Modeling the spatio-temporal evolution of fracture networks and fluid-rock interactions in GPU

Abstract

In this thesis, I present the theory and modeling of poro-elasto-plastic rheology coupled to a non-linear diffusion equation with a step increase in permeability at the onset of slip. This theoretical model is implemented in the graphic processing unit (GPU) architecture and programmed using the nVidia CUDA programming language. The numerical models are benchmarked by investigating fracture orientation for the solid-mechanical aspects, and by using the Method of Manufactured solutions for the diffusion part.<br /> I find that the GPU platform is ideal for these models because very high resolution simulations can be performed on an explicit finite difference algorithm using a single GPU card, outperforming CPU by a factor of at least five. The inherent problem with these coupled systems is the wide range of time and length scales that needs to be considered, and the advantage of GPU is its inherent parallel architecture that allows to do so. <br /> In these models, numerical fractures develop and evolve in response to prevailing far-field stresses, to local stress heterogeneity and pore-elastic stresses resulting from fracture growth, dislocation slip and fluid pressure diffusion within the domain. The numerical models, once benchmarked, are used to understand a variety of important and diverse lithospherical geodynamical problems, including enhanced geothermal systems (EGS), volcano-tectonic interactions and aftershocks. Envisaged future applications include hydro-fracture (’Fracking’), CO₂ sequestration, earthquake nucleation and nuclear waste isolation. <br /> The potential of this model is far-reaching, and future developments in 3 dimensions will open up countless new avenues of insight and understanding of fluid-rock interactions and lithospheric dynamics.