NS31B-01 INVITED
Water content determination in porous and granular media using dielectric petro-physical relationships and mulitipole simulation models.
Ground penetrating radar, time domain reflectometry, capacitance probes and active microwave remote sensing, all seek to exploit the contrast between the intrinsic permittivity of the constituents of the granular material to determine its water content. A strong relationship exists due to the relatively high permittivity of water (80) compared to that of air (1) and the mineral fraction (4-9). The permittivity of the individual components in bulk is dependent on the pressure, temperature and frequency at which they are measured. In the form of a composite material the arrangement of the phases, determined by structure, and the interaction between phases, determined by adsorption at interfaces play an important role in determining the bulk permittivity. In this presentation we present progress with measurements and modeling showing how structural arrangement affects the distribution of water and hence permittivity. This includes the effects of packing, particle shape, particle size distribution, and pore water arrangement in aggregates. Some simple models are presented that describe the permittivity response of unsaturated granular materials. Finally we present work that provides an exciting new direction for the future. A 3-D Multi-pole simulation is used to predict the effective permittivity of particle packs. The advantage of this simulation method is that wave scattering by the media can be observed and analyzed. The modeling has the further advantage that permittivity can be determined anywhere in the frequency domain. Initial results are presented and tested against measurements using well- defined cubic lattices of spheres and random packs. Ultimately we are working towards the development of high quality measurements and realistic models of granular materials that account for wave interaction with the material at the pore/grain scale. These models will form the basis for determining transport properties and accurately interpreting measurements to determine properties such as water content.
<a href='http://pangea.stanford.edu/research/enviro/darob/index.html'>http://pangea.stanford.edu/research/enviro/d arob/index.html</a>
NS31B-02
Coupled Petrophysical Relationships for the Dielectric and Elastic Properties of Glacial Ice
Ice mechanical properties, and hence the response of glaciers to climatic change, depend strongly on the proportion and distribution of unfrozen water at ice-grain boundaries. Because the dielectric and elastic properties of unfrozen water and ice are significantly different, radar and seismic techniques are also sensitive to pore water content. The inference of unfrozen water content within glaciers from these geophysical data is dependent on the nature of the petrophysical relationships used to convert electromagnetic and elastic wave velocity data into water content. Currently, volumetric mixing laws (e.g., the Looyenga and Riznichenko formulae for electromagnetic and elastic wave velocities, respectively) are commonly used; however, it has become apparent that these mixing formulae do not adequately describe these relationships. We present a coupled inclusion-based effective medium approximation for the dielectric and elastic properties of glacial ice. The coupling is achieved by using the same microstuctural description of the ice and equivalent forms of inclusion interaction to simultaneously estimate both physical properties. Our inclusion-based model views the system as an ice background with embedded inclusions representing the pore spaces. Two types of inclusions are used to describe the pore structure: spherical inclusions for the grain junction nodes and spheriodal inclusions for the grain boundary veins. For the inclusion interactions, it is assumed that the effective applied field experienced by an inclusion is the volumetric average field in the background medium. This approach results in an effective medium approximation that is consistent with the Hashin-Shtrikman bounds for all levels of porosity. Our preliminary modeling results clearly show that the dielectric and elastic properties of glacial ice are strongly dependent on the pore structure as well as the unfrozen water content.
NS31B-03
Electrical and Petrophysical modeling of Ferron Sandstone data
As part of the 3-D characterization of a fluvial reservoir analog site in the Ferron Sandstone in east-central Utah, new lab measurements of porosity, permeability, water content, and complex dielectric permittivity are collected and analyzed. Petrographic analysis of thin sections extracted from the same samples produced data on bulk, macro- and micro-porosity, lithology, and cementation. Thus, we have an unusually comprehensive data base for analysis. Complex dielectric permittivities are fitted using three frequency- dependent Debye relaxation mechanisms. Most ambient and dry samples are dominated by low-frequency relaxation mechanisms. The average dielectric constant and electrical conductivity at the typical GPR frequency of 75 MHz, are directly related to volumetric water content and are 3.86 and 0.20 mS/m for ovendried samples, 4.50 and 0.71 mS/m for ambient saturated samples, and 15.42 and 13.11 mS/m for fully saturated samples. Electrical conductivity is poorly estimated from the ovendried samples (for all clay content) since ion mobility is significantly reduced; thus, the dry conductivity is less useful for estimating petrophysical variations. Multivariate regressions with the petrophysical parameters estimate the electrical properties at 75 MHz and 1000 MHz with average correlation coefficients of ~0.921 and ~0.925, respectively. Empirically derived predictions of dielectric constant as a function of water content will always provide better fits to the observed values than either generic models (such as the CRIM model), or fits to other data sets (such as the Topp formula, which was derived for soils). The Topp model consistently underestimates the dielectric constant, while the CRIM model generally overestimates it at both 75 and 1000 MHz. The overall regression procedures can be applied to data from other sites, and potentially used as the basis of inversion of petrophysical properties from measurements of electric and dielectric properties
NS31B-04
Quantifying water content using GPR: impact of petrophysical variability
Electromagnetic signal velocity measurements are commonly used to quantify liquid water contents of near surface geomaterials. Typically, a single-valued function, such as Topp's equation, is used to convert dielectric permittivity (K) into water content ($\theta$). Several factors contribute to error in such water content estimates, including use of incorrect petrophysical relationships, dependence of dielectric permittivity on pore scale geometry, frequency dispersive behavior (for example caused by the presence of swelling clay minerals), and macroscopic heterogeneity that leads to incorrect estimates of dielectric permittivity from field data. We use field and laboratory measurements and synthetic examples to investigate the relative importance of these sources of error. Co-axial cell measurements on clean sand samples suggest that even where the K versus $\theta$ relationship is well characterized, heterogeneity in the distribution of water at the pore scale for example caused by wetting-drying hysteresis, can lead to moisture content errors of $\pm$2% volumetric water content, although more typically errors of $<$$\pm$1% can be expected. Measurements on sandstone samples suggest that larger errors, of up to $\pm$5% can arise at GPR frequencies (i.e. 100MHz), resulting from the presence of swelling clay, although the influence of clay is less important at higher frequencies (i.e. $>$300MHz). Similar sized errors can result from variations in pore-scale geometry. However, experience suggests that the largest errors in water content measurements arise from assumptions concerning radar ray path geometry. GPR estimates of water content in macroscopically layered media made by assuming that the first radar wave arrivals are direct rays, whereas in fact these are critically refracted rays, can result in water content estimates that are inaccurate by up to 20%. Synthetic modeling to investigate the dependence of the magnitude of such errors on the geometric characteristics of heterogeneity will be presented.
