Lessons from Field Studies at the Apache Leap Research Site in Arizona
This paper summarizes lessons learned from single-hole and cross-hole pneumatic injection tests recently completed by The University of Arizona in unsaturated fractured tuffs at the Apache Leap Research Site (ALRS) near Superior, Arizona. The research was designed to investigate, test, and confirm methods and conceptual-mathematical models that can be used to determine the role of fractures and fracture zones in flow and transport through partially saturated porous rocks, with emphasis on the characterization of fracture connectivity, permeability, and porosity, and their dependence on location, direction, and scale. Over 270 single-hole tests have been conducted in six shallow vertical and inclined boreholes at the site by Guzman et al. (1996). These authors used a steady-state analysis to obtain permeability values for borehole test intervals of various lengths, based solely on late pressure data from each test. We summarize briefly the results of this earlier work and discuss more recent pressure and pressure-derivative type-curve interpretations, as well as numerical inverse analyses, of transient data from some of the single-hole tests. Our transient analyses of single-hole tests yield information about
University of Arizona in Tucson
CNWRA, Southwest Research Institute, San Antonio, Texas
Geoanalysis Group, Los Alamos National Laboratory, New Mexico
City of Tucson Water Department, Arizona
Pinnacle West, Phoenix, Arizona
Water Management Consultants, Tucson, Arizona
air permeability, air-filled porosity, skin factor, borehole storage, phenomenology, and dimensionality of the flow regime on a nominal scale of 1 m in the immediate vicinity of each test interval. Transient air permeabilities agree well with previously determined steady-state values, which, however, correlate poorly with fracture density data. We used the single-hole test results, together with borehole televiewer data, to help design and conduct 44 cross-hole pneumatic tests in 16 boreholes at the site (one test included 22 boreholes), including those used previously for single-hole testing. In each cross-hole test, air was injected at a constant mass flow rate into a relatively short borehole interval of length 1-2 m while monitoring (a) air pressure and temperature in the injection interval; (b) barometric pressure, air temperature, and relative humidity at the surface; and (c) air pressure and temperature in 13 short (0.5-2 m) and 24 longer (4-20 m) intervals within the injection and surrounding boreholes. We focus here on one of these cross-hole tests, labeled PP4. During this test, pressure responses were detected in 12 of the 13 short monitoring intervals and 20 of the 24 longer intervals. We used two methods to analyze the test results: a graphical matching procedure of data against newly developed pressure and pressure-derivative type-curves, and an automatic parameter estimation method based on a three-dimensional finite volume code (FEHM) coupled with an inverse code (PEST). The type-curve approach treats short and longer intervals as points or lines, depending on distance between injection and monitoring intervals. The type-curve approach accounts indirectly for storage effects in monitoring intervals due to the compressibility of air. The finite volume code allows representing borehole geometry and storage more realistically, and directly, by treating each borehole as a high-permeability cylinder of finite length and radius. Analyses of pressure data from individual monitoring intervals by the two methods, under the assumption that the rock acts as a uniform and isotropic fractured porous continuum, yield comparable results. These results include information about pneumatic connections between the injection and monitoring intervals, corresponding directional air permeabilities, and air-filled porosities. All of these quantities are found to vary considerably from one monitoring interval to another on scales ranging from a few meters to over 20 m. Together with the results of earlier site investigations, our single- and cross-hole test analyses reveal that, at the ALRS, (a) the pneumatic pressure behavior of fractured tuff is amenable to analysis by methods that treat the rock as a continuum on scales ranging from meters to tens of meters; (b) this continuum is representative primarily of interconnected fractures; (c) its pneumatic properties vary strongly with location, direction and scale—in particular, the mean of pneumatic permeabilities increases, and their variance decreases, with scale; (d) this scale effect is most probably due to the presence in the rock of various size fractures that are interconnected on a variety of scales; and (e) given a sufficiently large sample of spatially varying pneumatic rock properties on a given scale of measurement, these properties are amenable to analysis by geostatistical methods, which treat them as correlated random fields defined over a continuum.
Issues associated with the site characterization of fractured rock terrains, the analysis of fluid flow and contaminant transport in such terrains, and the efficient handling of contaminated sites are typically very difficult to resolve. A major source of this difficulty is the complex nature of the subsurface “plumbing systems” of pores and fractures through which flow and transport in rocks take place. There is at present no well-established field methodology to characterize the fluid flow and contaminant transport properties of unsaturated fractured rocks. In order to characterize the ability of such rocks to conduct water, and to transport dissolved or suspended contaminants, one would ideally want to observe these phenomena directly by conducting controlled field hydraulic injection and tracer experiments within the rock. In order to characterize the ability of unsaturated fractured rocks to conduct nonaqueous-phase liquids such as chlorinated solvents, one would ideally want to observe the movement of such liquids under controlled conditions in the field. In practice, there are severe logistical obstacles to the injection of water into unsaturated geologic media, and logistical as well as regulatory obstacles to the injection of nonaqueous liquids. There also are important technical reasons why the injection of liquids, and dissolved or suspended tracers, into fractured rocks may not be the most feasible approach to site characterization when the rock is partially saturated with water. Injecting liquids and dissolved or suspended tracers into an unsaturated rock would cause them to move predominantly downward under the influence of gravity, and would therefore yield at best limited information about the ability of the rock to conduct liquids and chemical constituents in directions other than the vertical. It would further make it difficult to conduct more than a single test at any location because the injection of liquid modifies the ambient saturation of the rock, and the time required to recover ambient conditions may be exceedingly long.
Many of these limitations can be overcome by conducting field tests with gases rather than with liquids, and with gaseous tracers instead of chemicals dissolved in water. Experience with pneumatic injection and gaseous tracer experiments in fractured rocks is limited. Much of this experience has been accumulated in recent years by The University of Arizona at the Apache Leap Research Site (ALRS) near Superior, Arizona, and by the U.S. Geological Survey (USGS) near the ALRS (LeCain, 1995) and at Yucca Mountain in Nevada (LeCain, 1996; LeCain and Walker, 1996). To our knowledge, the earliest pneumatic injection tests were conducted by Boardman and Skrove (1966) to determine fracture permeability following a contained nuclear explosion. Their analysis was based on the steady-state, isothermal, radial flow equation for ideal gases. Other earlier work includes air injection tests conducted by Montazer (1982) in unsaturated fractured metamorphic rocks, and injection methods developed for fractured formations containing natural gas of the kind considered by Mishra et al. (1987).
