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Rock Fractures and Fluid Flow: Contemporary Understanding and Applications 5 Hydraulic and Tracer Testing of Fractured Rocks Hydraulic and tracer tests are field methods for investigating fluid flow and chemical transport in the subsurface. They generally involve artificially inducing perturbations into the subsurface and measuring the resulting responses. In a hydraulic test the perturbation is created by injecting or withdrawing fluid from a borehole. The response is the change in fluid pressure in the same or nearby observation boreholes. In a tracer test a concentration perturbation is created by introducing a solute (tracer) into the subsurface. The movement of this solute is monitored by sampling for solute concentration at locations downstream from the tracer introduction point. This chapter provides an overview of field techniques and methods of analysis and their advantages and limitations, but the intent is not to provide a manual for hydraulic and tracer testing. The discussion is limited to hydraulic and tracer tests under single-phase, isothermal flow conditions in which the solute concentration is sufficiently dilute that density effects can be neglected. Not covered are hydraulic and pneumatic tests for evaluation of the vadose zone. Hydraulic and transport properties are assumed to remain constant during the tests. In other words, it is assumed that coupling between fluid pressure and rock stress is negligible and that chemical reactions (such as precipitation) that alter fracture openings do not occur. These conditions are generally satisfied when testing at depths of less than a few hundred meters and when the induced pressure perturbation is relatively small (e.g., less than 10 bars). In contrast, the testing of deep petroleum or geothermal wells commonly involves large changes in fluid pressure to the extent that fractures are opened or closed. This coupling is addressed in Chapter 7, but it is beyond the scope of this report to discuss hydraulic tests in these settings.
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Rock Fractures and Fluid Flow: Contemporary Understanding and Applications The popular notion that hydraulic and tracer tests are methods to ''measure" hydraulic and tracer properties is somewhat misleading. In reality, the analysis of a hydraulic or tracer test is a modeling exercise consisting of two steps. The first step is to choose a model to represent flow and transport in the rock mass. In the petroleum industry this step is commonly known as the diagnostic phase. The choice of model is based on knowledge of the rock mass and the behavior of the test response. After a model is chosen, the second step is to determine values of model parameters such that model-computed responses match the field responses. This step is known as parameter estimation. If the model-generated response cannot be made to match the field response, the model must be revised. In other words, model selection and parameter estimation are an iterative process. In some cases there may be insufficient information to identify a unique model or a unique set of parameters for a given model. When faced with such nonuniqueness, several possible models and/or parameter sets may need to be considered until additional information is collected to better define the flow system. The hydraulic and transport properties determined from a hydraulic or tracer test are not unique. They must be considered within the context of the model chosen for analysis. HYDRAULIC TESTS In groundwater investigations, hydraulic tests are used to obtain estimates of hydraulic conductivity and specific storage of the aquifer medium. The term "transmissivity" refers to the product of hydraulic conductivity and aquifer thickness. "Storativity" is the product of specific storage and aquifer thickness. In the petroleum industry the properties obtained are permeability and total compressibility. The distinction between hydraulic conductivity and transmissivity, or specific storage and storativity, is clear-cut when testing a porous medium, but confusion may arise in fractured rocks, as illustrated by the following example. Consider a rock mass containing a single extensive horizontal fracture bounded by impermeable rock. A borehole is drilled through this fracture, and a packer test is conducted in a test interval of length L containing this fracture (Figure 5.1a). If a porous-medium approach is used to analyze the test data and flow is assumed to be confined to a porous slab of thickness L (Figure 5.1b), a transmissivity T and hydraulic conductivity, K (= T/L), of the test interval can be calculated. For this particular example, however, the computed hydraulic conductivity is not representative of the rock mass because its value depends on the length of the test interval. If the length of the test interval is doubled (Figure 5.1c), the calculated hydraulic conductivity is halved. The transmissivity, however, is independent of the length of the test interval as long as no additional permeable fractures are encountered as the test interval is lengthened. To the extent that a single fracture can be viewed as an aquifer, it is useful to assign the transmissivity of the interval
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Rock Fractures and Fluid Flow: Contemporary Understanding and Applications FIGURE 5.1 Packer test for determining transmissivity. (a) Packer interval of length L straddling a single fracture. (b) Packer interval of length L straddling a slab of fractured rock considered a porous medium. (c) Packer interval of length 2L straddling a single fracture. to the fracture. Thus, fracture transmissivity is a term that is receiving increasing usage. The point of this example is not to discourage the use of hydraulic conductivity in test analysis but to emphasize the importance of reporting the test results with sufficient detail on the method of analysis so that readers are not misled. Hydraulic Testing in a Single Borehole In many subsurface investigations, particularly during the initial exploratory phase, hydraulic measurements (e.g., hydraulic head and flow rate) are restricted to individual boreholes. These tests are known as single-borehole hydraulic tests. Although single-borehole tests do not yield as much information as tests involving multiple boreholes, they offer the advantage of economy and speed. Single-borehole tests are commonly used for deep geological investigations because of the prohibitive expense of drilling multiple boreholes. Single-borehole tests are also used in some geotechnical investigations where time constraints preclude extensive testing with multiple boreholes.
