| dc.description.abstract | Shales and mudstones tend to exhibit strong anisotropy so that assuming mechanical isotropy in wellbore failure analysis and completion design strategies in shale can lead to inaccurate results. This dissertation focuses on developing numerical and semi-analytical fracture propagation models to study the behavior of hydraulic fractures near and away from the wellbore in anisotropic rock. In addition to elastic anisotropy, the effect of fracture toughness anisotropy on hydraulic fracture propagation is addressed. A numerical model based on 2D displacement discontinuity method (DDM) for fracture deformation is developed. Fluid flow inside the fractures is approximated using lubrication equation and is fully coupled with rock deformation. Natural fractures are modeled using joint elements that can account for elastic deformation (closure, shear) and plastic slip. Thus, hydraulic fracture propagation in a network of natural fracture can be simulated. In addition, to better approximate real hydraulic fracturing, a semi-analytical planar 3D (P3D) fracture height growth model is developed using the analytical plane strain solution for a line fracture in orthotropic rock to investigate the 3D aspects of rock anisotropy on hydraulic fracture propagation. The analytical expression for fracture deformation is derived using a singular elastic integral equation that relates fracture aperture with net pressure. The semi-analytical P3D model is combined with a 2D anisotropic displacement discontinuity (DD) method to enable simulation of multiple interacting hydraulic fractures in anisotropic formations (P3D-DD model). Moreover, recognizing the importance of using the proper fracture tip aperture solution for stability, accuracy and the speed of hydraulic fracture propagation numerical models, fracture tip solutions for both viscous- and toughness-dominated propagation regimes are derived for orthotropic rock for the first time. The fracture propagation algorithms in this work recognize the regime of propagation at any given time during the injection so that the corresponding tip solution is implemented automatically allowing for correct pressure and fracture geometry calculations.
The models are applied to a number of problems of interest in reservoir geomechanics starting with the behavior of a pressurized crack. Analysis of a uniformly pressurized stationary fracture in an orthotropic rock indicates that fracture apertures and induced stresses around the fracture are functions of fracture orientation with respect to the rock’s axes of elastic symmetry and its degree of modulus anisotropy (i.e., ratio of Young’s modulus in the direction parallel to rock fabric to Young’s modulus in the direction perpendicular to the rock fabric). The spatial extent of the induced normal stresses (“stress shadow”) perpendicular to the fracture surface increases when the fracture is aligned with the direction of the least Young’s modulus. Analysis of stress indicates a substantial increase in the stress shadow for anisotropic rock even with a degree of anisotropy as low as 1.9. Numerical simulations of large scale hydraulic fracture propagation indicate that the larger spatial extent of the induced stresses in anisotropic rock leads to early termination of the fractures emanating from the inner perforation clusters, resulting in fracture networks with dominant outer fractures. In the presence of fracture toughness anisotropy and under low differential stress conditions, the fractures deviate towards the plane of the least fracture toughness. Near the wellbore, fracture toughness anisotropy results in severe constriction of fracture apertures at the locations of fracture turning. This effect becomes more severe with increase in fracture toughness anisotropy and perforation misalignment angle.
Propagation of a single planar hydraulic fracture is considered in a vertical transversely isotropic rock (VTI) using the P3D model and the resultant fracture height, length and aperture distribution are compared with the isotropic case. The results indicate that isotropic fracture models tend to overestimate fracture height and underestimate fracture width. For a rock with degree of anisotropy 4, isotropic model underestimates the fracture aperture by 11% and overestimates the fracture height by 31% when compared to anisotropic model. Also, fracture aperture distribution in anisotropic rock tends to be more uniform compared to the isotropic case.
Numerical simulations of hydraulic fracture in the presence of natural fractures indicate that the induced stress component parallel to the hydraulic fracture surface plays a critical role in the evolution of the fracture network. Natural fracture segments that are at a low angle (with respect to hydraulic fracture) are affected the most by the hydraulic fracture’s stress shadow. When the in-situ stress contrast is high (1000 psi), most of the natural fractures never mechanically open, however, they do experience slip. Under a low in-situ stress contrast (145 psi), segments of the natural fractures that are on the high angle side mechanically open. Under the condition of high in-situ stress contrast some natural fractures experienced bi-wing propagation due to higher shear stresses acting on the inclined natural fractures causing sufficient slip to initiate natural fracture propagation from both tips. The indication is that contrary to conventional wisdom in some cases a higher complexity may result under a high stress contrast. Fracture opening along the network shows drastic variation even under low in-situ stress contrast, where the lowest fracture apertures are observed along the natural fractures and at sites of fracture arrest.
Numerical analysis of propagation of dense parallel fracture strands show that closely spaced fracture strands can occur for a certain range of conditions and operational parameters. The in-situ stress contrast, perforations conditions, and injection rates exert a significant influence. Under the right conditions, closely-spaced fractures can extend to distances exceeding tens of feet from the wellbore. Early termination and/or coalescence of closely spaced fractures can also occur. Higher in-situ stress contrast and lower fracture toughness of rock appear to inhibit coalescence of closely spaced fractures .Propagation of dense fracture strands require higher net pressures inside fractures to keep them open compared to a single fracture. The increase in net pressure inside the fractures is directly proportional to number of fracture strands. Also, it appears that an average increase in net pressure required to propagate multiple fractures can be related to net pressure for a single fracture, which might allow one to infer the number of fractures propagating simultaneously.
These results suggest that the spacing between the fractures for optimum growth in anisotropic rock must be different from isotropic rock for successful completion design of horizontal wells. Moreover, the numerical model can be used as a tool to improve interpretation of micro-seismic maps and injection pressure data. | en_US |