This paper focuses on single- and cross-hole pneumatic injection tests conducted by our group at the ALRS. The site is situated near Superior in central Arizona. It consists of a cluster of 22 vertical and inclined (at 45°) boreholes that have been completed to a maximum vertical depth of 30 m within a layer of slightly welded unsaturated tuff. The boreholes span a surface area of 55 m by 35 m and a volume of rock on the order of 60,000 m3. The upper 1.8 m of each borehole was cased, and a surface area of 1,500 m2 was covered with a plastic sheet to minimize infiltration and evaporation. Core data and borehole television images are available for many of the boreholes.
Early work related to our area of study at the ALRS is described by Evans (1983), Schrauf and Evans (1984), Huang and Evans (1985), Green and Evans (1987), Rasmussen and Evans (1987, 1989, 1992), Tidwell et al. (1988), Yeh et al. (1988), Weber and Evans (1988), Chuang et al. (1990), Rasmussen et al. (1990, 1996), Evans and Rasmussen (1991), and Bassett et al. (1994). It included drilling 16 boreholes and conducting numerous field and laboratory investigations. Information about the location and geometry of fractures in the study area has been obtained from surface observations, the examination of oriented cores, and borehole televiewer records. Fracture density, defined by Rasmussen et al. (1990) as number of fractures per meter in a 3-m borehole interval, ranges from 0 to a maximum of 4.3 per meter. Though the fractures exhibit a wide range of inclinations and trends, most of them are near vertical, strike north-south, and dip steeply to the east. Surface fracture traces reveal a steeply dipping east-west set. An experimental study of aperture distributions in a large natural fracture at the ALRS was published by Vickers et al. (1992).
Single-hole pneumatic injection tests were conducted in 87 intervals of length 3 m in nine boreholes by Rasmussen et al. (1990, 1993). The tests were conducted by injecting air at a constant mass rate between two inflated packers while monitoring pressure within the injection interval. Pressure was said to have reached stable values within minutes in most test intervals, allowing the calculation of air permeability by means of steady-state formulae. Figure 5b of Rasmussen et al. (1993) suggests a good correlation (r = 0.876) between pneumatic and hydraulic permeabilities at the ALRS. Figure 10-1 shows a scatter plot of pneumatic permeability versus fracture density for 3-m borehole intervals based on the data of Rasmussen et al. (1990). It suggests a lack of correlation between fracture density and air permeability.
The single-hole tests of Rasmussen et al. (1990, 1993) were of relatively short duration and involved relatively long test intervals. Guzman et al. (1994, 1996) and Guzman and Neuman (1996) conducted a much larger number of single-hole pneumatic injection tests of considerably longer duration over shorter intervals in six boreholes. A total of 184 borehole segments were tested by setting the packers 1 m apart as shown in Figure 10-2. Additional tests were conducted in segments of lengths of 0.5, 2.0, and 3.0 m, bringing the total number of tests to over 270. The tests were conducted by maintaining a constant injection rate until
air pressure became relatively stable and remained so for some time. The injection rate was then incremented by a constant value and the procedure repeated. In most tests, three or more such incremental steps were conducted in each borehole segment while recording the air injection rate, pressure, temperature, and relative humidity. For each relatively stable period of injection rate and pressure, air permeability was estimated by treating the rock around each test interval as a uniform, isotropic continuum within which air flows as a single phase under steady state, in a pressure field exhibiting prolate spheroidal symmetry.
The results of these steady-state interpretations of single-hole air injection tests are listed in Guzman et al. (1996). They reveal that:
air permeabilities determined in situ from steady-state single-hole test data are much higher than those determined on core samples of rock matrix in the laboratory, suggesting that the in situ permeabilities represent the properties of fractures at the site;
it is generally not possible to distinguish between the permeabilities of individual fractures and the bulk permeability of the fractured rock in the immediate vicinity of a test interval by means of steady-state single-hole test data;
the time required for pressure in the injection interval to stabilize typically ranges from 30 to 60 min, increases with flow rate, and may at times exceed 24 h, suggesting that steady-state permeability values published in the literature for this and other sites, based on much shorter air injection tests, may not be entirely valid;
steady-state interpretation of single-hole injection tests, based on the assumption of radial flow, corresponds closely to prolate spheroidal in intervals of
length equal to or greater than 0.5 m in boreholes having a radius of 5 cm, as is the case at the ALRS;
pressure in the injection interval typically rises to a peak prior to stabilizing at a constant value, possibly due to a two-phase flow effect whereby water in the rock is displaced by air during injection;
in most test intervals, pneumatic permeabilities show a systematic increase with applied pressure as air apparently displaces water under two-phase flow;
in a few test intervals, intersected by widely open fractures, air permeabilities decrease with applied pressure due to apparent inertial effects;
air permeabilities exhibit a hysteretic variation with applied pressure;
the pressure-dependence of air permeability suggests that it is advisable to conduct single-hole air injection tests at several applied flow rates and/or pressures;
enhanced permeability due to slip flow [the Klinkenberg (1941) effect] appears to be of little relevance to the interpretation of single-hole air injection tests at the ALRS;
local-scale air permeabilities vary by orders of magnitude between test intervals across the site;
spatial variability is much greater than that due to applied pressure and lends itself to meaningful statistical and geostatistical analysis;
air permeabilities are poorly correlated with fracture densities, as is known to be the case for hydraulic conductivities at many water-saturated fractured rock sites worldwide (Neuman, 1987), providing further support for Neuman's conclusion that the permeability of fractured rocks cannot be reliably predicted from information about fracture geometry (density, trace lengths, orientations, apertures and their roughness) but must be determined directly by means of hydraulic and/or pneumatic tests; and
air permeabilities vary systematically with the scale of measurement as represented nominally by the distance between packers in an injection interval.
The work of Guzman et al. (1994, 1996) and Guzman and Neuman (1996) strongly suggests that air injection tests yield properties of the fracture system that are relevant to both unsaturated and saturated conditions. In particular, numerical simulations by these authors show that, whereas the intrinsic permeability one determines from such tests is generally lower than the intrinsic permeability to water of fractures that surround the test interval, it nevertheless approaches the latter as the applied pressure goes up. This is so because, under ambient conditions, capillary forces tend to draw water from fractures into the porous (matrix) blocks of rock between the fractures, thereby leaving the fractures saturated primarily with air. Water saturation in the matrix blocks is therefore typically much higher than that within the fractures, making it relatively difficult for air to flow through such blocks. It follows that, during a pneumatic injection test,
the air moves primarily through fractures (most of which contain relatively little water), and the test therefore yields flow and transport parameters that reflect the intrinsic properties of these largely air-filled fractures.
