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.
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.
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