Sakslima Sikaneta

Ph. D. Thesis

Novel Lattice Boltzmann Methods for Modeling Fracture and Flow

This thesis extends a computational modeling technique, the Lattice Boltzmann Method, to model aspects of fracture, solid deformation, and fluid flow. A new Multiple-Material Multiple-Relaxation-Time (MM-MRT) Lattice Boltzmann Method capable of simulating fluid and solid materials is developed, analysed, tested, and applied to a number of problems. Tests of the new method's ability to simulate Navier-Stokes ?ow and linear elastic wave propagation are presented. A new scheme for treating fully and partially reflective boundaries is developed within the context of the MM-MRT method and applied to model multi-scale Stokes-Brinkman fluid flow through anisotropic and heterogeneous materials. The model is used to illustrate the dependence of flow anisotropy upon fracture aperture in a network of fractures intersecting a material at right angles to the material's preferred direction of flow. The newly developed boundary scheme is further developed and used in conjunction with the MM-MRT method to determine the stress field around simple open fractures. Model results compare favourably to analytical solutions. A tensile failure criterion is used in conjunction with an elastic MM-MRT model and a novel fracture algorithm to simulate the evolution of a columnar fracture network in three dimensions. Model results support the previously published hypothesis that equiangular intersections in columnar fracture networks evolve from pre-existing intersections. The MM-MRT method is also used to model the evolution of tensile fractures under compressive shear. Model results highlight the important influence of triaxiality upon strength. Furthermore, a new microstructural feature that may play an important role in strength, referred to as 'screw cracks', is discovered. The ability of the boundary treatment scheme to independently treat partial re?ection of P- and S- mode stresses is used to investigate the differences between fracture networks formed in hydraulically sealed and hydraulically open environments. Model results indicate that localization of microfracture zones is favoured by hydraulically sealed conditions.

Pages: 162

Supervisor: Lawrence Plug