Core and single-hole measurements, conducted over short segments of a borehole, provide information only about a small volume of rock in the immediate vicinity of each measurement interval. Available data from the ALRS indicate that rock properties, measured on such small scales, vary erratically in space in a manner that renders the rock randomly heterogeneous and pneumatically anisotropic. Our analyses to date (Bassett et al., 1994, 1997; Guzman et al., 1996) suggest that it is possible to interpolate some of the core and single-hole measurements at the ALRS between boreholes by means of geostatistical methods, which view the corresponding variables as correlated random fields. This is especially true about air permeability, porosity, fracture density, water content, and the van Genuchten water retention parameter α, for each of which we possess enough measurements to constitute a workable geostatistical sample. A geostatistical analysis of these site variables has been conducted by Chen et al. (1997) and Illman et al. (1998).
Steady-state analyses of single-hole pneumatic test data yield only air permeability values (Guzman et al., 1996). In this paper, we discuss transient interpretations of the same data, which provide additional information about air-filled porosity, skin factor, and dimensionality of the flow regime.
Single-hole air injection tests provide information only about a small volume of rock in the close vicinity of the injection interval. Fractured rock properties measured on such small scales tend to vary rapidly and erratically in space so as to render the rock strongly and randomly heterogeneous. To determine the properties of the rock on a larger scale, cross-hole interference tests were conducted by Illman et al. (1998; see also Illman, 1999) by injecting air into an isolated interval within one borehole, while monitoring pressure responses in isolated intervals within this and other boreholes. Of the 16 boreholes used for cross-hole testing, 6 were previously subjected to single-hole testing. The results of the single-hole tests (primarily spatial distribution of air permeabilities and local flow geometry) together with other site information (primarily borehole tele-viewer images) served as a guide in designing the cross-hole tests.
A total of 44 cross-hole pneumatic interference tests of various types (constant injection rate, multiple step injection rates, instantaneous injection) have been conducted during 1995-1997 using various configurations of injection and monitoring intervals. The tests were conducted using modular straddle packer systems that were easily adapted to various test configurations and allowed rapid replacement of failed components, modification of the number of packers, and adjustment of distances between them in both the injection and monitoring boreholes. A typical cross-hole test consisted of packer inflation, a period of pressure recovery, air injection, and another period of pressure recovery. Once packer inflation pressure had dissipated in all (monitoring and injection) intervals, air
injection at a constant mass flow rate began. It generally continued for several days, until pressure in most monitoring intervals appeared to have stabilized. In some tests, injection pressure was allowed to dissipate until ambient conditions had been recovered. In other tests, air injection continued at incremental flow rates, each lasting until the corresponding pressure had stabilized, before the system was allowed to recover. In this paper we discuss results from one of these tests, labeled PP4.
TYPE-CURVE INTERPRETATION OF PNEUMATIC INJECTION TESTS
Most type-curve models currently available for the interpretation of single-hole and cross-hole fluid injection (or withdrawal) tests in fractured rocks fall into three broad categories: (1) those that treat the rock as a single porous continuum representing the fracture network; (2) those that treat the rock as two overlapping continua of the dual-porosity type; and (3) hybrid models that embed a major discrete fracture in a porous continuum so as to intersect the injection (or withdrawal) test interval at various angles. The prevailing interpretation of dual continua is that one represents the fracture network and the other embedded blocks of rock matrix. We take the broader view that multiple (including dual) continua may represent fractures on a multiplicity of scales, not necessarily fractures and matrix. When a dominant fracture is present in a type-curve model, it is usually pictured as a high-permeability slab of finite or infinitesimal thickness. To allow developing analytical solutions in support of type-curve models, the continua are taken to be uniform and either isotropic or anisotropic. The test interval is taken to intersect a dominant fracture at its center. Either flow across the walls of such a fracture, or incremental pressure within the fracture, is taken to be uniform in most models. Flow is usually taken to be transient with radial or spherical symmetry, which may transition into near-uniform flow as one approaches a major fracture that intersects the test interval. Some models account for borehole storage and skin effects in the injection (or withdrawal) interval.
In this paper, we interpret transient pressure data from the single-hole air injection tests previously conducted at the ALRS by Guzman et al. (1994, 1996) and Guzman and Neuman (1996) by means of modified single-continuum type-curve models developed for spherical flow by Joseph and Koederitz (1985), for radial flow by Agarwal et al. (1970), for a single horizontal fracture by Gringarten and Ramey (1974), and for a single vertical fracture by Gringarten et al. (1974). Our modifications, detailed by Illman et al. (1998) and Illman (1999), consist of recasting these models in terms of pseudopressure and developing corresponding expressions and type-curves in terms of (pseudo)pressure-derivatives. Pseudopressure is defined as (Al-Hussainy and Ramey, 1966; Raghavan, 1993)
where p is pressure, µ is dynamic viscosity, Z = pV/nRT is compressibility factor, V is volume, n is mass in mols, R is universal gas constant, and T is absolute temperature. We take p0 to represent barometric pressure. Under conditions of testing at the ALRS, µZ, is constant and so
Type-curves of pressure derivative versus the logarithm of time have become popular in recent years because they accentuate phenomena that might otherwise be missed, help diagnose the prevailing flow regime, and aid in constraining the calculation of corresponding flow parameters. The type-curves are derived analytically for single-phase gas flow by linearizing the otherwise nonlinear partial differential equations, which govern such flow in uniform, isotropic porous continua. Included in the type-curves are effects of gas storage in the injection interval (known as borehole storage effect) and reduced or enhanced permeability in the immediate vicinity of this interval (known as positive or negative skin effects). Our type-curve analyses of single-hole pneumatic test data yield information about air permeability, air-filled porosity, skin factor, and dimensionality of the flow regime on a nominal scale of 1 m in the immediate vicinity of each test interval.
For purposes of cross-hole test analysis by means of type-curves, we represent the fractured rock by an infinite three-dimensional uniform, anisotropic continuum as was done by Hsieh and Neuman (1985), and linearize the airflow equations in terms of pressure (Illman et al., 1998) or pseudopressure (Illman, 1999). Hsieh and Neuman treat injection and observation intervals as points or lines; we consider the special case where injection takes place at a point and observation along a line. However, we modify their solution to account for the effects of storage and skin on pressure, and its derivative (not considered by these authors), in the observation interval.
