Current Research--Martinez and Byrnes--page 8 of 13

Kansas Geological Survey, Current Research in Earth Sciences, Bulletin 247, part 1
Modeling Dielectric-constant Values of Geologic Materials: An Aid to Ground-penetrating Radar Data Collection and Interpretation--page 8 of 13

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Application of Dielectric Mixing Modeling, cont.

Example 3: Limestone Modeling

Lime wacke-packstone, siltstone, chert, and limey shale lithologies of the Merriam Limestone Member of the Upper Pennsylvanian Lansing Group were collected from the study site of Martinez, Kruger et al. (1998). Mineralogically, the samples consisted primarily of calcite with varying amounts of chert (quartz) and disseminated argillaceous material (mainly quartz). Helium porosity, hydraulic (air) permeability, and dry and water-saturated dielectric constant were measured on the core plugs, using the same techniques used for the samples from the Tonganoxie Sandstone Member. Bulk dielectric-constant measurements were complicated by the heterogeneous nature of the rocks. Many samples exhibited lithologies with patchy bioturbated mudstones and packstones, each of which had a different dielectric constant. Bulk dielectric constants of these samples were obtained by averaging point dielectric-constant values weighted appropriately for the relative portions of each lithology in the total sample. In contrast to the Tonganoxie shaly sands, the air- and oven-dried carbonate samples had similar dielectric-constant values, which is consistent with their low clay content. In dry samples, average dielectric-constant values ranged from 7.9 for packstone (with low amounts, less than 5% of argillaceous material) to 3.1 for chert. Average dielectric-constant values in water-saturated samples ranged from 21.7 to 8.8.

Dielectric-constant values were predicted by TP modeling for rock with a calcite ( = 8.0) and quartz ( = 4.5) matrix and were simulated over the range of porosity values exhibited by the data ( = 0% to 25%). The calculated values were plotted with the measured data (fig. 10A). Packstone samples that exhibited bulk dielectric-constant values less than the TP model-predicted values for a pure calcite ( = 8.0) matrix contained varying amounts of quartz in the matrix in the form of increasing argillaceousness or chert. Incorporating matrix composition and porosity in the TP model-predicted values provided a better correlation with measured dielectric-constant values (standard error of prediction of 0.58) than the correlation with the calcite and quartz matrix trends evident in fig. 10A.

Fig. 10A. Dry and water-saturated dielectric constant versus helium porosity. These values are based on laboratory measurements from carbonate samples collected at the Martinez, Kruger et al. (1998) study site. The TP-model results for wet and dry calcite ( = 8.5) and quartz ( = 4.5) are also shown.

These carbonate rocks exhibited a good log-linear correlation between hydraulic (air) permeability and porosity (R₂ = 0.87; fig. 10B). However, the complexity of the relationship between dielectric constant and porosity, introduced by mineralogy (evident in fig. 10A) and sample heterogeneity, significantly weakens the correlation between dielectric constant and hydraulic (air) permeability (fig. 10C). Multivariate regression, using both dielectric constant and amount of quartz in the matrix, would improve the correlation, but not enough samples were studied for this analysis to be meaningful on this data set.

Fig. 10B. Hydraulic (air) permeability versus helium porosity, with a log-linear correlation of R₂ = 0.8743 (line). These values are based on laboratory measurements from carbonate samples collected at the Martinez, Kruger et al. (1998) study site.

Fig. 10C. Dry and water-saturated dielectric constants versus hydraulic (air) permeability. These values are based on laboratory measurements from carbonate samples collected at the Martinez, Kruger et al. (1998) study site.

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Kansas Geological Survey
Web version December 3, 2001
http://www.kgs.ku.edu/Current/2001/martinez/martinez8.html
email:lbrosius@kgs.ku.edu