Upscaling experiments conducted on a block of volcanic tuff: Results for a bimodal permeability distribution

Tidwell, Vincent Carroll; Wilson, John L.

doi:10.1029/1999wr900161

Cited by 38 publications

(46 citation statements)

References 28 publications

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“…2 of Tidwell and Wilson, 1999). This was deemed by them to be consistent with the geologic structure of the tuff sample within which regions of high (associated with pumice fragments) and low (corresponding to solid matrix) permeability could be visually identified.…”

Section: Previous Analyses Of Experimental Datamentioning

confidence: 83%

“…Measurements were conducted at intervals of = 0.85 cm on a grid of 36 × 36 points along each face using four tip-seal sizes having inner radii r i = 0.15, 0.31, 0.63, 1.27 cm and outer radii 2 r i . As the precise nature and size of the support volume associated with each measurement is the subject of debate (Goggin et al, 1988;Molz et al, 2003;Tartakovsky et al, 2000;Neuman and Di Federico, 2003), we consider the inner radius of the tip-seal to represent a nominal measurement scale (data support) as proposed by Tidwell and Wilson (1999). We conclude from their analysis that measurements on face 6 of the block are less reliable than the rest and therefore limit our analysis below to those on faces 1-5.…”

Section: Previous Analyses Of Experimental Datamentioning

confidence: 94%

“…As the latter are not multifractal, neither must be processes revealed by ESS (or any other method of analysis) to yield nonlinear variations in ξ(q) with q. In this paper we use three methods to identify power-law scaling of log air permeability data collected by Tidwell and Wilson (1999) on the faces of a laboratory-scale cube of Topopah Spring tuff: method of moments (M) and extended power-law scaling via ESS and G-ESS. Most published analyses of extended power-law scaling concern time series or one-dimensional transects of spatial data associated with a unique measurement (support) scale.…”

Section: Introductionmentioning

confidence: 99%

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Extended power-law scaling of air permeabilities measured on a block of tuff

Siena

Guadagnini

Riva

et al. 2012

Hydrol. Earth Syst. Sci.

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Abstract. We use three methods to identify power-law scaling of multi-scale log air permeability data collected by Tidwell and Wilson on the faces of a laboratory-scale block of Topopah Spring tuff: method of moments (M), Extended Self-Similarity (ESS) and a generalized version thereof (G-ESS). All three methods focus on q-th-order sample structure functions of absolute increments. Most such functions exhibit power-law scaling at best over a limited midrange of experimental separation scales, or lags, which are sometimes difficult to identify unambiguously by means of M. ESS and G-ESS extend this range in a way that renders power-law scaling easier to characterize. Our analysis confirms the superiority of ESS and G-ESS over M in identifying the scaling exponents, ξ(q), of corresponding structure functions of orders q, suggesting further that ESS is more reliable than G-ESS. The exponents vary in a nonlinear fashion with q as is typical of real or apparent multifractals. Our estimates of the Hurst scaling coefficient increase with support scale, implying a reduction in roughness (anti-persistence) of the log permeability field with measurement volume. The finding by Tidwell and Wilson that log permeabilities associated with all tip sizes can be characterized by stationary variogram models, coupled with our findings that log permeability increments associated with the smallest tip size are approximately Gaussian and those associated with all tip sizes scale show nonlinear variations in ξ(q) with q, are consistent with a view of these data as a sample from a truncated version (tfBm) of self-affine fractional Brownian motion (fBm). Since in theory the scaling exponents, ξ(q), of tfBm vary linearly with q we conclude that nonlinear scaling in our case is not an indication of multifractality but an artifact of sampling from tfBm. This allows us to explain theoretically how power-law scaling of our data, as well as of non-Gaussian heavy-tailed signals subordinated to tfBm, are extended by ESS. It further allows us to identify the functional form and estimate all parameters of the corresponding tfBm based on sample structure functions of first and second orders.

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Section: Previous Analyses Of Experimental Datamentioning

confidence: 83%

Section: Previous Analyses Of Experimental Datamentioning

confidence: 94%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Extended power-law scaling of air permeabilities measured on a block of tuff

Siena

Guadagnini

Riva

et al. 2012

Hydrol. Earth Syst. Sci.