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Rock Fractures and Fluid Flow: Contemporary Understanding and Applications Open-Borehole Versus Packer Tests Single-borehole hydraulic tests can be performed in two configurations: in an open borehole or with packers. In an open-borehole test the entire uncased portion of a borehole is tested. Open-borehole tests are easy to set up and do not require expensive test equipment. They provide information on the hydraulic properties of the tested rock mass as a whole. They also provide valuable information for the design of packer tests, for example, on the expected range of pumping or injection rates. It is advantageous to conduct open-borehole tests prior to packer tests. There are several disadvantages to open-hole tests. First, water inflow zones in the borehole cannot be located unless a flowmeter survey (Chapter 4) is conducted during pumping. Second, if the borehole penetrates several fractures or rock formations, the test response will be controlled by the most permeable zone, and little information will be obtained on the less permeable portion of the borehole. Third, when performed in low-permeability rocks, the test response may be dominated by wellbore storage effects (explained below), which complicate the interpretation of test data. Packer tests utilize two or more packers to isolate a portion of the borehole for testing. Depending on the application, the test interval can vary from tens of centimeters to tens of meters in length. Packers can be used to isolate an individual fracture, a group of fractures, or an entire rock formation. In some test programs, a fixed test interval length is chosen, and the borehole is tested in consecutive sections throughout its length to obtain a hydraulic conductivity profile. Other test programs concentrate on testing only the more permeable portions of the borehole. In such cases the test intervals may vary in length, depending on borehole conditions as inferred from geophysical logs. Test Procedures The basic procedure of a single-hole hydraulic test is to inject or withdraw fluid from a test interval while measuring the hydraulic head in the same test interval. Prior to testing, borehole conditions are allowed to reequilibrate following installation of test equipment. Test equipment can be set up in many different ways, examples of which can be found in Zeigler (1976), Bennett and Anderson (1982), and Bureau of Reclamation (1985). In a packer test the hydraulic heads above and below the test interval are monitored to check for fluid leakage around the packers. Leakage can result from poor packer seals or the presence of "short-circuiting" fractures between the test interval and the rest of the borehole. When testing at depth, temperature in the test interval should be monitored because a change in temperature resulting from thermal disequilibrium (e.g., if the rock was cooled by drilling fluid prior to the test) can cause anomalous responses (see, e.g., Pickens et al., 1987).
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Rock Fractures and Fluid Flow: Contemporary Understanding and Applications During injection or withdrawal, the head change should be sufficiently large that the flow rate is measurable but not so large as to alter the hydraulic properties of the rock mass. A high injection head can open existing fractures and increase their transmissivities. In an extreme case, hydraulic fracturing can result. Conversely, a large reduction in head during fluid withdrawal can cause dissolved gas to come out of the solution. Gas bubbles lodged in fractures can reduce their transmissivities. Five common procedures for single-hole hydraulic tests are discussed below: (1) constant-flow tests, (2) constant-head tests, (3) slug tests, (4) pressure pulse tests, and (5) drillstem tests. Figure 5.2 shows schematic plots of head and flow FIGURE 5.2 Schematic plots of hydraulic head and flow rate versus time for single-hole hydraulic tests.
