On the basis of a review of recent theoretical and experimental studies of flow through fractured rocks, we have studied the fluid flow and solute transport in a tight fractured medium in terms of flow through channels of variable aperture. The channels are characterized by an aperture density distribution and a spatial correlation length. Aperture profiles along the channels are statistically generated and compared to laboratory measurements of fracture surfaces. Calculated tracer transport between two points in the fractured media is by way of a number of such channels. Tracer breakthrough curves display features that correspond well with recent data by Moreno et al., which lends support to the validity of our model. Calculated pressure profiles along the channels suggest possible measurements that may be useful in identifying the geometrical characteristics of the channels. Finally, predictions were made for tracer breakthrough curves in the case of single fractures under various degrees of normal stress. These suggest possible laboratory experiments which may be performed to validate this conceptual model.

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.

Calculations to investigate the effect of path tortuosity and connectivity on fluid flow rate through a single rough fracture were carried out. The flow paths are represented by electrical resistors placed on a two‐dimensional grid, and the resistances vary as the inverse of the fracture aperture cubed. The electric current through the circuit bears a one‐to‐one correspondence to the fluid flow rate. Both fracture apertures derived from measurements and from hypothetical analytic functions were used in a parameter study to investigate the dependence of tortuosity on fracture roughness characteristics. It was found that the more small apertures there are in the aperture distribution, the larger is the effect of tortuosity. When the fraction of contact area between the fracture surfaces rises above 30%, the aperture distributions are invariably large at small apertures, and the effect of fracture roughness and flow path tortuosity depresses flow rate from the value predicted by the parallel plate representation of a fracture by three or more orders of magnitude. The impact of these results on the calculations and measurements in fracture hydrology is discussed.

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This paper presents a conceptual and numerical model of multiphase flow in fractures. The void space of real rough‐walled rock fractures is conceptualized as a two‐dimensional heterogeneous porous medium, characterized by aperture as a function of position in the fracture plane. Portions of a fracture are occupied by wetting and nonwetting phase, respectively, according to local capillary pressure and global accessibility criteria. Phase occupancy and permeability are derived by assuming a parallel‐plate approximation for suitably small subregions in the fracture plane. For lognormal aperture distributions, a simple approximation to fracture capillary pressure is obtained in closed form; it is found to resemble the typical shape of Leverett's j function. Approximations to wetting and nonwetting phase relative permeabilities are calculated by numerically simulating single phase flows separately in the wetted and nonwetted pore spaces. Illustrative examples indicate that relative permeabilities depend sensitively on the nature and range of spatial correlation between apertures. It is also observed that interference between fluid phases flowing in a fracture tends to be strong, with the sum of wetting and nonwetting phase relative permeabilities being considerably less than 1 at intermediate saturations.

In the literature during the past several years there appear numerous references to the “equivalent aperture” of a rough‐walled rock fracture as derived from various hydraulic and tracer tests. However, the similar or even identical terms used by different researchers for “equivalent aperture” often do not have the same meaning. This has led to some confusion in the comparison of their results. In particular, there is a serious apparent contradiction in the claims of some authors that “equivalent apertures” derived from tracer tests are much larger than those derived from hydraulic tests, and the findings of others that apertures estimated from tracer tests are consistently smaller than those estimated from hydraulic tests. This apparent contradiction of the field results in fact arises from the different definitions of the so‐called “tracer aperture” as employed by different researchers. In this short technical note I have attempted to sort out the different definitions, denotations and usage of the various “equivalent apertures” and show that there are mainly three alternative definitions used in the literature. The meaning of each as related to experimental measurements is explained and their interrelationship discussed. It is shown that once the specific definition of “equivalent aperture” referred to by each researcher is identified, then the relative magnitudes of these “equivalent apertures” as reported by different groups of researchers are perfectly consistent with each other.

The void space of a rock fracture is conceptualized as a two‐dimensional heterogeneous system with variable apertures as a function of position in the fracture plane. The apertures are generated using geostatistical methods. Fluid flow is simulated with constant head boundary conditions on two opposite sides of the two‐dimensional flow region, with closed boundaries on the remaining two sides. The results show that the majority of flow tends to coalesce into certain preferred flow paths (channels) which offer the least resistance. Tracer transport is then simulated using a particle tracking method. The apertures along the paths taken by the tracer particles are found to obey a distribution different from that of all the apertures in the fracture. They obey a distribution with a larger mean and a smaller standard deviation. The shift in the distribution parameters increases with increasing values of variance for the apertures in the two‐dimensional fracture. Provided that the correlation length is no greater than one fifth of the scale of measurement, the aperture density distributions of tracer particle paths remain similar for flow in two orthogonal directions, even with anisotropy ratio of spatial correlation up to 5. These results may be applicable in general to flow and transport through a two‐dimensional strongly heterogeneous porous medium with a broad permeability distribution, where the dispersion of the system may be related to the parameters of the permeability distribution along preferred flow channels.

Flow and transport calculations are carried out by numerical simulation for different tracer designs: single‐well radially diverging /converging (huff‐puff), single well radially converging, and two‐well injection‐withdrawal (doublet) in a 2D fracture zone. The fractured rocks are conceptualized as a dual‐continuum: the well‐connected fractures forming a heterogeneous continuum for advective transport, and the less permeable matrix forming a second continuum for tracer diffusion. Results show that the huff‐puff design is a good diagnostic test for matrix diffusion. The two‐well doublet design averages over a large volume and corrects for the extreme sensitivity to spatial heterogeneities of the single well converging test, but requires prior knowledge of presence or absence of matrix diffusion to give reliable estimate of transport parameters. Results of this study demonstrate that using a suite of different tracer designs is important to reduce the uncertainty in association with solving the inverse problem of tracer test interpretation to characterize transport in fracture rocks.