LABORATORY MEASUREMENT OF PERMEABILITY UPSCALING:- R FOR THE TOPOPAH SPRING MEMBER OF THE PAINTBRUSH TUFF

Transcription

1 c J LABORATORY MEASUREMENT OF PERMEABILITY UPSCALING:- R FOR THE TOPOPAH SPRING MEMBER OF THE PAINTBRUSH TUFF Vincent C. Tidwell Sandia National Laboratories Geohydrology Department, MS 1324 Albuquerque, New Mexico WEC {ql &C John L. Wilson New Mexico Tech Dept. of Earth and Environmental Sciences Socorro, New Mexico Introduction Parameterization of predictive models is often complicated by our inability to make measurements at the same scale at which we wish to perform the analysis. This disparity in scales necessitates the use of some averaging or upscaling model to compute the desired effective media properties. In efforts to better model permeability upscaling, laboratory experiments have been conducted on a series of rock samples with different genetic origins. These experiments involve the collection of exhaustive permeability data sets at different sample sample volumes) using a specially designed minipermeameter test system. Here we present a synopsis of such a data set collected from a block of volcanic tuff. Materials and Methods Permeability data were acquired from a 8 1 by 74 by 63 cm block of moderately welded, devitrified ash flow tuff. The tuff sample is from the Miocene aged, Topopah Spring Member of the Paintbrush Tuff [Montazer and Wilson, The sample originated as a boulder collected from Fran Ridge on the Nevada Test Site, located approximately 0 km northwest of Las Vegas, Nevada. Preparation of the sample involved shipment to a quarry where it was shaped into a block with a diamond-impregnated wire line saw. The rock sample is characterized by an aphanitic fabric with conspicuous pumice and lithic phenocrysts. The pumice phenocrysts have an average diameter of 1-2 cm and comprise approximately 30% of the rock sample. However, each face is populated with a number of larger phenocrysts (>5 cm dia.). Lithic fragments account for another 2-3% of the rock; however, their size rarely exceeds 1 cm. Permeability data were acquired with an automated minipermeameter that operates by compressing a tip seal against a flat, fresh rock surface while injecting gas at a constant pressure. Using information on the seal geometry, gas flow rate, gas injection pressure, and barometric pressure, the permeability is calculated using a modified form of Darcy's Law [Goggin et al., Automation of this process is achieved by coupling the minipermeameter with an x-y positioner and computer control system. The minipermeameter consists of four electronic mass-flow meters (050,O-500,O-2000, and 0-20,000 cmvmin. [at standard conditions]), a pressure transducer (00 kpa gauge), a barometer, and a gas temperature sensor that are all connected to a regulated source of compressed nitrogen. Measurements are made according to a user specified sampling grid programmed into the x-y positioner. Along with locating the tip seal for sampling, the positioner also compresses the tip s a n ~ ais a multiprogram laboratory operated by Sandra Corporation, a Lockheed Martin Company, for the United States Department of Energy under contract DE-ACa4-94AL85m- D 0 X (cm) Ln(k) 20 Figure 1. Natural log permeability field the 1.27 cm tip seal on the tuff sample. mts is 30 OS

2 DISCLAIMER This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency thereof. nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, mornmendation. or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof.