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“…In short, it is one of the most uniform (deterministically homogeneous) rock samples we've encountered. Samples from other depositional environments, with much larger permeability variances and different spatial correlation structures, have likewise been investigated and are reported elsewhere (Tidwell and Wilson, 1999a;1999b).…”

Section: Resultsmentioning

confidence: 99%

Untitled

Tidwell

Wilson

1999

Mathematical Geology

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To physically investigate permeability upscaling over 13,000 permeability values were measured with four different sample supports (Le., sample volumes) on a block of Berea Sandstone. At each sample support spatially-exhaustive permeability data sets were measured, subject to consistent flow geometry and boundary conditions, with a specially adapted minipermeameter test system.Here, we present and analyze a subset of the data consisting of 2304 permeability values collected from a single block face oriented normal to stratification. Results reveal a number of distinct and consistent trends (i.e., upscaling) relating changes in key summary statistics to an increasing sample support. Examples include the sample mean and semivariogram range that increase with increasing sample support and the sample variance that decreases. To help interpret the measured mean upscaling we compared it to theoretical models that are only available for somewhat different flow geometries. The comparison suggests that the non-uniform flow imposed by the minipermeameter coupled with permeability anisotropy at the scale of the local support (i.e., smallest sample support for which data is available) are the primary controls on the measured upscaling. This work demonstrates, experimentally, that it is not always appropriate to treat the local-support permeability as an intrinsic feature of the porous medium; that is, independent of its conditions of measurement.

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“…Instead, they have proven theoretically that ESS of data having a normal frequency distribution is theoretically consistent with tfBm. This allowed them to identify the functional form and estimate all parameters of the particular tfBm corresponding to log air-permeability data collected by Tidwell and Wilson (1999) on the faces of a laboratory-scale block of Topopah Spring tuff. In this paper we employ ESS to analyze the scaling behaviors of two log permeability data sets showing heavy-tailed frequency distributions in three and two spatial dimensions, respectively.…”

Section: Introductionmentioning

confidence: 99%

Extended power-law scaling of heavy-tailed random air-permeability fields in fractured and sedimentary rocks

Guadagnini

Riva

Neuman

2012

Hydrol. Earth Syst. Sci.

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Abstract. We analyze the scaling behaviors of two fieldscale log permeability data sets showing heavy-tailed frequency distributions in three and two spatial dimensions, respectively. One set consists of 1-m scale pneumatic packer test data from six vertical and inclined boreholes spanning a decameters scale block of unsaturated fractured tuffs near Superior, Arizona, the other of pneumatic minipermeameter data measured at a spacing of 15 cm along three horizontal transects on a 21 m long and 6 m high outcrop of the Upper Cretaceous Straight Cliffs Formation, including lowershoreface bioturbated and cross-bedded sandstone near Escalante, Utah. Order q sample structure functions of each data set scale as a power ξ(q) of separation scale or lag, s, over limited ranges of s. A procedure known as extended self-similarity (ESS) extends this range to all lags and yields a nonlinear (concave) functional relationship between ξ(q) and q. Whereas the literature tends to associate extended and nonlinear power-law scaling with multifractals or fractional Laplace motions, we have shown elsewhere that (a) ESS of data having a normal frequency distribution is theoretically consistent with (Gaussian) truncated (additive, self-affine, monofractal) fractional Brownian motion (tfBm), the latter being unique in predicting a breakdown in power-law scaling at small and large lags, and (b) nonlinear power-law scaling of data having either normal or heavy-tailed frequency distributions is consistent with samples from sub-Gaussian random fields or processes subordinated to tfBm or truncated fractional Gaussian noise (tfGn), stemming from lack of ergodicity which causes sample moments to scale differently than do their ensemble counterparts. Here we (i) demonstrate that the above two data sets are consistent with sub-Gaussian random fields subordinated to tfBm or tfGn and (ii) provide maximum likelihood estimates of parameters characterizing the corresponding Lévy stable subordinators and tfBm or tfGn functions.

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Upscaling experiments conducted on a block of volcanic tuff: Results for a bimodal permeability distribution

Cited by 38 publications

References 28 publications

Extended power-law scaling of air permeabilities measured on a block of tuff

Extended power-law scaling of air permeabilities measured on a block of tuff

Untitled

Extended power-law scaling of heavy-tailed random air-permeability fields in fractured and sedimentary rocks

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