Fluid flow in discrete fractures: An experimental and lattice gas automata modeling study

The discrete fracture approach has been used by many investigators in the field of fracture flow hydrology as a means of obtaining a fundamental understanding of flow within single rock fractures. This understanding is necessary so that fluid flow and chemical transport in fractured rocks can be accurately characterized. The work presented here describes an investigation performed to explore some of the geometrical considerations of discrete fracture flow. The focus of this study was to determine how the cubic law, a flow rate prediction derived for fluid flow between parallel plates, could be modified to accommodate a rough and tortuous fracture geometry.; One component of this work involved a series of experiments undertaken to examine the flow of water through gaps between aluminum blocks. The surface topographies of these blocks were each based on different sinusoidal functions. Using this system, the roughness and tortuosity of these artificial fractures could be gauged by the ratio of the amplitude to wavelength of variation. The second component of this work involved fluid flow simulations through similar fracture geometries using a lattice gas automata (LGA) numerical model. This LGA model was used to check the experimental results and to obtain detailed pictures of the fluid velocity fields within these fractures. The flow experiments and LGA simulations, all performed under fully saturated flow conditions, used fracture apertures ranging from 0.25 to 1.80 mm. The Reynolds number, a dimensionless parameter used to gauge the limits of laminar fluid flow, ranged from 0.01 to 69 for the experiments and simulations.; A sensitivity study showed that there were limitations to the fracture geometry as well as the flow conditions that could be simulated with the LGA model. These limitations have been found by other researchers who use the same type of model. A more significant finding was that conditions typically considered fully laminar for flow in ducts and pipes resulted in a non-linear relationship between pressure and fluid velocity in the sinusoidal fractures. From an analysis of the experimental results it was determined that non-linear flow was a factor in these fractures at Reynolds numbers as low as 25.; Much insight into the geometric control on fracture flow was gained by comparing the observed experimental and numerical data to the cubic law. The traditional form of this law, which uses a fracture aperture that is measured strictly in the vertical dimension, was found to accurately predict the flow rate through the parallel plate fracture geometry. However, when applied to a variety of sinusoidal geometries, the traditional cubic law was found to be inadequate. The vertical separation, whether averaged arithmetically or harmonically, resulted in a overprediction of the observed flow rate in each case. When compared to a new form of the cubic law, however, a close match was seen to exist. This new form incorporates a fracture aperture that is measured normal to the flow path and is harmonically averaged, as well as a tortuosity correction term. When applied to the results of LGA simulations through fractures with a natural surface roughness, the modified cubic law was also found to give an accurate prediction. These findings have implications for interpreting laboratory fracture flow data and for improving the predictive numerical models used in this realm of fracture flow hydrology.