Björn Dverstorp

A variable aperture fracture network model for flow and transport in fractured rocks

A three-dimensional variable aperture fracture network model for flow and transport in fractured rocks was developed. The model generates both the network of fractures and the variable aperture distribution of individual fractures in the network. Before solving for the flow and transport of the whole network, a library of single-fracture permeabilities and particle transport residence time spectra is first established. The spatially varying aperture field within an individual fracture plane is constructed by geostatistical methods. Then the flow pattern, the fracture transmissivity, and the residence times for transport of particles through each fracture are calculated. The library of transmissivities and frequency distributions of residence times is used for all fractures in the network by a random selection procedure. The solution of flow through the fracture network and the particle-tracking calculation of solute transport for the whole network are derived from one side of the network to the other. The model thus developed can handle flow and transport from the single-fracture scale to the multiple-fracture scale. The single-fracture part of the model is consistent with earlier laboratory tests and field observations. The multiple-fracture aspect of the model was verified in the constant aperture fracture limit with an earlier code. The simulated breakthrough curves obtained from the model display dispersion on two different scales as has been reported from field experiments.

Tracer transport in a stochastic continuum model of fractured media

A stochastic continuum model of a fractured medium conditioned on a specific set of field data is developed. Both the more conductive fractures and the less permeable matrix are generated within the framework of a single-continuum stochastic model based on nonparametric indicator geostatistics. In the stochastic model the fracture zones are distinguished from the matrix by imposing a long-range correlation structure for a small fraction (the highest approximately 11%) of the hydraulic conductivity in the preferred planes of fracture zones. Results of flow arid transport simulation in three dimensions (3D) are used to illustrate the large spatial variability of point measurements, but for spatially integrated quantities the variability is reduced and results become less sensitive to correlation structure. Therefore it is suggested that spatially integrated quantities may be a more appropriate choice for predicting flow and transport in a strongly heterogeneous medium in that they are more commensurate with the level of our ignorance of the site. The issue of spatial variability giving rise to uncertainty in the site characterization of a heterogeneous medium and the prediction of transport results is also addressed. Simulations are carried out for 3D transport from point tracer sources at hundreds of locations in the medium. The breakthrough curve from each point source release is characterized by two parameters: the mean transport velocity and the dispersion coefficient. The results are presented as a statistical distribution of the transport parameters, thus quantifying the uncertainty in predicting flow and transport based on a limited amount of site characterization data.

Discrete fracture network interpretation of field tracer migration in sparsely fractured rock

Field tracer migration in sparsely fractured rock is analyzed with a discrete fracture network model that has been calibrated on fracture and flow data from the Stripa-3D experiment in Sweden. Comparison between transport simulations in the flow-calibrated discrete model and tracer tests of the field experiment confirms the fracture network parameters obtained from the flow analysis except for the variance of the fracture conductivities which had to be increased. The discrete model reproduces the uneven spatial distribution of flow and tracers, the complex dispersive behavior, and channeling effects that have been observed in the field experiment. As a result of flow channeling, transport occurs along preferential paths whose transport properties may substantially deviate from the medium average properties. For example, porosity and wetted fracture surface area available to sorption may be reduced by almost 2 orders of magnitude compared to the medium average values.

Effects of high variance of fracture transmissivity on transport and sorption at different scales in a discrete model for fractured rocks

Abstract A three-dimensional (3-D) variable-aperture fracture network model for flow and transport in fractured crystalline rocks has been applied to study the effects of large variability in fracture transmissivity on non-sorbing and sorbing tracer transport, and scale effects in transport distance. The variable-aperture character of the fractures is introduced into a 3-D network model through a library of single-fracture permeabilities and associated particle transport residence time spectra. Sorption onto the fracture walls is added by a mathematical model for linear sorption. The resulting variable-aperture fracture network model, VAPFRAC, can handle flow and transport from single-fracture scale to the multiple-fracture scale. The model produces multi-peak transport breakthrough curves even for relatively moderate values of the fracture transmissivity variance. These breakthrough curves display dispersion on two different scales in the same way as has been observed in several field experiments conducted in crystalline rocks. The multi-peak structure is due to so-called channeling. For high values of the fracture transmissivity variance the solute transport is unevenly distributed and the channeling effects are more prominent. The effect of linear sorption is not just a simple translation in mean residence time as in a homogeneous medium. The dispersion characteristics of the breakthrough curves also change when linear sorption is included. The degree of the change depends strongly on the fracture transmissivity variance, as does the translation. In particular, with a high fracture transmissivity variance the translation in mean residence time due to sorption is significantly smaller compared to the cases with a low fracture transmissivity variance. Finally, the high variability in the model output data suggests that extrapolation of results from a particular tracer experiment will be highly uncertain.

Heterogeneous matrix diffusion in crystalline rock — implications for geosphere retardation of migrating radionuclides

As a basis for an analysis of the effect of rock heterogeneity on radionuclide migration in a single fracture, the geostatistics of the main properties governing solute transport in crystalline rock have been determined experimentally for two granitic rock types. The rock samples were collected at the Aspö Hard Rock Laboratory, Sweden and used to deduce the auto-covariance functions for the porosity, effective diffusivity and partition coefficient, kd, and adsorption kinetics. One-dimensional analytical solutions for the mean values of the temporal moments of the residence time probability density function (PDF) show that the heterogeneity of the rock properties can have a substantial impact on the transport. A case study of the effect of heterogeneity in matrix diffusion for a single fracture could be performed by decomposing the transport problem into a one-dimensional mass transfer problem and a two-dimensional flow problem using a Lagrangian method of description. Monte Carlo simulations of the flow field indicate that the correlation length of the aperture is much longer along the trajectory paths than along an arbitrary direction. Increasing the correlation lengths and variances of the aperture and matrix diffusion increases significantly the variance of the travel time PDF.

Role of the bio- and geosphere interface on migration pathways for 135Cs and ecological effects

Abstract An approach is described for hydrological, geochemical, and ecological process modeling in assessing the migration pathways of radionuclides from a repository for radioactive waste in crystalline bedrock back to the surface environment where dose to individual humans can occur. The approach is based on the characterization residence times in geologic media of a unit pulse of 135Cs released from the repository. Performance assessment modeling of geosphere transport processes generally focuses on the properties of the host rock (crystalline bedrock in this case). Our approach includes a detailed representation of the quaternary deposits that overlie the bedrock. Although water residence times in quaternary deposits can be short, geochemical reactions, predominantly sorption, can increase solute residence times significantly. Moreover, the quaternary deposits govern the pathways to terrestrial and aquatic ecosystems and are of utmost importance for the assessment of doses to individual humans.

A Study of the Validity of Flow Predictions in Discrete Fracture Networks, Generated from Field Data Statistics

The applicability of the discrete fracture network concept for flow in fractured rock is studied. The fractures are modelled as circular discs of arbitrary size, orientation, transmissivity, and location. A numerical simulation model capable of generating fracture networks of desired statistics and solving for the steady-state flow through the network is used. The fracture network parameters’ size, orientation, and density are estimated with different techniques from observed fracture traces in the low-level nuclear waste repository in Forsmark, Sweden.