Transport In Fractured Rock Research Articles

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.

Solute transport in fracture channel and parallel plate models

Many studies of flow and solute transport in fractured rocks are based on a conceptual model whereby flow occurs between parallel plates which approximate the fracture walls. Recently, it has been observed that this representation is not consistent with actual fractures. Real fractures are actually composed of a complex system of void spaces of varying aperture, and contact areas which are closed to flow. In such fractures, flow takes place through a network of channels and dead‐end regions. The present investigation analyzes and compares the behavior of solute breakthrough curves in these channels and parallel plate representations. Numerical experinents show that breakthrough curves obtained with channel models are characterized by a long tail and jumps in the solute concentration, consistent with those observed experimentally. It is concluded that the considered channel models provide a sound explanation for the behavior of real breakthrough curves, which cannot be reproduced by parallel plate models.

Flow and Transport in Fractured Rocks

Laboratory‐scale studies of discrete fractures lead to better understanding of the relationship between flow properties and pore geometry. Field‐scale studies of fracture networks test the validity of classical continuum approaches for transport processes in heterogeneous media. During 1987 to 1990, earth scientists have made significant advances in quantifying flow channeling and solute breakthrough in rough‐walled fractures, analyzing transitions between fracture and matrix flows under multiphase conditions, and characterizing fracture networks with hydrological and geophysical studies. In this review, the effect of heterogeneity and the issue of scaling are discussed. Many common features and similiar approaches can be identified in microcracks, discrete fractures, soil macropores, fractured rock masses, and heterogeneous reservoirs at different scales.

Fluid and Solute Transport in a Network of Channels

ABSTRACTA model is proposed to describe flow and transport in fractured rocks. It is based on the concept of a network of channels. This approach is backed by observations in drifts and tunnels that flow in fractured rocks takes place in sparse narrow channels with widths typically less than 10 cm and a channel frequency of one channel per a few square meters to one channel per more than a hundred square meters. Observations in boreholes also indicate that there are large distances, tens to hundreds of meters, between the most conductive sections in boreholes.For visualization purposes our model is displayed on a rectangular grid. The individual channels are given stochastically selected conductances and volumes. Flowrate calculations have been performed in grids of sizes 20*20*20 channels in most cases but larger grids have also been used. For large standard.deviations in conductances, greater than 1.6 in the log normal distribution (base 10), channeling becomes pronounced with most of the water flowing in a few paths. The effluent patterns and flowrate distributions obtained in the simulations have been compared to three different field measurements in drifts and tunnels. Standard deviations of channels conductances were found to be between 1.6 and 2.4 or more in some cases. Channel lengths were found to vary between 1.2 m and 10.2 m in the different sites. In one site where detailed borehole measurements were available the channel length could be assessed independently and was found to be 1.2 m as compared to the 1.7 m obtained from the drift inflow measurements.A particle tracking technique was used to simulate solute transport in the network. Nonsorbing as well as sorbing tracer transport can be simulated and by a special technique also tracers which diffuse into the rock matrix can be simulated.Tracer measurements in one site, Stripa, were used to compare dispersivities. These were found to be large, having Peclet numbers less than 5 both in simulations and the field results. From the Stripa tracer data it was also found that the tracers were taken up into the rock matrix by molecular diffusion. The surface area needed for this uptake was estimated to be between 0.2-20 m2/m3 for different tracers. The wetted surface for the model estimated from flowrate distribution data indicate a wetted surface of 0.2- 0.4 m2/m3.

Adsorptive solute transport in fractured rock: analytical solutions for delta-type source conditions

Solutions for adsorptive solute transport equations in a single fracture-rock system were derived under two different delta-type source conditions. One was the delta-type, flux injection condition. The correspondent solution can be used for the analysis of experimental column breakthrough curves obtained by injecting the tracer into the rock fracture. The other was the delta-type, resident fluid injection condition. The solution can be used for the crude estimation of pollutant migration from the underground radioactive waste repository. In formalizing the resident fluid injection, an initial distribution of solute between solution and solid phase was assumed in order to satisfy the mass balance between injected and detected solute. Each of the two solutions was also expressed in two ways reflecting the flux and the resident fluid detection. Solutions expressed in terms of the flux detection correspond to the effluent concentration measured experimentally by a fraction collector system. On the other hand, solutions expressed in terms of the resident fluid detection describe spatial distribution of the solute in the fluid. Since considerably long tailings of breakthrough curves are often observed in column tracer experiments using fractured rocks effects of some parameter values on the tailing were also discussed. It was shown that the adsorption of solute rock matrix caused longer tailing. It was also shown that the resident fluid injection caused longer tailing of breakthrough curves than the flux injection condition.

