Jorge O. Parra

The transversely isotropic poroelastic wave equation including the Biot and the squirt mechanisms; theory and application

The transversely isotropic poroelastic wave equation can be formulated to include the Biot and the squirt-flow mechanisms to yield a new analytical solution in terms of the elements of the squirt-flow tensor. The new model gives estimates of the vertical and the horizontal per- meabilities, as well as other measurable rock and fluid properties. In particular, the model estimates phase ve- locity and attenuation of waves traveling at different an- gles of incidence with respect to the principal axis of anisotropy. The attenuation and dispersion of the fast quasi P-wave and the quasi SV-wave are related to the vertical and the horizontal permeabilities. Modeling sug- gests that the attenuation of both the quasi P-wave and quasi SV-wave depend on the direction of permeability. For frequencies from 500 to 4500 Hz, the quasi P-wave attenuation will be of maximum permeability. To test the theory, interwell seismic waveforms, well logs, and hydraulic conductivity measurements (recorded in the fluvial Gypsy sandstone reservoir, Oklahoma) provide the material and fluid property parameters. For exam- ple, the analysis of petrophysical data suggests that the vertical permeability (1 md ) is affected by the presence of mudstone and siltstone bodies, which are barriers to vertical fluid movement, and the horizontal permeabil- ity (1640 md) is controlled by cross-bedded and planar- laminated sandstones. The theoretical dispersion curves based on measurable rock and fluid properties, and the phase velocity curve obtained from seismic signatures, give the ingredients to evaluate the model. Theoreti- cal predictions show the influence of the permeability anisotropy on the dispersion of seismic waves. These dispersion values derived from interwell seismic signa- tures are consistent with the theoretical model and with the direction of propagation of the seismic waves that travel parallel to the maximum permeability. This analy- sis with the new analytical solution is the first step toward a quantitative evaluation of the preferential directions of fluid flow in reservoir formation containing hydrocar- bons. The results of the present work may lead to the development of algorithms to extract the permeability anisotropy from attenuation and dispersion data ( de- rived from sonic logs and crosswell seismics) to map the fluid flow distribution in a reservoir.

Poroelastic model to relate seismic wave attenuation and dispersion to permeability anisotropy

A transversely isotropic model with a horizontal axis of symmetry, based on the Biot and squirt‐flow mechanisms, predicts seismic waves in poroelastic media. The model estimates velocity dispersion and attenuation of waves propagating in the frequency range of crosswell and high‐resolution reverse vertical seismic profiling (VSP) (250–1250 Hz) for vertical permeability values much greater than horizontal permeability parameters. The model assumes the principal axes of the stiffness constant tensor are aligned with the axes of the permeability and squirt‐flow tensors. In addition, the unified Biot and squirt‐flow mechanism (BISQ) model is adapted to simulate cracks in permeable media. Under these conditions, the model simulations demonstrate that the preferential direction of fluid flow in a reservoir containing fluid‐filled cracks can be determined by analyzing the phase velocity and attenuation of seismic waves propagating at different azimuth and incident angles. As a result, the fast compressional wave...

Improving Q estimates from seismic reflection data using well-log-based localized spectral correction

Most methods for deriving Q from surface-seismic data depend on the spectral content of the reflection. The spectrum of the reflected wave may be affected by the presence of thin beds in the formation, which makes Q estimates less reliable. We incorporate a method for correcting the reflected spectrum to remove local thin-bed effects into the Q-versus-offset (QVO) method for determining attenuation from seismic-reflection data. By dividing the observed spectrum by the local spectrum of the known reflectivity sequence from a nearby well log, we obtain a spectrum more closely resembling that which would be produced by a single primary reflector. This operation, equivalent to deconvolution in the time domain, is demonstrated to be successful using synthetic data. As a test case, we also apply the correction method to QVO with a real seismic line over a south Florida site containing many thin sandstone and carbonate beds. When corrected spectra are used, there is significantly less variance in the estimated Q values, and fewer unphysical negative Q values are obtained. Based on this method, it appears that sediments at the Florida site have a Q near 33 that is roughly constant from 170- to 600-m depth over the length of the line.

Electrical response of a leak in a geomembrane liner

A leak in a geomembrane lined impoundment or landfill has a characteristic electrical response. I simulate the waste material, the liner, and the soil under the liner by infinite horizontal layers and express the secondary potential for a leak in the geomembrane liner in terms of a three‐layer medium Green’s function and the unknown current density distribution at the leak. The area of the leak is sufficiently small for the leak current density to be essentially uniform. I add the primary potential associated with a leak‐free liner to the secondary potential to form an integral equation and derive a general expression for the current density at the boundary between the waste material and the liner. From the expression for the current density, I determine the current flow through the leak by assuming that the total current distribution flows vertically across a finite region of the infinite, thin liner layer. This finite region has the same surface area as does the waste disposal site or landfill. My analy...