Type-Curve Interpretation of Single-Hole Tests
We have interpreted over 40 sets of 1-m scale single-hole pneumatic injection test data by means of the spherical, radial, vertical, and horizontal fracture flow models described in the previous section (Illman et al., 1998; Illman, 1999). The majority of these data conform to the spherical flow model regardless of number or orientation of fractures in a test interval. We interpret this to mean that flow around most test intervals is controlled by a single continuum, representative of a three-dimensional network of interconnected fractures, rather than by discrete planar features. Only in a small number of test intervals, known to be intersected by widely open fractures, have planar features dominated flow as evidenced by the development of an early half-slope on logarithmic plots of
pressure versus time; unfortunately, the corresponding data do not fully conform to available type-curve models of fracture flow. Some pressure records conform to the radial flow model during early and intermediate times but none do so fully at late time.
Figure 10-3 shows visual fits between incremental squared pressure (circles) and corresponding derivative (triangles) data from test CAC0813 (in a 1-m interval) and type-curves corresponding to a spherical flow model expressed in terms of dimensionless pseudopressure wD and its derivative ∂wD/∂lntD; we recall that pseudopressure, w, is proportional to incremental squared pressure when µZ is constant, as is the case at the ALRS. The data exhibit a good match with type curves that correspond to zero skin (s = 0); indeed, most test data from the ALRS show little evidence of a skin effect. The match yields an air permeability value of 1.56 × 10−15 m2. The early-time data fall on a straight line with unit slope, indicative of compressible air storage within the test interval.
Figure 10-4 shows a similar type-curve match for test CHB0617 (in a 1-m interval). The data exhibit a fair match with type curves that correspond to zero skin for early to intermediate data, yielding an air permeability of 6.01 × 10−17 m2. Late data do not match the type curves due to apparent displacement of water by air, which manifests itself as a gradually decreasing skin effect. Early-time data are strongly affected by compressible air storage within the test interval. A pressure peak, possibly due to two-phase flow, is discernible on the logarithmic scale of Figure 10-4.
Figure 10-5 compares permeabilities obtained by steady-state and spherical transient analyses, showing that they agree reasonably well.
Figure 10-6 shows type-curve matches for single-hole test JGA0605 in a 1-m interval. In this case, the early and intermediate data appear to fit the radial flow model but the late pressure data stabilize, and the late pressure derivative data
drop, in manners characteristic of three-dimensional flow. The same is seen to happen when we consider Figure 10-7 data from single-hole test JJA0616 in a 1-m interval. We take this to indicate that the flow regime evolves from radial to spherical with time.
The 1-m test interval JHB0612 intersects a fracture, which on televiewer (Figure 10-8) appears to be widely open. Figure 10-9 depicts an attempt on our part to match the corresponding incremental squared pressure data to type curves of pseudopressure based on the horizontal fracture flow model described in the previous section. Only the early time data appear to match one of these curves. We suspect that deviation of the late data from the type curves is due to the fact that whereas in reality the flow evolves with time to become three-dimensional, in the model it evolves to become radial. Upon ignoring the late data and considering only the early match, we obtain an air permeability of 1.3 × 10−13 m2. This is about four times the value of 4.8 × 10−14 m2 obtained by Guzman et al. (1996) on the basis of a steady-state analysis of the late data.
An unsuccessful attempt to match the same data with a type-curve corresponding to a vertical fracture flow model, described in the previous section, is depicted in Figure 10-10.
Incremental pressure and, to a much greater extent, derivative data from several single-hole pneumatic injection tests, one of which is illustrated in Figure 10-11, exhibit inflections that are suggestive of dual or multiple continuum behaviors. If so, we ascribe such behavior not to fractures and rock matrix as is common in the literature (Warren and Root, 1963; Odeh, 1965; Gringarten, 1979, 1982), but to fractures associated with two or more distinct length scales. However, these inflections show some correlation with barometric pressure fluctuations,
implying that they might have been caused by the latter rather than by dual or multiple continuum phenomena.
Our type-curve interpretations of single-hole tests appear to be insensitive to how one linearizes the airflow equations; writing these equations in terms of pressure or pseudopressure (incremental pressure squared) leads to very similar results (Illman et al., 1998; Illman, 1999).
Type-Curve Interpretation of Cross-Hole Test PP4
A total of 44 cross-hole pneumatic interference tests of various types (constant injection rate, multiple step injection rates, instantaneous injection) were conducted during the years 1995-1997 using various configurations of injection and monitoring intervals (Illman et al., 1998; Illman, 1999). The tests were conducted using modular straddle packer systems that were easily adapted to various test configurations and allowed rapid replacement of failed components, modification of the number of packers, and adjustment of distances between them in both the injection and monitoring boreholes. A typical cross-hole test consisted of packer inflation, a period of pressure recovery, air injection and another period of pressure recovery. Once packer inflation pressure had dissipated in all (monitoring and injection) intervals, air injection at a constant mass flow rate began. It generally continued for several days, until pressure in most monitoring intervals appeared to have stabilized. In some tests, injection pressure was allowed to
dissipate until ambient conditions had been recovered. In other tests, air injection continued at incremental flow rates, each lasting until the corresponding pressure had stabilized, before the system was allowed to recover.
In this paper we focus on the analysis of test PP4 conducted during the latter phase of our program. This test was selected because it involved:
injection into a high-permeability zone, which helped pressure to propagate rapidly across much of the site;
injection at a relatively high flow rate, which led to unambiguous pressure responses in a relatively large number of monitoring intervals;
the largest number of pressure and temperature monitoring intervals among all tests;
a complete record of relative humidity, battery voltage, atmospheric pressure, packer pressure, and injection pressure;
the lowest number of equipment failures among all tests;
flow conditions (such as injection rate, fluctuations in barometric pressure, battery voltage, and relative humidity) that were better controlled, and more stable, than in all other tests;
minimum boundary effects due to injection into the central part of the tested rock mass;
a relatively long injection period;
rapid recovery; and
a test configuration that allowed direct comparison of test results with those obtained from two line-injection/line-monitoring tests, and a point-injection/fine-monitoring test, at the same location. Stable flow rate and barometric pressure made type-curve analysis of test PP4 results relatively straightforward.
Test PP4 was conducted by injecting air at a rate of 50 slpm into a 2-m interval located 15-17 m below the lower lip of casing in borehole Y2, as indicated by a large solid circle in Figure 10-12. The figure also shows a system of Cartesian coordinates x, y, z with origin at the center of the injection interval, which we use to identify the placement of monitoring intervals relative to this center. Responses were monitored in 13 relatively short intervals (0.5-2 m) whose centers are indicated in the figure by small white circles, and 24 relatively long intervals (4-42.6 m) whose centers are indicated by small solid circles, located in 16 boreholes. Several of the short monitoring intervals were designed to intersect a high permeability region that extends across much of the site at a depth comparable to that of the injection interval.
