Rosemary Knight

The dielectric constant of sandstones, 60 kHz to 4 MHz

Complex impedance data were collected for eight sandstones at various levels of water saturation (Sw) in the frequency range of 5 Hz to 4 MHz. The measurements were made using a two‐electrode technique with platinum electrodes sputtered onto the flat faces of disk‐ shaped samples. Presentation of the data in the complex impedance plane shows clear separation of the response due to polarization at the sample‐electrode interface from the bulk sample response. Electrode polarization effects were limited to frequencies of less than 60 kHz, allowing us to study the dielectric constant κ′ of the sandstones in the frequency range of 60 kHz to 4 MHz. κ′ of all samples at all levels of saturation shows a clear power‐law dependence upon frequency. Comparing the data from the eight sandstones at Sw=0.36, the magnitude of the frequency dependence was found to be proportional to the surface area‐to‐volume ratio of the pore space of the sandstones. The surface area‐to‐volume ratio of the pore space of each sandstone wa...

RESINVM3D: A 3D resistivity inversion package

We have developed an open source 3D, MATLAB based, resistivity inversion package. The forward solution to the governing partial differential equation is efficiently computed using a second-order finite volume discretization coupled with a preconditioned, biconjugate, stabilized gradient algorithm. Using the analytical solution to a potential field in a homogeneous half space, we evaluate the accuracy of our numerical forward solution and, subsequently, develop a source correction factor that reduces forward modeling errors associated with boundary effects and source electrode singularities. For the inversion algorithm we have implemented an inexact Gauss-Newton solver, with the model update being calculated using a preconditioned conjugate gradient algorithm. The inversion uses a combination of zero and first order Tikhonov regularization. Two synthetic examples demonstrate the usefulness of this code. The first example considers a surface resistivity survey with 3813 measurements. The discretized model s...

Numerical modeling of ground-penetrating radar in 2-D using MATLAB

We present MATLAB codes for finite-difference time-domain (FDTD) modeling of ground-penetrating radar (GPR) in two dimensions. Surface-based reflection GPR is modeled using a transverse magnetic (TM-) mode formulation. Crosshole and vertical radar profiling (VRP) geometries are modeled using a transverse electric (TE-) mode formulation. Matrix notation is used in the codes wherever possible to optimize them for speed in the MATLAB environment. To absorb waves at the edges of the modeling grid, we implement perfectly matched layer (PML) absorbing boundaries. Although our codes are two-dimensional and do not incorporate features such as dispersion in electrical properties, they capture many of the important elements of GPR surveying and run at a fraction of the computational cost of more elaborate algorithms. In addition, the codes are well commented, relatively easy to understand, and can be easily modified for the users specific purpose.

Geostatistical analysis of ground‐penetrating radar data: A means of describing spatial variation in the subsurface

We have investigated the use of ground-penetrating radar (GFR) as a means of characterizing the heterogeneity of the subsurface. Radar data were collected at several sites in southwestern British Columbia underlain by glaciodeltaic sediments. A cliff face study was conducted in which geostatistical analysis of a digitized photograph of the face and the radar image of the face showed excellent agreement in the maximum correlation direction and the correlation length determined from these two data sets. Other two-dimensional (2-D) sections of radar data were divided into sedimentary architectural elements on the basis of the distinct radar appearance of these sedimentary units. Examples of four sedimentary units were used to obtain semivariograms from the radar data and resulted in maximum correlation lengths between 0.5 and 4.8 m. A 3-D radar survey, collected over a package of gravel and sand foresets, was analyzed to determine the paleoflow direction; a correlation length of 4 m was found in that direction.

Hysteresis in the electrical resistivity of partially saturated sandstones

Laboratory measurements of the resistivity of three sandstone samples collected during imbibition (increasing Sw) and drainage (decreasing Sw) show pronounced hysteresis in resistivity throughout much of the saturation range. The variation in resistivity can be related to changes in pore-scale fluid distribution caused by changes in saturation history. The form of the hysteresis is such that resistivity measured during imbibition is consistently less than that measured, at the same saturation, during drainage. This can be attributed to the presence of conduction at the air/ water interface in partially saturated samples; an effect that is enhanced by fluid geometries associated with the imbibition process. The results of this study suggest that the dependence of geophysical data on saturation history should be considered when interpreting data from the unsaturated zone.

