Understanding and Solving Fracture Flow Problems
The mention of "fractures" conjures up images in variability and unpredictability to many groundwater hydrologists. Anecdotal evidence of this variability is prevalent. Indications of fracture behavior include single narrow fractures dominating flow to wells or drawdowns to a pumping well bypassing nearby observation points to affect more distant wells. Fortunately, over two decades of basic research on the structural geology and hydrogeology of fracture networks has led to new understandings of fracture geometry, new techniques for conductive fracture detection and new tools for computer simulation. This article outlines the major issues that distinguish fracture flow from flow in more conventional porous systems and suggests solutions for solving fracture flow problems.
What are fractures and why do they pose challenges for groundwater hydrologists? Fractures are formed through the deformation of rocks and soils. Fractures may occur in almost any competent material, but the more brittle the rock or soil, the smaller the deformations are that can result in fracturing. Any deformation can create fractures.
The causes of fracturing may be deep-seated, such as tectonic forces or subsurface subsidence. Fractures may also form from relatively shallow phenomena such as slope movements, settlement, thermal expansion or the density and volume changes associated with some chemical processes. Once formed, the permeability may be enhanced by erosion and chemical dissolution or continued deformation, or the permeability may decrease from mechanical closure, chemical precipitation or fracture-wall alteration.
Groundwater flow across distances greater than a few meters usually involve multiple fractures or fracture networks. The flow of groundwater though a fracture network is strongly influenced by the geometry of fractures. Fractures often have preferred orientations that impart an overall anisotropy, or enhanced direction of flow. This effect can be compounded by deformations that even more strongly enhance the flow in certain directions. This is why measurements of the rock stresses have been used to predict flow anisotropy in some petroleum reservoirs.
Even more important than anisotropy may be the heterogeneity of properties within a fracture network. Statistical work on fracture systems in the 1970s and 1980s showed that fractures usually come in a wide range of sizes and spacings. Highly skewed statistical distributions (such as lognormal or exponential distributions) often describe fracture properties.
The most important property may be the opening of the fracture, or its aperture. The flow capacity of a fracture varies by a power of the opening. Fluid mechanics theory suggests that this relationship is cubic, therefore a small difference in the opening between fractures can result in very large differences in flow capacity. Unevenness or irregularities in the fracture surface may form flow channels with power-law sensitivities of transmissivity to the fracture wall separations. Given this sensitivity to variability, fractures that are otherwise indistinguishable may be very different in their transmissive properties.
In many types of fracture networks, the most extensive and most open fractures may be the dominant conductors. Therefore, the extremities of the fracture population (rather than the average fractures) may be the controlling features for groundwater flow. The cubic relationship of fracture transmissivity implies that fractures that occupy only a small portion of the rock or soil mass may prove to be very efficient conductors of fluid. Exploration programs using boreholes may miss the major conductors if the geometry of the fractures is not accounted for in the design and layout of the boreholes. This basic sensitivity of flow properties to geometric variability underlies the reputation that fractured materials have for being difficult or unpredictable.
How does flow in fractured rocks differ from flow in more porous materials like sand and gravel? The main differences come from pathway geometry rather than flow processes. Flow in fractures is governed by the same flow equations as porous media (such as Darcy's law and diffusion equations). The major geometric difference between porous and fractured materials is one of connectivity. In porous media, all points have connections to all other points. In fracture networks, particularly in "hard," impermeable rocks, connections exist only along the fracture pathways and there is no requirement that all the pathways form continuous networks. The distinction between fracture flow and porous flow is much like differences in transportation systems such as ocean transport or rail transport. By sea, as in porous continua, all points are connected by straight-line paths. In fractures, like highway and rail transport, flow and transport follow distinct, discrete pathways.
Pumping tests often illustrate these geometric differences. In porous materials, pumping wells produce drawdowns that vary symmetrically with radial distance. In fracture-dominated systems, the flow is largely confined to the fracture network with less participation from the intergranular pore of the rock matrix. Not all points in the mass are equally connected, and flow proceeds dominantly along the fracture pathways. Drawdowns may vary with distance along the fracture pathways, but the tortuosity of the fracture pathways may result in drawdown patterns that bypass nearby wells to affect more distant, connected points.
Therefore, the major challenge of fracture flow is in defining the fractures geometry. Defining the geometry means understanding the important, conducting fractures that occur determining their hydraulic properties.
Fractures can significantly affect the performance of dams and other impoundments. Investigation programs commonly involve intense drilling and characterization efforts where significant fracturing is suspected. In addition, grouting programs often provide fracture control. If major fractures go undetected, not only may leakage be unacceptably large, but unfavorable fracture geometry also may result in piping of earth materials on the downstream side of the dam.
Water resource development needs to account for fractures in the exploration, development and protection of water supplies. An understanding of fracture geometry and indicators of fracture zones can significantly improve the likelihood of success in water supply exploration. Once wells are developed, an understanding of fracture network geometry is necessary to safeguard water supplies by defining wellhead protection zones. Unlike continuous porous systems, wells in fractured rock may draw water non-uniformly from the region surrounding the well. Well test interpretation methods that do not assume cylindrical flow and measurements of surface deformations around the well head can provide indicators of non-uniform production from fracture networks.