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Rock Fractures and Fluid Flow: Contemporary Understanding and Applications rate versus time for these tests. Typically, the decision on which test to perform is based on the expected transmissivity of the test interval, the volume of rock to be sampled, and the availability of time and equipment. Test duration can range from 10 minutes in a geotechnical investigation to many days in a petroleum or water production test. Other factors being equal, a test of longer duration, involving a larger volume of injected or withdrawn fluid, will sample a larger volume of rock in the vicinity of the borehole. Quantifying the volume of rock sampled by these tests is a topic of current research. The constant-flow pumping test (Figure 5.3), in which fluid is withdrawn at a constant rate from the test interval, is the most common test method in the FIGURE 5.3 Equipment setup for a constant-flow pumping test in a single borehole.
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Rock Fractures and Fluid Flow: Contemporary Understanding and Applications groundwater and petroleum industries. Despite its popularity, this test is not without drawbacks. When performed with packers, the test is equipment intensive because a submersible pump must be used (Figure 5.3). Because most pumps operate over a limited discharge range, it is necessary to know the approximate transmissivity of the test interval in order to select the appropriate pump. Consecutive interval testing along a borehole becomes impractical, as the transmissivity variation from one test interval to another necessitates frequent changing of pumps. When testing an interval of low transmissivity, constant flow can be difficult to maintain and the pump can stall. For these reasons, constant-flow pumping tests are commonly reserved for testing more permeable intervals. An exception to this generalization occurs when testing in an environment where the hydraulic head is higher than the discharge point (e.g., in an underground facility, a naturally flowing well). In this case a constant outflow can be controlled by a flow regulator and a pump is not needed. During a constant-head test (Figure 5.4), fluid is injected into or withdrawn from a test interval while keeping the head of the test interval at a constant value. Constant-head injection is common practice in geotechnical investigations. Constant-head withdrawal is practical when testing in an underground chamber. If the hydraulic head in the test interval is higher than the chamber floor, the test interval can be opened to free drainage. A key advantage of constant-head testing is that it generally presents no special technical difficulties when applied to test intervals of low transmissivity, as long as the flow rate is measurable. The effects of wellbore storage also are minimal, which simplifies data analysis. A slug test (Figure 5.5) is performed by rapidly raising or lowering the fluid level in the pipe string or tubing connected to a test interval and monitoring its recovery to an equilibrium level. Typically, the test equipment includes a downhole valve in the test interval (Figure 5.5). After the packers are inflated, the test interval is isolated from the pipe string by closing the downhole valve. The fluid level in the pipe string is then raised or lowered by addition or removal of fluid. At the start of the test, the downhole valve is opened so that the hydraulic head in the pipe string is imposed on the test interval. If the fluid level in the pipe string were to be raised, fluid would drain from the pipe into the rock. If the fluid level was lowered, fluid would drain from the rock into the pipe. The downhole valve is kept open until the fluid level recovers to its equilibrium position. Slug tests are suitable for test intervals of moderate to low transmissivity. The test duration depends on the transmissivity of the test interval and the inside diameter of the pipe string. Lower transmissivities and larger pipe diameters lead to longer test times. Because pipe diameter can be varied, the duration of a slug test is controllable to a limited extent. A pressure pulse test (Bredehoeft and Papadopulos, 1980) is similar in concept to a slug test, with the exception that the downhole valve is closed after the hydraulic head in the test interval is abruptly increased or decreased. The downhole valve is opened just long enough for the head in the pipe string to be
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Rock Fractures and Fluid Flow: Contemporary Understanding and Applications FIGURE 5.4 Equipment setup for a constant-head injection test in a single borehole. transmitted into the test interval. Alternatively, the initial head disturbance can be created by using a hydraulic piston to inject a known volume of fluid into the test interval. The duration of a pressure pulse test depends on the transmissivity and the "system compressibility" of the test interval. System compressibility is
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Rock Fractures and Fluid Flow: Contemporary Understanding and Applications FIGURE 5.5 Equipment setup for a slug test in a single borehole. a function of the fluid compressibility and the compliance of the test equipment (e.g., Neuzil, 1982). Because head recovery is controlled by compressibility effects rather than filling or draining fluid from the pipe string, the duration of a pressure pulse test is much shorter than that of a slug test, all other factors being equal. For this reason, the pressure pulse test is commonly applied to test intervals of very low transmissivity. However, the volume of rock tested by a pressure pulse test is significantly smaller than that tested by a slug test.