Type-curve interpretation of pressure data from cross-hole test PP4 included 31 intervals; pressure data from 5 intervals were not amenable to type-curve interpretation and have therefore been excluded. A special set of type-curves was developed for each pressure monitoring interval by treating the medium as if it was pneumatically isotropic. Indeed, our type-curve analysis additionally treats
the rock as if it was pneumatically uniform. However, since the analyses of pressure data from different monitoring intervals yield different values of pneumatic parameters, our analysis ultimately yields information about the spatial and directional dependence of these parameters.
Figure 10-13, Figure 10-14, Figure 10-15 through Figure 10-16 show how we matched typical records of pressure buildup, and pressure derivatives, from cross-hole injection test PP4 to corresponding type-curves on logarithmic paper. Most of the matches are excellent to good, but a few are poor. Fluctuations in barometric pressure affect some
of the late pressure buildup data and cause their derivatives to fluctuate, at times wildly.
Our finding that most pressure buildup data match the type-curves well is a clear indication that the majority of cross-hole test PP4 results are amenable to interpretation by means of a continuum model, which treats the rock as being pneumatically uniform and isotropic while describing airflow by means of linearized, pressure-based equations. The fact that some of our data do not fit this model shows that the latter does not provide a complete description of pneumatic pressure behavior at the site. That the site is not pneumatically uniform or isotropic on the scale of cross-hole test PP4 is made evident by pneumatic parameters derived from our type-curve matches. Values of pneumatic permeability and air-filled porosity derived from these matches represent bulk properties of the rock between the corresponding monitoring interval and the injection interval. The permeabilities additionally represent directional values along lines that connect the centers of these intervals. The directional permeabilities range from 1.1 × 10−16m2 to 4.6 × 10−13m2 with a mean of −13.5 for log10-based k, while a corresponding (antilog) value is 2.9 × 10−14m2. The corresponding variance and coefficient of variation (CV) are 5.3 × 10−1 and −5.4 × 10−1, respectively. Air-filled porosities range from 1.7 × 10−5 to 2.2 × 10−1 with a geometric mean of 3.5 × 10−3, while their variance and coefficient of variation are 8.0 × 10−1 and −3.6 × 10−1, respectively. Permeabilities derived from cross-hole tests have a much higher mean, and lower variance, than those from the smaller-scale single-hole tests.
NUMERICAL INVERSE INTERPRETATION OF PNEUMATIC INJECTION TESTS
We have also interpreted data from several single-hole and cross-hole tests at the ALRS by means of a three-dimensional finite-volume numerical simulator, FEHM (Zyvoloski et al., 1988, 1996, 1997), coupled to a numerical inverse code, PEST (Doherty et al., 1994), based on the assumption of single-phase airflow through a uniform, isotropic porous continuum. Our numerical model accounts directly for the ability of all boreholes, and packed-off borehole intervals, to store and conduct air through the system. The model does so by treating these as high-permeability and high-porosity cylinders of finite length and radius. It solves the airflow equations in nonlinear form, and is able to account for atmospheric pressure fluctuations at the soil surface. Our numerical model thus accounts more fully and accurately for nonlinear pressure propagation and storage through both the rock and the boreholes than do our type curves, which rely on linearized airflow equations and ignore the effect of boreholes (other than the injection interval) on pressure distribution through the system. Both allow one (in principle) to interpret multiple injection-step and recovery data simultaneously. The
numerical inverse model yields information about air permeability, air-filled porosity, and effective porosity of the injection interval.
There is little information in the literature about the effect that open borehole intervals may have on pressure propagation and response during interference tests. Paillet (1993) noted that the drilling of an additional observation borehole had an effect on drawdowns created by an aquifer test. We likewise found through numerical simulations (Illman et al., 1998) that the presence of open borehole intervals has a considerable impact on pressure propagation through the site, and on pressure responses within monitoring borehole intervals during cross-hole air injection tests.
As we consider only single-phase airflow, the saturation of air and associated pneumatic properties of the rock remain constant during each simulation. The only initial condition we need to specify is air pressure, which we take to be the average barometric pressure of 0.1 MPa. The side and bottom boundaries of the flow model are impermeable to airflow. Our results suggest that these boundaries have been placed sufficiently far from injection intervals to have virtually no effect on simulated single-hole tests. The top boundary coincides with the soil surface and is maintained at a constant and uniform barometric pressure of 0.1 MPa. Though barometric pressure fluctuated during each single-hole test, these fluctuations were small and are ignored in our analysis.
The air permeability k and air-filled porosity are taken to be uniform within the computational region. In our inverse analyses, these two parameters are adjusted simultaneously with the effective porosity of the injection interval. The latter parameter is allowed to take on values in excess of 1 as a way to account for effective borehole volumes larger than those originally built into the computational grid.
We used the same computational grid for the analysis of single-hole and cross-hole tests. The grid measures 63 m in the x direction, 54 m in the y direction, and 45 m in the z direction, encompassing a rock volume of 153,090 m3 (Figure 10-17). The computational grid is illustrated for the case of single-hole tests, during which injection takes place into various packed-off intervals along borehole Y2, by means of two-dimensional images in Figure 10-18 and Figure 10-19. Boreholes are treated as porous media having much higher permeability and porosity than the surrounding rock. Figure 10-18 shows three views of the grid perpendicular to the x-y, x-z, and y-z planes. As the grid in the vicinity of bore-holes is relatively fine, the corresponding areas appear dark in the figures. Figure 10-19 shows four cross-sectional views of the grid along vertical planes that contain selected boreholes. Since the grid is three-dimensional, its intersections with these planes do not necessarily occur along nodal points (i.e., what may appear as nodes in the figure need not be such). The grid includes 39,264 nodes, 228,035 tetrahedral elements, and is divided into three parts: a regular grid at the center of the modeled area, which has a node spacing of 1 m; a surrounding regular grid having a node spacing of 3 m; and a much finer and more complex
unstructured grid surrounding each borehole. The three-dimensional grid represents quite accurately the geometry, flow properties, and storage capabilities of vertical and inclined boreholes at the site; is capable of resolving medium heterogeneity on a support scale of 1 m; is able to represent, with a high degree of resolution, steep gradients around the injection test interval, as well as pressure interference between boreholes, no matter how closely spaced; and assures smooth transition between fine borehole grids having radial structures and surrounding coarser grids having regular structures.
