Evaluation of laboratory dolomite core sample size using representative elementary volume concepts

Abstract

Abstract. The adequacy for laboratory testing of four dolomite cores from the Culebra Dolomite of the Rustler Formation at the Waste Isolation Pilot Plant near Carlsbad, NewMexico, were evaluated using representative elementary volume (REV) theory. Gamma ray computerized tomography created three-dimensional grids of bulk density and macropore index over volumes from 1.4 x 10 -7 to 1.6 L. Three different methods for both volume averaging and REV analysis were applied and compared. Both density and macropore index converged to single values with increasing volume, which meets the most common qualitative definition of a REV. Statistical test results for the relatively homogeneous samples indicate that volumes larger than 1 to 7 mL have constant properties. Contrarily, a highly varied sample required 250 and 373 mL to achieve invariant density and macropore characteristics, respectively. Prismatic volume averaging was found to be better than slice averaging, while a qualitative test for the REV provided similar results as a rigorous statistical method. All cores were larger than the REV but were significantly different from one another. This implies that multiple cores are necessary to determine the entire range of transport properties within the rock. In practice, the concept has also been applied to characterize both nonhomogeneous porous media and large-scale properties in fractured media [Bear, 1993]. In those cases a REV was defined for both matrix and fractures. Expansion of the definition has added complications to sampling, testing, and verification procedures and has produced some debate. As Baveye and Sposito [1984] observed, while intuitively appealing, no known data had been presented to quantify the dimension and operational significance of the REV. Only recently, have Buchter et al. [1994] extrapolated limited two-dimensional porosity data to directly describe a three-dimensional REV relationship, and Clausnitzer and Hopmans [1999] presented a simple REV plot for glass beads. Thus, while almost every advanced groundwater textbook has a hypothetical plot of the REV, there is little insight on the actual shape of the REV curve, much less wisdom into how the concept may be applied.To some extent the concept of the REV has become obsolete because of the recent advances in characterization of spatial variability. We no longer expect to represent an aquifer or soil with a single value of porosity and conductivity but instead model those systems with complex stochastic representations. One may rightly ask if the REV concept holds any value beyond the narrow distinction between pore-scale processes and the bulk porous medium. To that, we answer the concept is still important in the design and interpretation of laboratory col-1199

Heterogeneity of Infiltration Rates in Alluvial Floodplains as Measured with a Berm Infiltration Technique

“…It was hypothesized that as the scale of measurement increases, the measured infiltration rate and calculated hydraulic conductivity of the topsoil will increase due to an increased likelihood of a very large but infrequent macropore occurring in a large plot size, and that the variability will decrease until an REV is attained (Bear, 1972;Brown et al, 2000). At all sites, the K eff increased until the plot scale was reached (1 m × 1 m), but K eff did not consistently increase or decrease as the plot scale increased from 1 m × 1 m to 10 m × 10 m. While variability in K eff decreased as the scale increased from 1 m × 1 m to 3 m × 3 m at the Pumpkin Hollow and Clear Creek sites, the variability actually increased at the Barren Fork site as the scale of measurement increased from 1 m × 1 m to 3 m × 3 m. More specifically, the K eff values were relatively constant within the plot scale for the shallow gravel formation (Barren Fork), the control plots (Pumpkin Hollow), and Formation B (Clear Creek).…”

“…For measurement volumes less than V min , the property fluctuates rapidly in space due to the influence of individual pores. For measurement volumes above V max , "additional morphological structures allow the property to drift to new values, which results in large field variability" (Brown et al, 2000). While the REV was originally applied to small scales, the influence of infrequent but large macropores, especially on hydraulic conductivity, may justify applying the REV to larger scales.…”

“…As the scale of measurement increases, the physical properties of a porous medium like soil tend to have decreasing variability until a representative elementary volume (REV) is reached (Bear, 1972;Brown et al, 2000). The REV is bounded by a minimum (V min ) and maximum (V max ) volume.…”

Scale effect on porosity and permeability: Kinetics, model, and correlation

“…The representative elementary volume is an optimum bulk size of porous media over which the microscopic properties of pore fluids and porous matrix can be averaged to obtain a consistent and continuous macroscopic description. Brown et al (2000) define it as "the range of volumes for which all averaged geometrical characteristics are single-valued functions of the location of that point and time." As pointed out by Nelson (2000>, the total porosity of porous formations can be classified into the contributing and noncontributing porosities.…”

Berm Method for Quantification of Infiltration at the Plot Scale in High Conductivity Soils

“…Physical properties of a porous media like soil tend to be highly variable in space until a representative elementary volume (REV) is reached (Brown et al 2000). It is unknown how well point measurements of infiltration can be extrapolated to the plot or field scale.…”