Abstract Fractures induced by folds are pivotal in hydrocarbon exploration, ground water transport and harnessing of geothermal energy. This is because of the need to predict and understand fracture propagation in reservoirs which have folded rock formations. Despite its prominence, there is a lack of reliable numerical models for simulating fractures resulting from rock folding. This is partially due to the difficulty involved in fracture modelling. As a contribution to fold-fracture modelling, this work applies a coupled plasticity-damage model to rock fracturing and anticlinal folds. Parametric studies on a single folded layer give insight into the fold formation and behaviour. The anisotropic continuum damage model which considers both tension and compression is formulated using the power damage evolution law. For ease in formulation, strain equivalence hypothesis is adopted whereby the strain is the same for both damaged and undamaged configurations. Lubliner plasticity yield criterion is adopted for plastic deformation. The model is coded in Abaqus user subroutine UMAT and is applicable to quasi-brittle materials.
Introduction The understanding of fractures in the earth's crust helps in the prediction, evaluation and characterization of fractured reservoirs, whether they are petroleum, geothermal or underground water reservoirs. This is partly because reservoir permeability and stability are dependent on fracture properties (Nelson, 2001). To achieve this, various approaches have been developed to analyze reservoir rock fractures. These could be grouped intodiscrete approaches – where the rock mass is represented by a finite number of well-defined components and
continuum approaches – where the mathematical assumption of an infinitesimal element is made (Jing, 2003).
Ivanova (Ivanova, 1998) comprehensively studied fracture systems in nature and highlighted folds as one of the major geologic settings that produce fractures. Naturally occurring folds in reservoirs sometimes compound fracture analysis. It might not be clear whether the fractures formed before, during or after rock folding. Fractures formed during the folding process are expected to show stress orientations related to folding and are thus of primary concern in rock folding simulation. It could be argued that there are no numerical models that assuredly simulate rock folding and fracturing simultaneously (Jäger, Schmalholz, Schmid, & Kuhl, 2008).
Folds are formed when planar or straight surfaces of the earth become curved or bent due to plastic deformation. The process of folding has two mechanisms: flexure and shear. Flexural folding could be in the form of bending or buckling depending on the compressive force. When the force is parallel to the bedding, buckling occurs; when stresses are applied across layers causing torque, bending occurs. Shear folding occurs due to small displacements along closely spaced planes perpendicular to the bedding. Flexural folding is associated with competent (strong, thick and stiff) rock layers while shear folding is found in incompetent formations (Ivanova, 1998). Fractures resulting from flexural folding are expected to be more pronounced. In this study, fractures due to bending are investigated. Numerical models based on continuum approaches majorly describe material deformation while discrete approaches describe element movement of the system (Bobet et al., 2009). The former will be more appropriate to study the initiation and propagation of fractures due to rock bending. Hence, Finite Element Method (FEM) is adopted.