Inverse Analysis of Single-Hole Tests
A steady-state interpretation of pressure buildup data recorded during the first injection step (labeled A) of single-hole test JG0921 by means of an analytical formula gave a pneumatic permeability of 2.8 × 10−14 m2 (Guzman et al., 1996), and a transient type-curve analysis based on the spherical flow model gave 2.6 × 10−14 m2 (Illman et al., 1998); neither of these two analyses was able to provide air-filled porosity estimates. When open borehole intervals (including that used for injection) are not considered in the simulation, our numerical inverse
model yields a match that is less than satisfactory ( Figure 10-20), with air permeability k = 2.3 × 10−14 ± 2.6 × 10−16 m2 and air-filled porosity = 4.5 × 10−1 ± 1.9 × 10−3, where the ± range represents 95% confidence intervals identified by PEST. The porosity estimate is much too high for fractures, suggesting that the corresponding confidence interval computed by PEST is overly optimistic. When only steady-state pressure data are included in the inverse analysis, the match at early time is poor, yielding k = 2.8 × 10−14 m2 and = 4.6 × 10−3, respectively. Here the estimate of porosity is based entirely on our specification of the time at which steady state commences (approximately 0.008 days, as indicated by open circles in Figure 10-20), which renders model sensitivity to so low as to preclude it from computing confidence intervals for either parameter. When the effect of all open borehole intervals is included and the effective porosity of the injection interval is allowed to vary simultaneously with k and , the match improves, yielding k = 2.2 × 10−14 ± 4.4 × 10−16 m2, = 6.7 × 10−3± 4.7 × 10−3, and = 7.0 × 10−1 ± 6.7 × 10−2.The relatively large confidence interval associated with (of the same order as its estimate) reflects the fact that transient data are dominated by borehole storage, which is the reason type-curve analysis has been unable to identify this parameter (Illman et al., 1998).
Air storage in the injection interval has theoretically no effect on early recovery data, which should therefore be ideal for the estimation of air-filled porosity.
We in fact find that such storage effects are most pronounced during the first step of a test, and less so during subsequent steps. This is seen in Figure 10-21, where pressure during each step and recovery is plotted relative to pressure established during the previous step, versus time measured relative to the end of the previous step. The figure demonstrates that pressure data from the first injection step, labeled A, exhibit the most pronounced one-to-one slope at early time, which is indicative of borehole storage; there is no discernible storage effect during the second step, labeled B, or the recovery phase, labeled R. We therefore expect a simultaneous analysis of pressure data from the entire test to yield a more reliable estimate of parameters, especially air-filled porosity, than is possible based only on data from the first step.
A reasonably good fit of our model (which now accounts for all open borehole intervals) to the entire two-step pressure record, including recovery data, is shown in Figure 10-22. The corresponding parameter estimates are k = 2.4 × 10−14 ± 7.1 × 10−16 m2, = 1.4 × 10−2 ± 1.7 × 10−3, and = 8.0 × 10−1 ± 4.6 × 10−2. We consider these values reasonable and reliable.
It is of interest to note that a 2-m borehole interval used for injection during cross-hole test PP4 (discussed below) lay 0.1 m above that of the 1-m injection interval during single-hole test JG0921, so that the two overlapped. Injection rate during the cross-hole test (1 × 10−3 kg/s or 5 × 104 cm3/s) was over 100 times higher than that during JG0921A. Pressure data recorded in the injection interval
during the cross-hole test varied little with time and were therefore not suitable for a reliable estimation of air-filled porosity. They were, however, suitable for the estimation of air permeability, giving a value of k = 2.2 × 10−14 ± 2.7 × 10−16 m2, which is very close to those we derived from the single-hole test data.
Steady-state analysis of pressure buildup data from the first injection step (A) of single-hole test JGC0609 gave a pneumatic permeability of k = 2.0 × 10−15 m2 (Guzman et al., 1996), and transient type-curve analysis with a spherical flow model yielded k = 2.9 × 10−15 m2 (Illman et al., 1998). In the absence of open borehole intervals, the inverse model yields a poor fit with k = 1.8 × 10−15 ± 3.9 × 10−15 m2 and = 5.0 × 10−1 ± 4.2 × 10−2. Upon including the injection interval, the fit improves dramatically to yield k = 1.6 × 10−15 ± 2.6 × 10−17 m2, = 4.8 × 10−3 ± 9.4 × 10−3, and = 1.3 ± 2.6 × 10−2. Incorporating the effects of all open boreholes results in an equally good fit with k = 1.6 × 10−15 ± 1.3 × 10−17 m2, = 5.5 × 10−3 ± 4.7 × 10−3, and = 1.3 ± 1.7 × 10−2 (Figure 10-23). Despite such good fits, the above porosity estimates are evidently unreliable due to the dominance of borehole storage effects during the transient period of the test. A bore-hole porosity in excess of 1 is plausible, implying that the effective volume VS of the injection interval exceeds its nominal volume Vw.
Figure 10-24 depicts relative pressure versus relative time for injection steps 1-4 (labeled A-D, respectively) and recovery (labeled R). Here again we see that
only data corresponding to step A exhibit a pronounced one-to-one slope at early time, while all other data appear to be free of borehole storage influence. We therefore expect a simultaneous analysis of pressure data from the entire test to yield a more reliable estimate of parameters, especially air-filled porosity, than is possible based only on data from the first step.
A fit of our model to the entire four-step pressure record, including recovery data, yields a good match (Figure 10-25) with k = 1.7 × 10−15 ± 4.1 × 10−17 m2, = 3.6 × 10−3 ± 2.8 × 10−4, and = 1.5 ± 6.3 × 10−2. The model appears sensitive to all three parameters whose estimates seem reasonable to us: both k and are smaller, by about one order of magnitude, than they were in the case of single-hole test JG0921.
Inverse Analysis of Cross-Hole Test PP4
In the inverse analysis we describe here, pressure data from each monitoring interval are considered separately while pneumatic permeability and air-filled porosity are treated as if they were uniform across the site, in a manner similar to our type-curve analyses. Hence any major difference between results we obtain
by these two methods of analysis can be attributed to differences between the ways they handle nonlinearity of the governing airflow equations (without or with linearization, numerically or analytically), boundary conditions (at finite or infinite distances), and boreholes (directly or indirectly, completely or incompletely).
