Flow and tracer transport in a single fracture: A stochastic model and its relation to some field observations

Abstract

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.

Tracer Transport in Fractures: Analysis of Field Data Based on a Variable‐Aperture Channel Model

“…Neretnieks et al, 1982), we find that the dispersion measure (t(0.9)-t(0.1))/t(0.5) ranges from 0.5 to 1.7. Tsang et al (1988) give a graphical rela--tionship between this dispersion measure and the aperture variance s = crJb. Applying that relationship, we obtain values of crJb ranging from 0.35 to 0.75.…”

“…For this, we follow the procedure presented in Tsang et al (1988). Starting with the Pe numbers for the first peak or first channels given in Tables 1 and 2, and assuming that the channel flow obeys 1D advective dispersive equation (see e.g.…”

“…It was demonstrated that this averaging should be over two or three spatial correlation lengths A.. The dispersion value of such averaged tracer breakthrough may then be related to fracture aperture parameters b and ab (Tsang et al, 1988). In data analysis discussed below, the spatial averaging is done by summing the products of the concentration of a particular tracer and the instanteous flow rate at each collection sheet, and then dividing by the sum of flow rates from all the contributing collection sheets.…”

“…6 In many tracer transport experiments the measuring scale is such that the transport distances cover only a few fracture spacings in a fracture network, in which case transport can be studied as flow through a number of fractures in series. A large number of fractures may be generated by a geostatistical method with a specified aperture probability density distribution and a spatial correlation length, and the local flow rates in each of these fractures may be solved separately following our earlier model (Moreno et al 1988). Then the fracture may be put in series, satisfying the continuity requirement that the identical total flow rate must occur in each fracture.…”

“…A number of approaches for tran-, sport in fractured media have been proposed in the literature (Endo et al, 1984;Robin-... , 1984;Schwartz and Smith, 1988). In this paper we extend and apply a variableaperture channel model (Tsang and Tsang, 1987;Tsang et al, 1988;Tsang and Tsang, 1989) as the basis for the analysis of the Stripa-3D data .…”