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Rock Fractures and Fluid Flow: Contemporary Understanding and Applications The drillstem test was originally developed in the petroleum industry for testing wells before casing is installed. The equipment for a drillstem test is similar to that for a slug test. After the packers are inflated, the downhole valve (known as the tester valve in the petroleum industry) is shut and fluid is removed from the pipe string. The actual test comprises four stages (identified as I, II, III, and IV in Figure 5.2e). The first stage is the initial flow period, when the tester valve is opened for five to 10 minutes, allowing formation fluid to enter the pipe string. During the second stage, which lasts about an hour and is known as the initial shut-in period, the tester valve is shut so that fluid pressure in the test interval can recover toward the undisturbed formation pressure. In the third stage the tester valve is opened for the final flow period of approximately an hour. This is followed by the fourth state, final shut-in period of one to two hours, when the tester valve is again closed and the pressure in the test interval is allowed to recover. The flow period of a drillstem test is equivalent to a slug test, and the test data can be analyzed in the same fashion. Discussions of drillstem testing can be found in petroleum texts such as that by Earlougher (1977). Karasaki (1990) has proposed a variant of the drillstem test that consists of only one flow period, with the shut-in occurring at the time when the initial head drop has recovered by 50 percent. According to Karasaki, such a procedure improves the estimation of formation properties when a skin of low permeability (e.g., a mudcake) surrounds the wellbore. Models of Single-Borehole Hydraulic Tests Many common models of single-borehole hydraulic tests assume that the tested rock can be approximated as an isotropic homogeneous porous medium. Simple additions such as a highly transmissive fracture intersected by the borehole can be included in the analysis. The assumption of isotropy is made for a practical reason: reliable methods to characterize anisotropy generally require multiple boreholes. Homogeneity is assumed because the test response in a single borehole is insensitive to changes in hydraulic properties far from the test interval. Unless flow boundaries are close to the test interval, they are difficult to detect with confidence. For these reasons, models for single-borehole hydraulic tests are primarily concerned with fluid flow in the immediate vicinity of the test interval. Flow in the vicinity of the test interval can be envisioned in terms of three basic geometries: spherical flow, radial flow, and linear flow. Combinations of these geometries are possible. The discussion of these geometries below assumes that flow is caused by pumping from the test interval, causing a drawdown in hydraulic head. To the extent that the head change is sufficiently small that the hydraulic conductivity is not changed, the discussion is equally applicable to an injection test, in which case the flow direction is merely reversed.
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Rock Fractures and Fluid Flow: Contemporary Understanding and Applications Spherical flow geometry describes fluid flow toward a spherical cavity in a homogeneous porous medium of infinite extent in all directions (Figure 5.6a). Equipotential surfaces are concentric spheres around the spherical cavity. When applied to hydraulic testing, the cavity can represent a short test interval, the length of which is not significantly greater than the borehole diameter (Figure 5.6b). Spherical flow is commonly characterized as "three-dimensional" because the hydraulic head varies in the three spatial dimensions. Radial flow geometry describes flow toward a well that pumps from a homogeneous layer of infinite lateral extent (Figure 5.7a). This flow geometry serves as the model for a well test in a confined aquifer, which is bounded above and below by impervious materials. In the aquifer, equipotential surfaces are cylinders centered about the well axis. Thus, radial flow is also known as cylindrical flow. When applied to fractured-rock testing, the layer of porous medium represents a horizontal fracture zone or a single fracture bounded by impermeable rock (Figure 5.7b). Radial flow is commonly characterized as "two-dimensional" because the hydraulic head varies in the plane perpendicular to the well axis but remains constant along the direction parallel to the axis. Linear flow geometry describes flow that is unidirectional, that is, flow that does not vary in space (Figure 5.8a). An example of linear flow is flow to a well that intersects a highly transmissive vertical fracture that extends a long distance FIGURE 5.6 (a) Spherical flow to a cavity in a homogeneous porous medium. (b) Flow to a short test interval in a borehole that approximates spherical geometry.