Effects of single vertical fluid‐filled fractures on full waveform dipole sonic logs

We conducted a parametric study of the effects of single, finite‐width, adjacent, vertical, fluid‐filled fractures on full‐wave borehole dipole logs using the transformed boundary integral equation method. We found that a fracture has significant effects on dipole response if it is within half the wavelength, or two to three times the borehole diameter, from the borehole center. Dual flexural waves and a leaky fracture mode resulted from the waveguide composed of the borehole and fracture. The first flexural wave was controlled by both the borehole and fracture, whereas the second flexural wave was controlled primarily by the borehole but influenced by the fracture. The separation of these two flexural waves increased and the strength of the first one decreased when the distance between the fracture and the borehole increased. The leaky fracture mode was represented by a sharp minimum in the amplitude spectrum, and energy leakage to the fracture reached a maximum when the fracture intersected the borehole...

Wave attenuation attributes as flow unit indicators

In this article we present a model-based interpretation algorithm to predict attenuation signatures associated with a reservoirs structure and its intrinsic properties. Scattering losses are caused by multiple reflections associated with the impedance contrast between different reservoir boundaries. Intrinsic losses are due to the fluids in the reservoir, the rock fabric, and the anisotropy due to vertical fractures. Because amplitude data are sensitive to these reservoir characteristics, we calculate the wave attenuation response of the reservoir in the frequency range of surface seismic, VSP, crosswell seismic, and borehole sonic. A model of a plane wave traveling in a poroelastic multilayer earth medium allows us to include anisotropy. The multilayer part of the model simulates elastic scattering; the poroelastic part of the model simulates fluid-flow effects in the reservoir; and the anisotropic part of the model simulates reservoir fractures.

Model studies of electrical leak detection surveys in geomembrane‐lined impoundments

Pole‐dipole array electrical potential distributions are calculated for a geomembrane‐lined liquid impoundment having single or multiple leaks. A three‐dimensional numerical model is employed to represent a small circular leak in the highly resistive plastic liner. The liquid waste material, the liner, and the soil under the impoundment are simulated by infinite horizontal layers, with approximate corrections for the finite size of the impoundment. Parametric curves for a single leak show that with optimum selection of electrode spacing and positioning and other field survey parameters, leaks can be detected effectively. To identify and resolve the presence of a cluster of leaks, the potential measurements must be made close to the liner and the detector dipole spacing must be smaller than the separation of the leaks. The results also indicate that the survey speed may be increased when portable leak detection equipment employing a vertical dipole detector is used.

Attenuation analysis of acoustic waveforms in a borehole intercepted by a sand-shale sequence reservoir

We applied a new processing algorithm to extract intrinsic attenuation (1/Q) from the head P-wave of a full waveform sonic log. The sonic log was acquired in an oil reservoir in northeast Texas (USA). The reservoir is a sand-shale sequence characterized at the pore, core, and borehole scales. We found that the attenuation correlates with the lithology, including a sandstone zone partially saturated with oil and water. A comparison of 1/Q with the microseismogram and the petrophysics of other well logs provides a way of evaluating the consistency of Q at each borehole depth location. An analysis of the results explains the different attenuation anomalies found in the Q log.

Permeability and porosity images based on NMR, sonic, and seismic reflectivity Application to a carbonate aquifer

Carbonate formations generally have a large distribution of pore sizes, ranging from microcrystalline to large vugs. Knowledge of these pore spaces and their connectivity is crucial to hydrocarbon reservoir characterization and to hydrogeological and near surface environmental applications. In this paper, we present permeability and porosity images based on crosswell seismic measurements integrated with well logs and petrography from a carbonate aquifer underlying Palm Beach County, Florida, U.S. Petrography and core analyses reveal relationships between the rock physical properties that control the compressional- and shear-wave velocities of the formation. In addition, core data and petrography characterized the matrix permeability and pore spaces as well as the lithology. The lithology integrated with well logs determined the hydraulic and rock properties of a 500-ft zone intercepted by a borehole. We delineated vuggy and permeable/impermeable zones at the borehole and interwell scales in the upper Floridan aquifer in south Florida by inverting reflection seismic data for impedance which, when correlated with borehole permeability and porosity logs, led to empirical relationships that are used to transform impedance images to permeability and porosity images. The images showed continuity between the major geologic units and lateral changes in the porosity image. The high-resolution reflections observed at the field scale in the carbonate formation are associated with changes in porosity due to the presence of vugs. This was corroborated with P-wave and borehole data, which showed that, as P-wave velocity decreases, porosity increases. The images show that porous zones in the carbonate aquifer are laterally continuous up to 200 ft from the well and then become relatively discontinuous, and that these porous and permeable flow units are characterized by interconnected vugs. To analyze the pore structure of the carbonate rocks of the upper Floridan aquifer in South Florida, we processed x-ray CT and optical microscopic (OM) thin …

The electrical leak location method for geomembrane liners

Abstract An electrical method for locating leaks in geomembrane liners was developed and demonstrated for a wide variety of applications. Geomembrane liners are Tests on a doubled-lined physical model demonstrated the applicability of the method for a variety of drainage layers under various test conditions suc The method was adapted for locating leaks in the geomembrane liner of landfill cover systems. Scale model tests demonstrated the applicability of the m