NS31B-05 INVITED
Inferred Zonation and Petrophysical Relationships in Unsaturated Sherwood Sandstone From Jointly Inverted ERT and GPR Traveltime Data
Zonation of lithofacies and inference of petrophysical relationships can be obtained by comparing geophysical models that were separately inverted, but the results are often strongly affected by the regularization of the inverse problem and by inversion artifacts in poorly constrained parts of the model. These problems might be decreased if joint inversion is performed without assuming known relationships between different geophysical model properties. Crosshole electrical resistance tomography and ground penetrating radar traveltime data collected between boreholes in unsaturated Sherwood Sandstone were individually and jointly inverted by enforcing structural similarity in three dimensions. The resulting space-varying relationships between electrical conductivity and the dielectric constant were used to derive an improved zonation of the sandstone, compared with what could be obtained from the individual inversion models. A petrophysical model that relates electrical conductivity and the dielectric constant to the same textural parameters was used together with the space- varying relationships obtained from the joint inversion and available downhole and core measurements to determine the hydrogeological characteristics of the different zones. The complementary nature of the dielectric and electric properties make it possible to distinguish the geophysical response of water saturation from surface conduction, which is inversely related to the dominant pore radius of the sandstone. We discuss the conditions for which the proposed joint inversion scheme is valid and assess its validity for the application to unsaturated Sherwood Sandstone.
NS31B-06 INVITED
Quantifying Apparent Petrophysical Relations in Resistivity Tomograms
While geophysical data have frequently been used to provide qualitative information about geologic structure, their use for quantitative assessment of hydrologic parameters and processes has been limited by a number of factors, including: (1) spatially variable measurement physics, (2) parameterization and regularization of the inverse problem, (3) measurement error, and (4) the difficulty in developing appropriate petrophysical relations at the field scale. We present a framework to upscale Archie's law from the core-scale to the pixel-scale using the model resolution matrix from the inversion, random field averaging, and the spatial statistics of electrical conductivity. The limited resolution of the tomographic reconstruction results in a loss of information at the pixel-scale, as compared to the core-scale. Results indicate that application of Archie's law to the resistivity tomograms in our examples would yield misleading estimates of water content, but that the correlation between estimated electrical conductivity and water content is quantifiable through space. To address this issue, we develop apparent, non-stationary petrophysical relations between tomographic estimates of electrical conductivity and true water content based on numerical simulation of hydrogeologic processes and electrical current flow.
NS31B-07
Accounting for Variable Environmental Conditions in Time-Lapse Electrical Resistivity Images
Time-lapse electrical resistivity imaging (ERI) is being used to monitor salt transport at a remediation site in Alberta, Canada. The goal is to use ERI to produce images of salt concentration in soil. Mapping the salt concentration is possible because soil electrical conductivity (EC) is strongly correlated with salt concentration. However, soil EC is also affected by the temperature of the soil and the soil moisture content. Temperature and soil moisture conditions vary with changing environmental conditions. Three-D ERI results show that dramatically incorrect interpretations will result by neglecting differences in environmental conditions at the time of surveys. These results have two important implications 1) the petrophysical relationship that maps ERI values to salt concentration must be applied to images that have been converted to a standard condition equivalent EC value, and 2) auxiliary field measurements are required to establish temperature and saturation profiles at the time of surveys. We have chosen to standardize our images to 6 Deg. C and saturation of 1 because these values are most representative of the average conditions at the site. Laboratory measurements show that the temperature correction is 3.0% EC per Deg. C. The Waxman-Smits equation is used to correct for saturation differences. Finally, laboratory measurements have established an empirical relationship between soil EC at standard conditions and the regulatory measure of soil paste EC.