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Rock Fractures and Fluid Flow: Contemporary Understanding and Applications APPENDIX 5.F DIAGNOSTIC WELL TEST ANALYSIS AT THE FRACTURE RESEARCH INVESTIGATION The Fracture Research Investigation (FRI) in the Grimsel Rock Laboratory, which is located in the Alps in southern Switzerland, provides an excellent example of diagnostic well test analysis. A hydrologically active and accessible fracture zone was selected for investigation, and five studies were jointly undertaken (Majer et al., 1990). A detailed geological investigation provided background information. Extensive cross-hole tomographic studies imaged the fracture zone, which was observed crossing two parallel drifts. Hydrological tests were designed based on the results of the geological and geophysical investigations. Hydraulic tests were planned in two boreholes drilled from the two drifts using the 1987 tomography results (Figure 5.F1). Each test consisted of pumping water in a given interval at a constant pressure and monitoring in all the other intervals. Test 1 was undertaken to provide a hydrological characterization of the main fracture zone that was identified in the tomographic images (feature A in Figure 5.F1). Packers were placed such that they confined the main fracture zone as tightly as possible in order to minimize wellbore storage and isolate the hydrological system (Figure 5.F2). This isolated interval (interval I1.2) was used as the inflow interval, and pressure was monitored in all the other intervals. Based on these results (Wyss, 1988), feature A is clearly the most significant hydrological feature at the FRI site. Figure 5.F3 shows the pressure transient interference data at various observation points during Test 1. Note that the interval I3.1 responded most markedly during pumping. The response data at I3.1 are compared to the theoretical response in Figure 5.F4. As can be seen from the figure, the pressure observed at I3.1 is significantly lower than predicted by the analytical solution, although the shapes of the curves are almost identical. The analytical solution assumes that the fracture is infinite, isotropic, and homogeneous. Therefore, conditions must exist where one or more of the above assumptions are not appropriate. A number of violating conditions may exist, including: Skin: there is a low-permeability zone around the injection well, that is, a skin that causes the effective pressure at I1.2 to be lower. Anisotropy: the fracture is anisotropic, and the maximum permeability direction is oriented vertically. Leakage: there is leakage from the fracture to the adjacent rock, so the pressure is more dispersed. Boundary effect: the boundary effect of the laboratory tunnel keeps the pressure low in I3.1. Skin effect is usually suspected when an anomalous result is obtained. However, the flow rate curve (not shown) does not match any of the skin curves, and
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Rock Fractures and Fluid Flow: Contemporary Understanding and Applications FIGURE 5.F1 Tomographic image of the FRI site obtained from the algebraic reconstruction technique (ART) invasion seismic data collected during 1987 survey. From Majer et al. (1990).
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Rock Fractures and Fluid Flow: Contemporary Understanding and Applications FIGURE 5.F2 Packer locations used in hydraulic tests at the FRI site. From Majer et al. (1990).
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Rock Fractures and Fluid Flow: Contemporary Understanding and Applications FIGURE 5.F3 Interference buildup data for test 1 at various observation points. From Majer et al. (1990). the match for I3.1 is not very good. Therefore, it seems that the conventional skin effect cannot explain the observed behavior. Alternatively, if a constant pressure drop independent of the flow rate is assumed at the borehole wall, the flow rate curve would not exhibit the skin effect. Although the no-skin curve is closer to the observed curve, it still does not explain the observed inflection in the flow rate curve. Geological observations indicate that the fracture zone may be highly anisotropic with the highest permeability in the vertical direction. Thus, injected water may flow preferentially in the vertical direction. As a result, the observed pressure head in the horizontal direction in interval I3.1 may be lower than for the isotropic case. Analytical solutions for flow to a well in an anisotropic medium can be obtained through a transformation of coordinates (Kucuk and Brigham, 1979). However, an unreasonably large anisotropy ratio (2 × 109) is necessary to explain the pressure drop. Therefore, it is unlikely that anisotropy is the sole cause for the low-pressure measurement. As can be seen from Figure 5.F3, small interference responses were observed at various intervals that are not in the plane of the fracture zone. This implies
