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Title: Effective transmissivity of two-dimensional fracture networks

Abstract

Many of the sites that have been proposed as potential locations of underground radioactive waste repositories contain fractured rocks. For example, both the saturated and unsaturated zone at Yucca Mountain, Nevada, contains many hydrogeologic units that are extensively fractured. When modeling the hydrological behavior of these sites, for either the purpose of site characterization of performance assessment, computational grid-blocks are often used that contain large number of fractures. In order to treat these as equivalent continua, it is necessary to develop a procedure for relating the hydraulic properties of the individual fractures and he topology of the fracture network to the overall scale permeability. One aspect of this problem is that of determining the in situ hydraulic properties of the individual fractures. Another aspect is to reconstruct the three-dimensional geometry of the fracture network based on borehole or outcrop measurements. The final stage in the problem is that of taking a network of known geometry and determining it effective scale conductivity. The purpose of this paper is to describe a simple procedure for solving this latter problem,a nd to demonstrate it use in cases of both saturated and unsaturated flow. The TOUGH simulator was used.

Authors:
;
Publication Date:
Research Org.:
Lawrence Berkeley Lab., CA (United States)
Sponsoring Org.:
USDOE, Washington, DC (United States)
OSTI Identifier:
87080
Report Number(s):
LBL-37332
ON: DE95015139; TRN: 95:017375
DOE Contract Number:
AC03-76SF00098
Resource Type:
Technical Report
Resource Relation:
Other Information: PBD: Apr 1995
Country of Publication:
United States
Language:
English
Subject:
05 NUCLEAR FUELS; 54 ENVIRONMENTAL SCIENCES; 58 GEOSCIENCES; HIGH-LEVEL RADIOACTIVE WASTES; UNDERGROUND DISPOSAL; ROCKS; HYDRAULIC CONDUCTIVITY; HYDROLOGY; T CODES; HYDRAULIC FRACTURES; COMPUTERIZED SIMULATION; YUCCA MOUNTAIN; Yucca Mountain Project

Citation Formats

Zimmerman, R.W., and Bodvarsson, G.S.. Effective transmissivity of two-dimensional fracture networks. United States: N. p., 1995. Web. doi:10.2172/87080.
Zimmerman, R.W., & Bodvarsson, G.S.. Effective transmissivity of two-dimensional fracture networks. United States. doi:10.2172/87080.
Zimmerman, R.W., and Bodvarsson, G.S.. Sat . "Effective transmissivity of two-dimensional fracture networks". United States. doi:10.2172/87080. https://www.osti.gov/servlets/purl/87080.
@article{osti_87080,
title = {Effective transmissivity of two-dimensional fracture networks},
author = {Zimmerman, R.W. and Bodvarsson, G.S.},
abstractNote = {Many of the sites that have been proposed as potential locations of underground radioactive waste repositories contain fractured rocks. For example, both the saturated and unsaturated zone at Yucca Mountain, Nevada, contains many hydrogeologic units that are extensively fractured. When modeling the hydrological behavior of these sites, for either the purpose of site characterization of performance assessment, computational grid-blocks are often used that contain large number of fractures. In order to treat these as equivalent continua, it is necessary to develop a procedure for relating the hydraulic properties of the individual fractures and he topology of the fracture network to the overall scale permeability. One aspect of this problem is that of determining the in situ hydraulic properties of the individual fractures. Another aspect is to reconstruct the three-dimensional geometry of the fracture network based on borehole or outcrop measurements. The final stage in the problem is that of taking a network of known geometry and determining it effective scale conductivity. The purpose of this paper is to describe a simple procedure for solving this latter problem,a nd to demonstrate it use in cases of both saturated and unsaturated flow. The TOUGH simulator was used.},
doi = {10.2172/87080},
journal = {},
number = ,
volume = ,
place = {United States},
year = {Sat Apr 01 00:00:00 EST 1995},
month = {Sat Apr 01 00:00:00 EST 1995}
}

Technical Report:

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  • This report describes some of the programs developed at Lawrence Berkeley Laboratory for network modelling. By themselves, these programs form a complete chain for the study of the equivalent permeability of two-dimensional fracture networks. FMG generates the fractures considered as line discontinuities, with any desired distribution of aperture, length, and orientation. The locations of these fractures on a plane can be either specified or generated randomly. The intersections of these fractures with each other, and with the boundaries of a specified flow region, are determined, and a finite element line network is output. RENUM is a line network optimizer. Nodesmore » very close to each other are merged, deadends are removed, and the nodes are then renumbered in order to minimize the bandwidth of the corresponding linear system of equations. LINEL computes the steady state flux through a mesh of line elements previously processed by program RENUM. Equivalent directional permeabilities are output. ELLFMG determines the three components of the permeability tensor which best fits the directional permeabilities output by LINEL. A measure of the goodness fit is also computed. Two plotting programs, DIMES and ELLP, help visualize the outputs of these programs. DIMES plots the line network at various stages of the process. ELLP plots the equivalent permeability results. 14 refs., 25 figs.« less
  • In order to apply these theories to random systems, the authors (1) define the equivalent to the case where probability, p = 1, (2) define p in terms of the statistical parameters of the random network, and (3) define the equivalent of the coordination number, z. An equivalent for p is found as a function of the connectivity, {zeta}, which is defined as the average number of intersections per fracture. This number can be calculated from the fracture density and distributions of fracture length and orientation. Then the equivalent p is defined by equating the average run length for amore » random network as a function of {zeta} to the average run length for a lattice as a function of p. The average run length in a random system is the average number of segments that a fracture is divided into by intersections with other fractures. In a lattice, it is the average number of bonds contiguous to a given bond. Also, an average coordination number can be calculated for the random systems as a function of {zeta}. Given these definitions of p and z, expressions for permeability are found based on percolation theory and equivalent medial theory on regular lattices. When the expression for p is used to calculate the correlation length from percolation theory, an empirical formula for the size of the REV can be developed. To apply the models to random length systems, the expression for {zeta} must be modified to remove short fractures which do not contribute to flow. This leads to a quantitative prediction of how permeability decreases as one removes shorter fractures from a network. Numerical studies provide strong support for these models. These results also apply to the analogous electrical conduction problem. 25 refs., 11 figs., 9 tabs.« less
  • The purpose of this report is to provide the user with sufficient information to run the programs FMG, RENUM, LINEL, and ELLFMG. A previous report explained the theory and the design of these programs, so that by using the two reports, a thorough understanding of the codes is possible. This report should familiarize the user with program options and modes of operation, input variables, input and output files. Information not strictly needed to run the programs, but useful in understanding their internal structure is provided in appendices. The appendices cover program variables and arrays, subroutine outlines, a short description ofmore » each subroutine, and finally listings of codes. The additional information on FMG, RENUM, LINEL, and ELLFMG is in Appendices A, C, E, G respectively, and the listings are in Appendices B, D, F, and H.« less
  • We characterize how different fracture size-transmissivity relationships influence flow and transport simulations through sparse three-dimensional discrete fracture networks. Although it is generally accepted that there is a positive correlation between a fracture's size and its transmissivity/aperture, the functional form of that relationship remains a matter of debate. Relationships that assume perfect correlation, semicorrelation, and noncorrelation between the two have been proposed. To study the impact that adopting one of these relationships has on transport properties, we generate multiple sparse fracture networks composed of circular fractures whose radii follow a truncated power law distribution. The distribution of transmissivities are selected somore » that the mean transmissivity of the fracture networks are the same and the distributions of aperture and transmissivity in models that include a stochastic term are also the same. We observe that adopting a correlation between a fracture size and its transmissivity leads to earlier breakthrough times and higher effective permeability when compared to networks where no correlation is used. While fracture network geometry plays the principal role in determining where transport occurs within the network, the relationship between size and transmissivity controls the flow speed. Lastly, these observations indicate DFN modelers should be aware that breakthrough times and effective permeabilities can be strongly influenced by such a relationship in addition to fracture and network statistics.« less
  • The report presents the results of the study at a test site in Preston County, West Virginia, to determine if a correlation exists between the direction of maximum transmissivity in a coal aquifer and the orientation of the face cleat in the coal bed. A secondary objective was to determine the direction of maximum transmissivity and variation in hydrologic conductivity with depth in the overlying rock (overburden) aquifers. The results are based on multiple-well aquifer tests in the Upper Freeport coal bed and overburden. The report describes (1) the geology and the occurrence and movement of ground water in themore » coal and overburden aquifers, (2) aquifer-test design and methods of data analyses, (3) hydraulic properties of the coal and overburden aquifers, and (4) orientation of the face cleat in the Upper Freeport coal bed.« less