Fractures can significantly affect the transport of contaminants and the design of groundwater remediation efforts. When forming percolating networks, the potential efficiency of fractures as conductors can result in highly preferential movement in distinct pathways.
Tools and Techniques for Fracture Assessment
Fractures have been recognized as significant and problematic features in groundwater for at least the past 30 years. Over the past 20 years, research organizations have intensely pursued the fracture problem, particularly in the area of radioactive waste disposal and to a lesser degree in the areas of non-radioactive hazardous waste. Several facilities including the Stripa Mine (Fairhurst and others, 1993) and the Hard Rock Laboratory (Sweden; SKB, 1996), the Grimsel rock laboratory (Switzerland; Frick and others, 1992), the Kamaishi Mine (Japan), the Atomic Energy of Canada Underground Research Laboratory (Simmons and others, 1992) and the Raymond Quarry test sites (California; Cohen and others, 1995) have performed significant experiments in fracture flow. In addition to these efforts, an increased awareness of the importance of fractures for oil and gas reservoirs has stimulated the development tools and testing methods that are making their way into groundwater use.
Particularly promising progress has been made in the areas of borehole imaging and borehole flow logging. Although methods of analyzing data from maps and surfaces have also advanced, boreholes remain the primary means of groundwater exploration. Only boreholes provide direct measurement of flows under aquifer conditions.
Some borehole imaging methods include borehole television, borehole acoustic televiewer and formation microscanner (FMS). Borehole television methods have made major advances through developments in processing software developed in Japan. Several companies have developed methods to process television signals into an "unwrapped," undistorted color view of the entire borehole wall, with resolution to approximately 0.1 mm. The processing program also can prepare a virtual core and has a program to rapidly analyze fracture information from the images (Figure 1).
While television provides a very complete visual record of borehole walls, its applicability is limited to holes with clear water. For less advantageous conditions, the acoustic televiewer and Formation Micro-Scanner (produced by Schlumberger) provide useful alternatives. The acoustic televiewer creates an image of the topography or roughness of the borehole wall using reflected acoustic waves. Open fractures or fractures that the drilling has eroded have a clear topographic expression on the unwrapped images of the borehole wall. The micro-scanner (FMS) uses multiple pads to measure the resistivity of the rock along strips as the tool is brought up the borehole. This method has proven very effective in detecting fractures.
Despite the advances in borehole imaging quality, images must be complemented by direct measurements of hydraulic properties. Due to the sensitivity of flow capacity to fracture opening, fractures that are only slightly more open than others can dominate the flow to a borehole. Therefore, fractures that appear similar in borehole images may have very different flow characteristics.
Fortunately, new methods for measuring borehole flow provide these hydraulic data. Two recent developments include the borehole heat pulse flow meter, developed by the US Geological survey, and the electromagnetic flowmeter developed by the Tennessee Valley Authority. These tools extend the range of flow measurement well below the limits of the more established spinner flow meter technologies. Heat pulse and electromagnetic flow meters can be used in either ambient or pumping conditions. Under ambient conditions, the flow meter measures the cross-flow between the conductor in a borehole under natural gradients. With this data, the vertical components and directions of hydraulic head gradient can be defined. Under pumping conditions, the flow meter measurements can locate specific conducting features and define their hydraulic properties. Another promising logging method was developed in part under cooperation by the United States and Switzerland in radioactive waste disposal research. This method replaces the water in a well with a water having contrasting properties of electrical conductivity. Repeated water conductivity logs, under either pumped or unpumped conditions, record the locations of inflow and then give information on rates that can be used to infer hydraulic properties. Figure 2 shows a comparison of hydrophysical logs and borehole imaging results from the Raymond quarry.
Several numerical methods of fracture analysis provide insight into the structure of fracture networks. Neural net analyses are an artificial intelligence approach to understanding the correlation between conductive fractures and other geologic indicators. Initially, the neural net analysis uses a "training" set consisting of data from locations where both conductive fractures and information on potential indicators, such as geophysical or geological properties, are known. This training set provides insight into the correlation structure of the independent and dependent parameters (i.e., the capacity of indirect geological and geophysical data to predict conductive features).
As mentioned earlier, fundamental work on the statistical description of fracture geometry in the 1970s and 1980s discovered a number probability function that could fit fracture data from a wide range of geologic settings. These descriptions initially provided a basis for designing rock slopes with an understanding of the probabilities and risks of failures. Extensions of these models to include flow properties were an early basis for probabilistic fracture flow models.
More recently, fractal and geostatistical approaches have appeared as new tools for further understanding the structure of conductive fracture networks. "Geostatistics," despite its broad sounding name, is a set of methods initially developed to estimate ore reserves based on spatial correlation. Spatial correlation refers to the likelihood that properties sampled at two nearby locations are more alike than properties sampled at two more distant locations. Geostatistical methods establish the range of spatial correlation as a measure of how far and how reliably measurements can be extrapolated. Geostatistical methods can be useful when the data indicate spatial correlation. For fracture systems, geostatistical methods should be used with care, since the range of fracture property extrapolation may be very small in situations where even a few feet offset of borehole locations can make a difference in hitting a fracture or not.