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Rock Fractures and Fluid Flow: Contemporary Understanding and Applications FIGURE 5.F4 Comparison between interference buildup data for test 1 and the theoretical response curve. From Majer et al. (1990). that there is leakage from the fracture zone into adjacent rocks, which may explain why the interference response in I3.1 was low. The solution for pressure in a constant-pressure test in a leaky aquifer is not readily available in the literature. However, if the thickness of the rock into which leakage occurs is assumed to be of finite size and the leakage is at quasi-steady state, the solution presented by Da Prat et al. (1981) for a double-porosity medium can be used. The match between the flow rate data and the Da Prat solution (not shown) is very good, but the match between the pressure data and the solution in I3.1 (not shown) is poor. The theoretical pressure is too high compared to the data because in the model the rock is assumed to be of finite size. Leakage into an infinite-sized rock was considered through a Laplace space solution for the normalized pressure in the fracture zone at a nondimensional distance, rD, under a constant-pressure test with leakage into an infinite-sized rock. Values of drawdown and flow for the Laplace space solution are plotted in Figures 5.F5 and 5.F6 for various combinations of fracture and matrix proper-
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Rock Fractures and Fluid Flow: Contemporary Understanding and Applications FIGURE 5.F5 Comparison of drawdown and flow for leakage into an infinite-sized rock with data from I3.1. From Majer et al. (1990). ties. Also plotted are the observed data. The match with the interference data in I3.1 is much better than in Figure 5.F4. However, the match between the data and the theoretical curves at long times is not good. In particular, the observed flow rate data are much flatter than the theoretical curves at long times (Figure 5.F6). Nonetheless, the concept of leakage appears to explain the trend of the data: low interference pressure and flattening of the flow rate curve at long times. The weak hydraulic connection between I1.2 and I2.2 may be through this low-permeability rock matrix. It is worth noting that the 1988 seismic tomography results (Figure 5.F1) indicate the existence of a feature (feature B) that extends diagonally from the access tunnel toward borehole 87.001. This may be a conduit for the leaking water. This localized leakage is not taken into account by the analytical solution; it could explain the low pressure in I3.1 and the flattening of the flow rate curve. Hydraulic tests have confirmed the hydrological significance of this fracture zone, which was previously identified by seismic tomography. It appears that the majority of flow occurs in the relatively thin fracture zone that connects I1.2
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Rock Fractures and Fluid Flow: Contemporary Understanding and Applications FIGURE 5.F6 Comparison of drawdown and flow for leakage into an infinite-sized rock with data from I2.1. From Wyss (1988). and I3.1 (feature A). A weak but definite hydrological connection between I1.2 and I2.2 also was observed. Feature B in Figure 5.F1, which extends diagonally from the access tunnel to borehole 87.001, may partially explain this hydrological connection.
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Rock Fractures and Fluid Flow: Contemporary Understanding and Applications APPENDIX 5.G THE FRACTURE ZONE PROJECT AT FINNSJÖN The fracture zone project sponsored by SKB (Swedish Nuclear Fuel and Waste Management Co.) was run between the years 1984 and 1990 at the Finnsjön site, which is located in central Sweden about 140 km north of Stockholm. Its main goal was to characterize a major fracture zone in crystalline bedrock, especially the flow and transport properties of a fracture zone, the localization of potential pathways for groundwater flow, and transport of solutes essential for the safety assessment of a nuclear waste repository. At the Finnsjön site, there are a number of gently dipping fracture zones (0° to 30° to the horizontal), which are common in such crystalline rock formations (Andersson, 1993). Geological identification and characterization of these fracture zones were accomplished through a broad range of geological, geophysical, geomechanical, geochemical, and hydrological investigations. Through these investigations, a gently dipping fracture zone, zone 2, was defined in nine boreholes in an area of about 1,500 × 500 m in the northern part of the Finnsjön Rock Block at depths of 100 to 300 m. This zone was singled out for detailed flow studies aimed at understanding flow and transport in