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4 seal squarely against the rock surface with a consistent and constant force. A full description and analysis of the experimental system is given by Tidwell and Wilson [ Gas is directed into the rock sample via the tip seal. Measurements are made at different sample supports (i.e., sample volumes) subject to consistent boundary conditions and flow geometry by simply varying the radius of the tip seal. Tip seals used in this study have inner radii (ri) of 0.15, 0.31, 0.63, 1.27, and 7.62 cm and an outer radii measuring twice the inner. Assuming a hemispherical flow geometry, the sample support varies as r? and hence increases by a power of 8 for each doubling of ri. Permeability data were acquired from all six faces of the tuff block. Measurements were made according to a uniform grid with each of the four smaller tip seals. A 36 by 36 node grid on 0.85 cm centers was employed in the 1296 measurements by each tip seal). The sampling grid was centered on the block to avoid interference of the block margins with the measurements. In addition, a single measurement, designed to integrate over most of the sampling domain, was made with the largest tip seal (7.62 cm). Results Although all six rock faces have been sampled and analyzed, we limit our discussion to a single rock face that we term Face 1. Each of the rock faces are noted to exhibit very similar statistical characteristics (distribution and spatial features) and permeability upscaling (i.e., measured trends between the summary statistics and associated sample support). Differences between rock faces are limited to the absolute values of the various statistics and the rate at which they upscale. The natural log permeability field ln(k) measured with the 1.27 cm ri tip seal on Face 1 of the tuff block is shown in Figure 1. Comparisons drawn between the permeability field and rock face reveal that the high permeability zones are associated with the large pumice phenocrysts that are dispersed in a matrix of significantlylower permeability. Measurements made on the same rock face but with different sized tip seals (not shown) meticulously reproduce the same spatial features. The only significant difference is a distinct smoothing of the permeability field accompanying increasing tip seal size. This smoothing occurs because larger tip seals integrate over more heterogeneity and thus average out the short-scale variability. Each of the other rock faces show similar structural features; that is, high permeability pumice distributed in an otherwise low permeability matrix. The cumulative distribution functions (CDFs) for the permeability data measured with each of the four smaller tip seals are given in Figure 2. The CDFs span a range of almost five orders of magnitude in permeability and exhibit a correspondingly high variance. The CDFs are also seen to be non-guassian, displaying a strong positive skew. Several distinct trends with changing sample support are evident. Both the ln(k) sample mean (p= , , , and where k is in units of m*) and variance (02=4.06, 3.02,1.81, 1.09) are seen to decrease with increasing sample support..,...,...,...,*..,...,..., 99.99(.. To investigate the spatial continuity of the permeability data, two-dimensional semivariograms were calculated using Fourier analysis for each of the data sets acquired from Face 1. The semivariograms indicate that the permeability is isotropically distributed with relatively poor spatial correlation. Transects taken through the two-dimensional semivariograms (oriented along the X and Y axes shown in Figure 1) are presented in Figure 3 and Figure 2. CDFs measured with the four smaller tip seals on the tuff block.

5 fitted with a spherical semivariogram model. Several distinct trends are evident among the semivariograms. First, the magnitude of the semivariogram (i.e. variance) decreases with increasing sample support, while the general shape of the semivariogram remains consistent. Second, the nugget decreases with increasing sample support reflecting the increased overlap between neighboring measurements. Finally, the fitted semivariogram range h increases linearly (h= 3.5, 3.9,4.7, and 6.0 cm) with increasing tip seal size (i.e., 5 is proportional to the size of the tip seal with which it was measured [Clark, 19771). s, E.-$ 3 $ 2-5 (I) Separation (cm) 15 Figure 3. Semivariogram transects measured on the tuff block (filled symbols for the X-axis, open for the Y-axis, see Figure 1) with the four smaller tip seals. The solid lines are the fitted spherical semivariogram model. Discussion Inspection of the detailed permeability data measured with different-sized tip seals provides insight into some of the important processes governing permeability upscaling for this sample. Consider the sample mean shown in Figure 4. Plotted is the geometric mean (E[ln(k)]) verses the characteristic measurement length, taken for comparison purposes as equal to the outer diameter of the tip seal. The mean is seen to be a decreasing function of tip seal size, decreasing sharply at first and then to a much lesser extent at larger characteristic measurement lengths. A similar trend is exhibited by the other five block faces of the tuff sample. The decreasing trend is believed to result from the strongly skewed nature of the ln(k) distribution coupled with the spatially disconnected nature of the pumice phenocrysts (evident in Figure 1). As the tip seal size increases with respect to the size of the pumice phenocrysts, fewer opportunities are available for gas flow to short-circuit the system through the pumice. This causes more of the high permeability pumice to be averaged with the low permeability groundmass forcing the mean permeability to shift toward the median of the distribution. This interpretation is further supported by the shape of the mean upscaling trend (Figure 4). Specifically, a notable break in slope of the mean trend occurs at about 3-6 cm, which is consistent with the magnitude of the correlation length scale of the tuff sample. References Clark, I., Regularization of a semi-variogram, Computers and Geosciences, 3, , Goggin, D. J., R. L. Thrasher, and L. W. Lake, A theoretical and experimental analysis of minipermeameter response including gas slippage and high velocity flow effects, In Situ, 12(1-2), , Montazer, P. and W.E. Wilson, Conceptual Hydrologic Model of Flow in the Unsaturated Zone, Yucca Mountain, Nevada, USGS Water-Resources Investigation Report , Tidwell, V.C. and J.L. Wilson, Laboratory method for investigating permeability upscaling, Water Resour. Res., 33(7), , ,,., :. *....5 * I....,....,....,...., , I... CharacteristicMeasurement Length (cm) 30 :.35 Figure 4. Mean upscaling measured on tuff sample. First four points are sample means of 1296 points while the last data point (at cm) is associated with the single measurement made with the 7.62 cm tip.