Removal of wavelet dispersion from ground‐penetrating radar data

Wavelet dispersion caused by frequency‐dependent attenuation is a common occurrence in ground‐penetrating radar (GPR) data, and is displayed in the radar image as a characteristic “blurriness” that increases with depth. Correcting for wavelet dispersion is an important step that should be performed before GPR data are used for either qualitative interpretation or the quantitative determination of subsurface electrical properties. Over the bandwidth of a GPR wavelet, the attenuation of electromagnetic waves in many geological materials is approximately linear with frequency. As a result, the change in shape of a radar pulse as it propagates through these materials can be well described using one parameter, Q*, related to the slope of the linear region. Assuming that all subsurface materials can be characterized by some Q* value, the problem of estimating and correcting for wavelet dispersion becomes one of determining Q* in the subsurface and deconvolving its effects using an inverse‐Q filter. We present a...

Acoustic signatures of partial saturation

The relationship between elastic wave velocities and water saturation in a water/gas reservoir depends strongly on whether saturation is heterogeneous (patchy) or homogeneous. Heterogeneity in saturation may result from lithologic heterogeneity because under conditions of capillary equilibrium, different lithologies within a reservoir can have different saturations, depending on their porosities and permeabilities. We investigate this phenomenon by generating models of a reservoir in which we control the distribution of lithologic units and theoretically determine the corresponding velocity-saturation relationship. We assume a state of capillary equilibrium in the reservoir and determine the saturation level of each region within the reservoir from the corresponding capillary pressure curve for the lithologic unit at that location. The velocities we calculate for these models show that saturation heterogeneity, caused by lithologic variation, can lead to a distinct dependence of velocity on saturation. In a water-gas saturated reservoir, a patchy distribution of the different lithologic units is found to cause P-wave velocity to exhibit a noticeable and almost continuous velocity variation across the entire saturation range. This is in distinct contrast to the response of a homogeneous reservoir where there is only a large change in velocity at water saturations close to 100%.

A new concept in modeling the dielectric response of sandstones; defining a wetted rock and bulk water system

Experimental data for the real part of the dielectric constant (K′) of three sandstone samples are considered as a function of the level of water saturation (Sw) in the frequency range 60 kHz to 4 MHz. Existing theoretical models have previously shown poor agreement with K′ versus Sw data for rock samples, undoubtedly due to the complexity involved in adequately accounting for geometrical and electrochemical effects. In analyzing the data presented here, we find a pronounced increase in K′ in the low saturation region which in all cases can be attributed to the establishment of geometrical and surface effects associated with the rock‐water interface. When this increase in K′ is accounted for by defining wetted matrix parameters, the data show excellent agreement with existing theoretical models.

A laboratory study to determine the effect of iron oxides on proton NMR measurements

Using laboratory methods, we investigate the effect of the presence and mineralogic form of iron on measured proton nuclear magnetic resonance (NMR) relaxation rates. Five samples of quartz sand were coated with ferrihydrite, goethite, hematite, lepidocrocite, and magnetite. The relaxation rates for these iron-oxide-coated sands saturated with water were measured and compared to the relaxation rate of quartz sand saturated with water. We found that the presence of the iron oxides led to increases in the relaxation rates by increasing the surface relaxation rate. The magnitude of the surface relaxation rate was different for the various iron-oxide minerals because of changes in both the surface-area-to-volume ratio of the pore space, and the surface relaxivity. The relaxation rate of the magnetite-coated sand was further increased because of internal magnetic field gradients caused by the presence of magnetite. We conclude that both the concentration and mineralogical form of iron can have a significant impact on NMR relaxation behavior.

Effects of pore structure and wettability on the electrical resistivity of partially saturated rocks—A network study

A network model of porous media is used to assess the effects of pore structure and matrix wettability on the resistivity of partially saturated rocks. Our focus is the magnitude of the saturation exponent n from Archies law and the hysteresis in resistivity between drainage and imbibition cycles. Wettability is found to have the dominant effect on resistivity. The network model is used to investigate the role of a wetting film in water-wet systems, and the behavior of oil-wet systems. In the presence of a thin wetting film in water-wet systems, the observed variation in n with saturation is reduced significantly resulting in lower n values and reduced hysteresis. This is attributed to the electrical continuity provided by the film at low-water saturation between otherwise physically isolated portions of water. Oil-wet systems, when compared with the water-wet systems, are found to have higher n values. In addition, the oil-wet systems exhibit a different form of hysteresis and more pronounced hysteresis. These differences in the resistivity response are attributed to differences in the pore scale distribution of water. The effects of pore structure are assessed by varying pore size distribution and standard deviation of the pore size distribution and considering networks with pore size correlation. The most significant parameter is found to be the pore size correlation. When the sizes of the neighboring pores of the network are correlated positively, the magnitude of n and hysteresis are reduced substantially in both the water-wet and oil-wet systems. This is attributed to higher pore accessibility in the correlated networks. The results of the present study emphasize the importance of conducting laboratory measurements on core samples with reservoir fluids and wettability that is representative of the reservoir. Hysteresis in resistivity can be present, particularly in oil-wet systems, and should be considered in the interpretation of resistivity data.