Several material properties and geometric features are varied to test their influence on fracture initiation. The modeling results show that fracturing is most heavily influenced by permeability, initial overburden thickness, and erosional unloading. Further analysis reveals that six fracture sets, which are observed in natural buckle folds, are also observed in the modeling results: outer arc tensile fractures, outer arc normal faults, and inner arc thrusts, all of which strike parallel to the fold axis, are determined to be common fracture sets; outer arc tensile fractures that strike perpendicular to the fold axis, and thrusts in the limb that strike roughly parallel to the fold axis are determined to be less common fracture sets that require low permeability (< 10-21 m2) folding layers in order to initiate; vertical conjugate shear fractures in the outer arc, where the fold axis bisects the acute angle between fracture planes, are determined to be a rare fracture set. Most importantly, the timing of initiation is determined for each set, thus providing the most difficult information to obtain from a field study on fold related fractures. iv ACKNOWLEDGMENTS I would like to thank my advisor, Dr. Andreas Eckert, for accepting me into the geomechanical modeling group. During my time as an undergraduate he was very influential in my decision to pursue a master’s degree, and throughout my last two years as a graduate student he has been a supportive and encouraging mentor and friend. His theoretical knowledge and technical guidance have proven to be invaluable tools that have helped guide me through my research and on to the completion of this thesis. I would also like to thank Dr. John Hogan and Dr. Runar Nygaard for the time and effort they have put forth as members of my graduate committee. Your advice regarding this thesis, my current academic career, and my future career in the petroleum industry has been very much appreciated. My thanks also go to my friends and colleagues that are, or have been a part of the geomechanical modeling group: Xiaolong Liu, Weicheng Zhang, Davi Rodrigues Damasceno, Huining Zhang, Zhe Yuan, and Mengke Li. Thank you all for all your help and support during my time as a master’s student; and most importantly, thank you for your friendship, and for keeping me sane during all those hours spent in B21 McNutt. Lastly I would like to thank my family: my parents, my sister Hannah, and my fiancée Erika Miller. Thank you for your unwavering love, and endless support and encouragement in all of my endeavors. You will always be my primary motivator to strive for success in everything that I do. v TABLE OF CONTENTS Page ABSTRACT ....................................................................................................................... iii ACKNOWLEDGMENTS ................................................................................................. iv LIST OF ILLUSTRATIONS ........................................................................................... viii LIST OF TABLES ............................................................................................................. xi NOMENCLATURE ......................................................................................................... xii SECTION 1. INTRODUCTION ...................................................................................................... 1 1.1. OVERVIEW ....................................................................................................... 1 1.2. LITERATURE REVIEW ................................................................................... 5 1.2.1. Non-cylindrical Folding in Three Dimensions ......................................... 5 1.2.2. Periclines .................................................................................................. 8 1.2.3. Fracture Patterns Associated With Buckle Folding ............................... 10 1.2.4. Limitations of Existing Literature .......................................................... 13 1.3. RESEARCH OBJECTIVES AND QUESTIONS ............................................ 14 2. THEORETICAL BACKGROUND ......................................................................... 16 2.1. ROCK PROPERTIES AND ROCK MECHANICS......................................... 16 2.2. BUCKLE FOLDING THEORY ....................................................................... 17 2.2.1. Single Layer Fold Theory ....................................................................... 17 2.2.2. Stress Distribution and Evolution in Buckle Folds ................................ 19 2.2.3. Strain Distribution in Buckle Folds ........................................................ 20 2.3. FRACTURE PREDICTION ............................................................................. 22 2.3.1. Combined Griffith/Navier-Coulomb Failure Criterion .......................... 23 2.3.2. Fracture Potential ................................................................................... 26 2.4. STEREOGRAPHIC PROJECTIONS AND STEREONETS ........................... 28 2.4.1. Plotting Lines on a Stereonet .................................................................. 29 2.4.2. Plotting Planes on a Stereonet ................................................................ 30 2.5. FINITE ELEMENT METHOD ........................................................................ 31 2.5.1. The Standard Discrete System ............................................................... 32 vi 2.5.2. The General Finite Element Method ...................................................... 33 3. METHODOLOGY ................................................................................................... 36 3.1. NUMERICAL MODELING APPROACH ...................................................... 36 3.1.1. Governing Equations for 3D Viscoelastic Folding ................................ 36 3.1.2. The ABAQUSTM Solver ......................................................................... 38 3.2. MODEL SETUP ............................................................................................... 39 3.2.1. Material Properties ................................................................................. 39 3.2.2. Model Geometry ..................................................................................... 42 3.2.3. Loading Procedures ................................................................................ 45 4. RESULTS ................................................................................................................. 48 4.1. BASE MODEL RESULTS ANALYSIS .......................................................... 48 4.1.1. Stress Analysis ....................................................................................... 51 4.1.2. Fracture Potential Results ....................................................................... 55 4.2. PARAMETRIC ANALYSIS ............................................................................ 58 4.2.1. Influence of Permeability Magnitude ..................................................... 58 4.2.2. Influence of Anisotropic Permeability ................................................... 61 4.2.2.1 High permeability buckling ........................................................61 4.2.2.2 Low permeability buckling .........................................................63