Matches between computed and recorded pressures are shown in Figure 10-26. Some of these matches are very poor due to barometric pressure effects, some are of intermediate quality, and some are good. Corresponding estimates of air permeability range from 3.8 × 10−15 to 3.0 × 10−12 m2 with a mean of 2.8 × 10−13 m2, variance of 4.9 × 10−25, and coefficient of variation equal to 2.5. The mean, variance, and coefficient of variation of log-transformed permeability are −13.5 (corresponding to 2.9 × 10−14 m2), 6.9 × 10−1, and 6.0 × 10−2, respectively. The mean, variance, and coefficient of variation of corresponding type-curve results are −13.5 (corresponding to 3.5 × 10−14 m2), 3.2 × 10−1, and −2.4 × 10−2, respectively. The type-curve analysis excluded intervals X3 and Y2M but included interval Y1U, which was not considered in the inverse analysis. The two sets of air permeability values are compared in Figure 10-27.
Air-filled porosity estimated by our inverse model on the basis of pressure data from injection interval Y2M during cross-hole test PP4 is highly uncertain, due to a very rapid pressure buildup in this interval. The large air-filled porosity
estimates (0.5) obtained on the basis of pressure data from monitoring intervals X3, Z2L, Z2B, and Z3B are equal to their specified upper bound; we consider them highly unlikely due to poor fits between calculated and observed pressure responses in these intervals ( Figure 10-26), which appear to be pneumatically well connected to the atmosphere and therefore strongly influenced by barometric pressure fluctuations. Upon excluding air-filled porosity values obtained from these five borehole intervals, the range of this parameter narrows down to 5.1 × 10−3−1.0 × 10−1 with arithmetic mean, variance, and coefficient of variation equal to 3.6 × 10−2, 7.1 × 10−4, and 7.3 × 10−1, respectively. The corresponding mean, variance, and coefficient of variation of log-transformed air-filled porosities are −1.6 (corresponding to 2.7 × 10−2), 1.4 × 10−1, and −2.3 × 10−1. Log-transformed
air-filled porosities from type-curve analyses have mean −2.2 (corresponding to 6.6 × 10−3), variance 3.0 × 10−1, and coefficient of variation −4.0 × 10−1. The two sets of air-filled porosities, compared in Figure 10-28, are seen to agree poorly; values obtained by the inverse method are consistently larger than those from type-curve analyses.
The following are major lessons we have learned from our Apache Leap Research Site studies:
major source of this difficulty is the complex nature of the subsurface “plumbing systems” of pores and fractures through which flow and transport in rocks take place. There is at present no well-established field methodology to characterize the fluid flow and contaminant transport properties of unsaturated fractured rocks.
In order to characterize the ability of unsaturated fractured rocks to conduct water, and to transport dissolved or suspended contaminants, one would ideally want to observe these phenomena directly by conducting controlled field hydraulic injection and tracer experiments within the rock. In order to characterize the ability of unsaturated fractured rocks to conduct nonaqueous phase liquids such as chlorinated solvents, one would ideally want to observe the movement of such liquids under controlled conditions in the field. In practice, there are severe logistical obstacles to the injection of water into unsaturated geologic media, and logistical as well as regulatory obstacles to the injection of nonaqueous liquids. There also are important technical reasons why the injection of liquids, and dissolved or suspended tracers, into fractured rocks may not be the most feasible approach to site characterization when the rock is partially saturated with water. Many of these limitations can be overcome by conducting field tests with gases rather than with liquids, and with gaseous tracers instead of chemicals dissolved in water.
The University of Arizona has successfully conducted numerous single-hole and cross-hole pneumatic injection tests in unsaturated fractured tuffs at the ALRS near Superior, Arizona, under the auspices of the U.S. Nuclear Regulatory Commission (NRC). These tests were part of confirmatory research in support of NRC's role as the licensing agency for a potential high-level nuclear waste repository in unsaturated fractured tuffs at Yucca Mountain. However, unsaturated fractured porous rocks similar to tuffs are found at many locations, including some low-level radioactive waste disposal sites, nuclear decommissioning facilities, and sites contaminated with radioactive as well as other hazardous materials. The test methodologies we have developed, and the understanding we have gained concerning the pneumatic behavior and properties of tuffs at the ALRS, are directly relevant to such facilities and sites.
We found it possible to interpret both single-hole and cross-hole pneumatic injection tests at the ALRS by means of analytically derived type-curves and a numerical inverse model, which account only for single-phase airflow through the rock while treating water as if it was immobile. Our type-curves are based on linearized versions of the nonlinear partial differential equations that govern single-phase airflow in uniform, isotropic porous continua under three regimes: three-dimensional flow with spherical symmetry, two-dimensional flow with radial symmetry, and flow in a continuum with an embedded high-permeability planar feature (a major fracture). The particular method of linearization appears to have only a minor impact on the results of our type-curve analyses. Included in our type-curves are effects of compressible air storage and skin in the injection interval during single-hole tests, and in monitoring intervals during
cross-hole tests. Our analytical tools include type-curves of pressure derivative versus the logarithm of time, which accentuate phenomena that might otherwise be missed, help diagnose the prevailing flow regime, and aid in constraining the calculation of corresponding flow parameters. Our numerical inverse model does not require linearizing the governing airflow equations and represents pneumatic test conditions at the site more realistically than do our type-curves.
Despite these differences between them, type-curve and inverse methods yield comparable values of air permeability for both single-hole and cross-hole tests. On the other hand, the inverse method yields consistently higher air-filled porosities than do type-curve analyses for cross-hole tests. A key to obtaining reliable air-filled porosities from single-hole pneumatic injection tests is to include multiple step and/or recovery data in the analysis. This is so because storage of air in the injection interval dominates pressure transients during the first step of each test, but appears to do so less in subsequent steps, and has relatively small impact on pressure recovery data.
At the ALRS, air permeabilities obtained from steady state and transient type-curve interpretations of single-hole pneumatic injection tests, conducted in borehole intervals of 1 m, agree closely with each other but correlate poorly with fracture density data. Airflow around the vast majority of these relatively short test intervals appears to be three-dimensional; borehole storage due to air compressibility is pronounced at early time; and skin effects are minimal.
During a pneumatic injection test, air moves primarily through fractures, most of which contain relatively little water, and the test therefore yields permeabilities and porosities that reflect closely the intrinsic properties of the surrounding fractures. This is so because capillary forces tend to draw water from fractures into porous (matrix) blocks of rock, leaving the fractures saturated primarily with air, and making it difficult for air to flow through matrix blocks. Since the fractures contain some residual water, the corresponding pneumatic permeabilities and air-filled porosities tend to be somewhat lower than their intrinsic counterparts. The former nevertheless approach the latter as the rate of injection goes up. This is due to displacement of water by air, which, under a constant rate of injection, appears to manifest itself in a rapid increase in pressure within the injection interval, followed by a gradual decrease. Two-phase flow of water and air additionally causes air permeabilities from single-hole pneumatic injection tests to exhibit a hysteretic variation with applied pressure.