Fractal geometry (Barton and LaPointe, 1995) has been highly popularized in recent years as a powerful tool for describing many patterns in nature, including the patterns of fracture networks. Fractal descriptions of spatial geometry look at the space-filling properties of patterns. Included in fractal descriptions are the self-similarities of patterns (i.e., the replication of a pattern over a large range of scales). For fractures, the existence of self-similarity would suggest that maps of fractures might have similar patterns in the microcracks within a hand sample, in the joints of a several square-foot outcrop or in the fractures of a quarry floor. The dimension of a pattern or network describes how a pattern fills a space (e.g., how a mapped fracture network fills the two dimensional mapping surface). Fractal models can produce a number of interesting properties such as the tendency for fractures to cluster and form isolated networks. Where the primary information on fracture locations is derived from boreholes or outcrops, fractal geometry provides a means of constructing three-dimensional fracture models from the lesser dimensional sample, something much more difficult for non-fractal patterns.
In the past 15 years, computer simulators have used these geometric descriptions to build realistic models of fracture networks. Several simulators now exist such as the UK Atomic Energy Agency's NAPSAC code, which is mainly designed for mainframe computation, and Golder Associates' FracMan that is oriented towards personal computers and workstations. These codes were included in validation studies at the Stripa Mine in Sweden (Fairhurst and others, 1993). Discrete fracture codes consist of
- a fracture generator that builds simulated networks from the spatial information,
- meshing program that prepares a calculational grid, and
- a flow solver that calculates flow and solute transport.
FracMan also includes a set of routines for analyzing field data to produce the model inputs. Figure 3 shows an example of solute tracking through a simulated fracture network, and Figure 4 shows a 1-km model of fracture zones with heterogeneous hydraulic properties from the Swedish Hard Rock Laboratory.
The several approaches to generating fractures from spatial information include:
- Stochastic-samples randomly from probability functions
- Deterministic-specifically locates known features and assigns appropriate properties
- Conditioned-honors the locations and properties of fractures where they are known, such as boreholes, and generates fractures stochastically elsewhere.
Over the past ten years, international research programs for radioactive waste disposal in several countries including Sweden and Japan have demonstrated the practicality of network models. These programs, such as the Stripa Project in Sweden, ran underground flow and transport experiments that included fracture data collection, network modeling, flow prediction and a comparison of predictions and experimental results.
Although fractures remain a significant challenge for groundwater hydrologists and engineers, the past 20 years of research have significantly advanced the conceptual understanding of fracture networks and provided practical tools for solving fracture flow problems. Tools such as flow flogging methods help by efficiently and rapidly finding the conducting fractures. Borehole imaging methods give information on the geometry and geological characteristics of the conductors. Fracture network models provide computational tools for simulating flow and transport in the network. By defining geometric and flow properties in stochastic terms, the simulations can quantify the uncertainties in knowledge of the flow system, and thus support risk-based decision making.
- Barton, C. and P. LaPointe, 1995, "Fractals in the Earth Sciences," Plenum Press, New York.
- Cohen, A., K. Karasaki, B. Freifeld, P. Benito, P. Cook, J. Clyde, K. Grossenbacher, J. Peterson, R. Solbau, B. Thapa, D. Vasco, and P. Zawislanski, 1996, "Project Summary - Hydrogeologic Characterization of Fractured Rock Formations: A Guide for Groundwater Remediators," US Environmental Protection Agency EPA/600/S-96/001.
- Fairhurst, C., F. Gera, P. Gnirk, M. Gray, and B. Stillborg, OECD/NEA International Stripa Project, 1980p;1992, Overview Volume, OECD/NEA, Paris, 1993.
- Frick, U., W. Alexander, B. Baeyens, P. Bossart, M. Bradbury, Ch. BŸhler, J. Eikenberg, Th. Fierz, W. Heer, E. Hoehn, I. McKinley, and P. Smith, 1992, "The Radionuclide Migration Experiment - Overview of Investigations 1985p;1990," Nagra Technical Report 91-04, National Cooperative for the Disposal of Radioactive Waste, Wettingen, Switzerland.
- Simmons, G., D. Bilinsky, C. Davison, M. Gray, B. Kjartanson, C. Martin, and D. Peters. 1992, "Program of Experiments for the Operating Phase of the Underground Research Laboratory," AECL Report AECL-10554, Atomic Energy of Canada Ltd., Pinawa, Manitoba
- SKB (Swedish Nuclear Fuel and Waste Management Company), 1996. €spš Hard Rock Laboratory, 10 Years of Research.
About the Author:
Dr. Thomas Doe is a Principal at Golder Associates Inc. in Seattle, Washington. He has more than 19 years of experience in the research and application of geotechnology to radioactive waste disposal. His specialties are hydrologic test methods for fractured, low permeability rock and in-situ stress measurement.