| This study investigates the important role of matrix diffusion in the flow of fluids through fractured rock. Coupled equations for flow in a simple fracture/matrix system are solved by approximate analytical methods, and the results used to study wetting front stability and the partitioning of flow in a heterogeneous porous medium. The solutions are applicable to both semi-infinite and bounded domains, and provide quantitative estimates of water uptake by the matrix, cumulative and instantaneous fluxes in the fracture, and potential distributions in an idealized system.;The validity of the model is demonstrated by investigating field data from two tests in fractured, low permeability rock. For an initially dry system, the model accurately describes the early and late time response, and provides support for the hypothesis that fracture heterogeneity dominated the test response at intermediate times. A second injection test, conducted four and one half hours after the first test, showed little influence of heterogeneity, but a comparison with the model predictions implies that approximately 20% of the water injected may have migrated outside the test area.;In the final step, a hydrodynamic stability analysis is used to test the stabilizing effect of matrix diffusion on wetting front advance in the fracture domain. Non-dimensionalization reduces the problem to the equivalent of a one-dimensional porous medium, allowing analyses developed for soils to be applied to the more general case of flow in a dual permeability domain. Matrix diffusion is shown to be an important control on the distance over which an infiltrating front remains stable. For long wavelength disturbances (wave numbers near zero) wetting front stability increases approximately linearly with increasing matrix sorptivity. As the perturbation wavelength decreases, however, instabilities are dampened more strongly. Conditions controlling this phenomenon are presented, along with expressions for the most unstable wave number, and the length scale and minimum wave numbers needed to develop wetting front instability. |