In most single-hole pneumatic injection tests at the ALRS, pneumatic permeabilities increase systematically with applied pressure as air appears to displace water under two-phase flow. In a few single-hole tests, where the injection intervals are intersected by widely open fractures, air permeabilities decrease with applied pressure due to inertial effects. This pressure-dependence of air permeability suggests that it is advisable to conduct single-hole air injection tests at several applied flow rates and/or pressures. Pneumatic parameters derived from pressure data recorded in monitoring intervals during cross-hole tests appear
to be much less sensitive to the rate of injection, suggesting that two-phase flow and inertial phenomena decay rapidly with distance from the injection interval. Enhanced permeability due to slip flow (the Klinkenberg effect) appears to be of little relevance to the interpretation of single-hole or cross-hole air injection tests at the ALRS.
Flow in the vicinity of most 1-m single-hole pneumatic test intervals at the ALRS appears to be three-dimensional regardless of the number or orientation of fractures in the surrounding rock. We interpret this to mean that such flow is controlled by a single continuum, representative of a three-dimensional network of interconnected fractures, rather than by discrete planar features. Indeed, most single-hole and cross-hole pneumatic test data at the ALRS have proven amenable to analysis by means of a single fracture-dominated continuum representation of the fractured porous tuff at the site. Only in a small number of single-hole test intervals, known to be intersected by widely open fractures, have such features dominated flow as evidenced by the development of an early half-slope on logarithmic plots of pressure versus time; unfortunately, the corresponding data do not fully conform to available type-curve models of fracture flow. Some pressure records conform to the radial flow model during early and intermediate times, but none do so fully at late time.
It is generally not possible to distinguish between the permeabilities of individual fractures and the bulk permeability of the fractured rock in the immediate vicinity of a test interval by means of pneumatic injection tests. Hence there is little justification for attempting to model flow through individual fractures at the site. The explicit modeling of discrete features appears to be justified only when one can distinguish clearly between layers, faults, fracture zones, or major individual fractures on scales not much smaller than the domain of interest.
Air permeabilities obtained from single-hole tests are poorly correlated with fracture densities, as is known to be the case for hydraulic conductivities at many water-saturated fractured rock sites worldwide (Neuman, 1987). This provides further support for Neuman's conclusion that the permeability of fractured rocks cannot be reliably predicted from information about fracture geometry (density, trace lengths, orientations, apertures and their roughness) but must be determined directly by means of hydraulic and/or pneumatic tests.
Core and single-hole measurements, conducted over short segments of a borehole, provide information about only a small volume of rock in the immediate vicinity of each measurement interval. Available data from the ALRS indicate that rock properties, measured on such small scales, vary erratically in space in a manner that renders the rock randomly heterogeneous and pneumatically anisotropic. Local-scale air permeabilities from single-hole tests vary by orders of magnitude between test intervals across the site; their spatial variability is much more pronounced than their dependence on applied pressure. We found it possible to interpolate some of the core and single-hole measurements at the ALRS between boreholes by means of geostatistical methods, which view the corresponding
variables as correlated random fields defined over a continuum. This was especially true about air permeability, porosity, fracture density, water content, and the van Genuchten water retention parameter a, for each of which we possess enough measurements to constitute a workable geostatistical sample. To differentiate between geostatistical models that appear to fit these data equally well, we used formal model discrimination criteria based on maximum likelihood and the principle of parsimony (which places a premium on simplicity; Illman et al., 1998). Standard geostatistical analysis provides best (minimum variance) linear unbiased estimates of how each such quantity varies in three-dimensional space, together with information about the quality of these estimates. Our finding supports the application of continuum flow and transport theories and models to unsaturated fractured porous tuffs at the ALRS on scales of 1 m or more.
Cross-hole pneumatic injection test data from individual monitoring intervals at the ALRS have proven amenable to analysis by type-curve and numerical inverse models that treat the rock as a uniform and isotropic fractured porous continuum. Analyses of pressure data from individual monitoring intervals by the two methods provided information about pneumatic connections between injection and monitoring intervals, corresponding directional air permeabilities, and air-filled porosities. All of these quantities were found to vary considerably from one monitoring interval to another in a given cross-hole test on scales ranging from a few to over 20 meters. Thus, even though the analyses treat the rock as if it was pneumatically uniform and isotropic, they ultimately yield information about the spatial and directional dependence of pneumatic connectivity, permeability, and porosity across the site.
Some single-hole pressure records reveal an inflection that is characteristic of dual-continuum behavior. It is possible that this inflection is caused by barometric pressure fluctuations and not by a dual-continuum phenomenon. The prevailing interpretation of dual continua is that one represents the fracture network and the other embedded blocks of rock matrix. We take the broader view that multiple (including dual) continua may represent fractures on a multiplicity of scales, not necessarily fractures and matrix.
The pneumatic permeabilities of unsaturated fractured tuffs at the ALRS vary strongly with location, direction, and scale. In particular, the mean of pneumatic permeabilities increases, and their variance decreases, with distance between packers in a single-hole injection test, and with distance between injection and monitoring intervals in cross-hole injection tests. This scale effect is most probably due to the presence in the rock of various size fractures that are interconnected on a variety of scales.
This work was supported by the U.S. Nuclear Regulatory Commission under contracts NRC-04-95-038 and NRC-04-97-056. We wish to acknowledge with
gratitude the support, advice, and encouragement of our NRC Project Manager, Thomas J. Nicholson. Walter Illman was supported in part by a National Science Foundation Graduate Traineeship during 1994-1995, a University of Arizona Graduate College Fellowship during 1997-1998, the Horton Doctoral Research Grant from the American Geophysical Union during 1997-1998, and the John and Margaret Harshbarger Doctoral Fellowship from the Department of Hydrology and Water Resources at The University of Arizona during 1998-1999. Velimir (Monty) Vesselinov conducted part of his simulation and inverse modeling work during a summer internship with the Geoanalysis Group at Los Alamos National Laboratory in 1997. We are grateful to Dr. George A. Zyvoloski for his help in the implementation of FEHM, and to Dr. Carl W. Gable for his assistance in the use of the X3D code to generate the corresponding computational grid. All pneumatic cross-hole tests at the ALRS were conducted by Walter Illman with the help of Dick Thompson, our talented and dedicated technician. Type-curve development and analyses were performed by Walter Illman, geostatistical analyses by Guoliang Chen and Velimir Vesselinov, and the development and implementation of our inverse model by Velimir Vesselinov.
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