Modeling fracture flow with a stochastic discrete fracture network: Calibration and validation: 2. The transport model

As part of the development of a methodology for investigating flow and transport in fractured rocks, a large‐scale experiment was recently performed at Fanay‐Augères, France. In a companion paper (Cacas et al., this issue) (paper 1) the results of the flow measurements were analyzed. In this paper, the results of the tracer experiments are interpreted. A particle following is coupled to the flow model, described in paper 1. Microscopic dispersion in the fractures and retardation effects due to unevenness of the flow paths are taken into account. The transport model is calibrated on in situ tracer tests, whereas the parameters of the hydraulic model were initially fitted on structural and hydraulic measurements (paper 1). The dispersive properties of the model are reasonably comparable to those of the real site. It tends to confirm the validity of the preliminary hydraulic calibration of the model and thus to validate further the approach used to simulate hydraulic and transport phenomena.

886118 Chemical transport in fractured rock : Neretnieks, I; Abelin, H; Birgersson, L; Moreno, L; Rasmuson, A; Skagius, K In: Advances in Transport Phenomena in Porous Media, edited by J Bear and M Y CorapciogluP475–550. Publ Dordrecht: Martinus Nijhofj, 1987

886118 Chemical transport in fractured rock : Neretnieks, I; Abelin, H; Birgersson, L; Moreno, L; Rasmuson, A; Skagius, K In: Advances in Transport Phenomena in Porous Media, edited by J Bear and M Y CorapciogluP475–550. Publ Dordrecht: Martinus Nijhofj, 1987

A continuum approach for modeling mass transport in fractured media

A continuum approach has been developed for modeling mass transport in fractured rocks. It involves a new application of a particle‐tracking method in which physical transport is simulated in terms of velocity and the variations in velocity. Statistics describing the particle motion come from observing the actual pattern of particle motion in a discrete subdomain. This subdomain is a small but representative piece of the much larger continuum. In effect, particle motion in the continuum is forced to mimic that in the discrete subdomain. The model successfully duplicates patterns of anisotropic dispersion predicted by de Josselin de Jong (1972) and breakthrough curves simulated with a discrete fracture model. Applications demonstrate that the de Josselin de Jong approach for estimating dispersivities for idealized networks cannot generally be applied to networks formed from sets of finite, irregularly spaced fractures. In addition, this study reinforces indications from earlier studies about the complexity of dispersion in fractured media. Factors that contribute to spreading in the major and minor principal directions change with the orientation of the network relative to the mean hydraulic gradient.

Miscible and immiscible transport in groundwater

The current conventional theory for transport of solutes in groundwater was fully developed by the 1960s. Attention then focused on the development of analytical solutions to the governing equation. By the late 1960s, the increasing efficiency of digital computers, coupled with the restrictive assumptions required for analytical solutions, led to a major emphasis on developing deterministic, distributed‐parameter, numerical simulation models. Several numerical models that solved the conventional solute‐transport equation were developed in the early 1970s and initially applied to seawater‐intrusion problems. Toward the middle and late 1970s, many applications involved hazardous and radioactive waste disposal problems. Almost all of these applications involved miscible transport. With the increased application of transport models to field problems, certain deficiencies in transport theory were identified. The deficiencies include the mathematical descriptions of hydrodynamic dispersion, reaction processes, and flow and transport in fractured rocks. Therefore, in the latter half of the 1970s and the beginning of the 1980s, considerable research was and continues to be directed toward improving our understanding of these processes in the saturated zone.