| Fluid flow through a rock fracture is often approximated by the parallel plate model for which flow rate is proportional to the cube of the average or effective aperture width. It has been of longstanding interest to determine how actual fracture surface roughness and irregularity of contact modify the predictions of the parallel plate model. In this thesis, fluid flow through a mechanical fracture in Harcourt Granite is studied. We made numerical definitions of percolation threshold, fracture aperture, flux and permeability. Numerical results are compared with laboratory measurements in some fractures.; For the numerical flow studies, the lattice Boltzmann method (LBM) has been used. To accommodate the vastly different aspect ratios of a fracture, we utilize the finite difference lattice Boltzmann method (FDLBM) in order to apply nonuniform grids. The FDLBM implementation was validated on simple fluid flow simulations: Poiseuille flow between two parallel plates with and without a constrictive neck and decaying Taylor vortex flow. For the simulation of fluid flow in a real fracture, the velocity field and fracture permeability were obtained for different values of mean aperture (confining pressure). The numerical values of the permeability as a function of confining pressure agree qualitatively with experimental results.; The FDLBM computations are CPU intensive. This was addressed using parallel computation on a Beowulf class cluster of processors. |
