Calculations for the flow and solute transport through a single rough‐surfaced fracture were carried out. The fracture plane was discretized into a square mesh to which variable apertures were assigned. The spatially varying apertures of each single fracture were generated using geostatistical methods, based on a given aperture probability density distribution and a specified spatial correlation length. Constant head boundary conditions were assumed for the flow in the x direction of a single fracture with no flow boundaries in the y direction. The fluid potential at each node of the discretization mesh was computed and the steady state flow rates between all the nodes were obtained. Our calculations showed that fluid flow occurs predominantly in a few preferred paths. Hence, the large range of apertures in the single fracture gives rise to flow channeling. The solute transport was calculated using a particle tracking method. Both the spatial and time variations of tracer breakthrough results are presented. The spatial variation of tracer transport between a line of injection points and a line of observation points are displayed in contour plots which we labeled “transfer matrix.” Our results indicate that such plots can give information on the spatial correlation length of the heterogeneity in the fracture. The tracer breakthrough curve obtained from a line of point measurements is shown to be controlled by the aperture density distribution and is insensitive to statistical realization and spatial correlation length. These results suggest the importance of making line measurements in the laboratory and the field. Sensitivity of our results on parameter variations was also investigated.

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Tracer tests in natural fissures performed in the laboratory are analyzed by means of fitting two different models. In the experiments, sorbing and nonsorbing tracers were injected into a natural fissure running parallel to the axis of a drill core. The models take into account advection, dispersion, diffusion into the rock matrix, and sorption onto the surface of the fissure and on the microfissures inside the matrix. For the second mechanism, one of the models considers hydrodynamic dispersion, while the other model assumes channeling dispersion. The models take into account time delays in the inlet and outlet channels. The dispersion characteristics and water residence time were determined from the experiments with nonsorbing tracers. Surface and volume sorption coefficients and data on diffusion into the rock matrix were determined for the sorbing tracers. The results are compared with values independently determined in the laboratory. Good agreement was obtained using either model. When these models are used for prediction of tracer transport over larger distances, the results will depend on the model. The model with channeling dispersion will show a greater dispersion than the model with hydrodynamic dispersion, assuming constant dispersivity.

Flow and solute transport through porous media having strongly variable permeability were studied for parallel and convergent/divergent flows. The variation in hydraulic conductivity K causes (1) the fluid to flow through a porous medium along least resistive pathways and (2) solute dissolved in the fluid to be transported with widely differing velocities. Numerical simulations were performed to study flow and solute transport in a three‐dimensional heterogeneous porous block. It is found that for a strongly heterogeneous medium the particles (or solutes) travel through the medium along preferred flow paths, which we call channels. These channels possess hydraulic properties that are different from those of the global porous medium and which are invariant regardless of the direction from which the hydraulic gradient is applied to the porous block. The log‐hydraulic conductivities along these channels have a greater mean value and a smaller standard deviation than for the global porous medium. These differences or “shifts” were calculated as a function of the hydraulic conductivity variance of the global porous medium. Tracer breakthrough curves for a pulse injection were also calculated. For small standard deviations of the global hydraulic conductivity distribution, a peak in the breakthrough curve is found which spreads out around its peak value as the standard deviation is increased. However, as the standard deviation is increased further, a new peak emerges at a much earlier time. This may be the result of increasing channeling effects at large standard deviations. For the case of a spherical pressure boundary around point tracer injection, the flow follows the usual divergent pattern only for small variations in hydraulic conductivity. When the standard deviation in log K is large, a significant portion of the flow becomes channelized; i.e., it tends toward a linear flow pattern.

Field evidences indicate that the bulk of water flow in fractured crystalline rock often occurs in preferred flow paths, or channels. A theoretical approach was proposed by Tsang and Tsang (1987) to interpret flow and transport through a two‐ or three‐dimensional fractured medium in terms of a system of statistically equivalent one‐dimensional channels. The apertures along the flow channels are characterized by an aperture density distribution and a spatial correlation length. In this paper, we present detailed studies on the properties of these channels: channel volume, channel residence time, and channel volumetric flow rate. We also calculated the dispersion in tracer transport through groups of statistically equivalent channels. The one‐dimensional channel model is then applied to breakthrough data from transport in a two‐dimensional single fracture (Moreno et al., this issue) in both a forward and an inverse calculation. We show from the inverse calculation that the aperture density distribution parameters of the one‐dimensional flow channels may be estimated from the dispersion and mean residence time of the tracer data. The tracer breakthrough curve should be obtained from line measurements with tracer sampled over several spatial correlation lengths of the variable apertures. This is in contrast to conventional point tracer measurements which is expected to fluctuate with statistical realization and may not yield pertinent information on the flow system. Based on the insight gained in such calculations, design, and analysis of field measurements are discussed. Both tracer breakthrough measurements and flow rate measurements are needed to obtain the aperture parameters of the flow systems. The permeability measurements alone are controlled by the small constrictions along the flow paths and therefore do not yield a good measure of the mean aperture in channel.