the zone and interactions with surrounding bedrock. Flow measurements on this zone included piezometric measurements, single-hole hydraulic tests at different scales, interference tests, groundwater flow measurements, and tracer tests, radially converging and dipole. A number of hydrological modeling efforts were then undertaken. These efforts were carried out in conjunction with field experiments, so there was a close interaction between modeling and field measurements. In this interaction the modeling and field measurements mutually support each other; measurements can be used to test and improve the predictive ability of models, and models can be used to design and interpret field measurements. The overall sequence of this interaction was as follows: model predictions of interference tests interference tests updated flow models based on interference tests predictions of radially converging tracer tests radially converging tracer tests comparison of model predictions with radially converging tracer tests prediction of dipole tracer test, and comparison of model predictions with dipole tracer test. The main conclusion regarding flow in zone 2 showed that the zone, which is about 100 m thick, is composed of two to five highly transmissive sections (T = 1 - 4 × 10-4 m2/s). These highly transmissive sections have widths of
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Rock Fractures and Fluid Flow: Contemporary Understanding and Applications about 0.5 m. Interference tests showed that the uppermost section was interconnected over distances of several hundred meters, and tracer experiments showed travel times differing by a factor of 10 between two observation boreholes at approximately the same distance from an injection borehole. Modeling efforts showed that zone 2 has a complicated structure where transport occurs in a few well-defined pathways and that this heterogeneity must be an important component in transport models. REFERENCES Abelin, H., L. Birgersson, J. Gidlund, and I. Neretnieks. 1991a. A large-scale flow and tracer experiment in granite 1. Experimental design and flow distribution. Water Resources Research, 27(12):3017–3117. Abelin, H., L. Birgersson, L. Moreno, H. Widen, T. Agren, and I. Neretnieks. 1991b. A large-scale flow and tracer experiment in granite 2. Results and interpretation. Water Resources Research, 27(12):3019–3135. Andersson, J. E., L. Ekman, R. Nordquist, and A. Winberg. 1991. Hydraulic testing and modeling of a low-angle fracture zone at Finnsjon, Sweden. Journal of Hydrology, 126:45–77. Andersson, P. 1993. SKB Report 93-20, Swedish Nuclear Fuel and Waste Management Co., Stockholm. Barker, J. A. 1988. A generalized radial flow model for hydraulic tests in fractured rock. Water Resources Research, 24(10):1796–1804. Bear, J. 1979. Hydraulics of Groundwater. New York: McGraw-Hill. Bennett, R. D., and R. F. Anderson. 1982. New pressure test for determining coefficient of permeability of rock masses. Technical Report GL-82-3, U.S. Army Engineer Waterways Experiment Station, Vicksburg, Miss., p. 61. Black, J. H., and K. L. Kipp. 1981. Determination of hydrogeological parameters using sinusoidal pressure test: a theoretical appraisal. Water Resources Research, 17(3):686–692. Bourdet, D., T. M. Whittle, A. A. Douglas, and Y. M. Pirard. 1983. A new set of type curves simplifies well test analysis. World Oil, 196:95–106. Bourdet, D., J. A. Ayoub, and Y. M. Pirard. 1989. Use of pressure derivative in well test interpretation. SPE Formation Evaluation, 4(2):293–302. Bredehoeft, J. D., and S. S. Papadopulos. 1980. A method for determining the hydraulic properties of tight formations. Water Resources Research, 16(1):233–238. Bureau of Reclamation. 1985. Ground Water Manual. Denver: U.S. Department of the Interior, Bureau of Reclamation, p. 480. Carrera, J., and S. P. Neuman. 1986. Estimation of aquifer parameters under transient and steady-state conditions: 2. Uniqueness, stability, and solution algorithm. Water Resources Research, 22(2):211–227. Carrera, J., and J. Heredia. 1988. Inverse modeling of Chalk River block. NAGRA Technical Report 88-14, National Cooperative for the Disposal of Radioactive Waste (NAGRA), Baden, Switzerland, 117 pp. Cooper, H. H., J. D. Bredehoeft, and I. S. Papadopulos. 1967. Response of a finite-diameter well to an instantaneous charge of water. Water Resources Research, 3(1):263–269. Dagan, G. 1986. Statistical theory of groundwater flow and transport: Pore to laboratory, laboratory to formation, and formation to regional scale. Water Resources Research, 22(9):120S–134S. Dagan, G., V. Cvetkovic, and A. Shapiro. 1992. A solute flux approach to transport in heterogeneous formations 1. The general framework. Water Resources Research, 28(5):1369–1376.
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Representative terms from entire chapter: