Pei-Cheng Xu

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...

Dispersion and attenuation of acoustic guided waves in layered fluid‐filled porous media

The analysis of acoustic wave propagation in fluid‐filled porous media based on Biot and homogenization theories has been adapted to calculate dispersion and attenuation of guided waves trapped in low‐velocity layered media. Constitutive relations, the balance equation, and the generalized Darcy law of the modified Biot theory yield a coupled system of differential equations which governs the wave motion in each layer. The displacement and stress fields satisfy the boundary conditions of continuity of displacements and tractions across each interface, and the radiation condition at infinity. To avoid precision problems caused by the growing exponential in individual matrices for large wave numbers, the global matrix method was implemented as an alternative to the traditional propagation approach to determine the periodic equations. The complex wave numbers of the guided wave modes were determined using a combination of two‐dimensional bracketing and minimization techniques. The results of this work indica...

A borehole-model-derived algorithm for estimating QP logs from full-waveform sonic logs

We develop a processing algorithm to estimate the intrinsic seismic attenuation QP −1 from P head waves of full-waveform sonic logs. The algorithm, based on an extended version of the amplitude spectral ratio (ASR) method, corrects the apparent attenuation for the effects of multiple raypaths within the borehole, geometric spreading of head waves, and formation inhomogeneity. The algorithm is derived from two ray models. The first model simulates the interaction among rays reflected within the borehole and rays reflected from layer interfaces. This model removes these reflections and extracts the leading borehole wavelet. The second model uses a single-ray model for the borehole head wave in layered formations. This model provides the transmission coefficients across the layer interfaces between the source depth and the receiver depth with sectional geometric spreading within these layers. We use these two models to simultaneously separate, correct for, and normalize the effects of the borehole, geometric...

Characterization of fractured low Q zones at the Buena Vista Hills reservoir, California

We show that attenuation of high‐resolution interwell seismic and acoustic waves based on velocity dispersion analysis relates to fluid‐flow effects in fractured and shale–sand sequence formations at the Buena Vista Hills reservoir, California. Fractured low quality factor (Q‐factor) zones in the Brown Shale and Antelope Shale reservoir intervals in the Monterrey Formation correlate with a system of fractures having permeabilities of 2.5 to 5 md. Vertical fractures oriented at azimuths from 0° to 30° are detected in the frequency range of 1 to 10 kHz. We establish that a poroelastic model based on the Biot/squirt‐flow (BISQ) mechanism can be used to relate the low Q‐factor zones in the Brown and Antelope Shales. Because the Brown Shale has no sands, we use it to evaluate a fracture systems response to attenuation. We adapt the BISQ mechanism to simulate fluid flow in fracture‐induced anisotropy, which provides flow properties parallel and perpendicular to fractures in the siliceous shale formations. The ...

Attenuation and velocity estimation using rock physics and neural network methods for calibrating reflection seismograms

AbstractVelocity logs are the most important data used to evaluate rock, fluid, and geotechnical properties of hydrocarbon reservoirs. As a complementary physical property, P-wave attenuation (Q−1) can be used as an indicator of lithology and fluid saturation in oil and gas reservoir characterization. We implemented an inversion self-consistent rock physical model to predict P- and S-wave velocities in two old wells near a new well containing a complete suite of logs at the Waggoner Ranch oil reservoir in northeast Texas. We selected a training data set from the new well to test the algorithm that was subsequently applied to predict velocity data in the two old wells. We used an attenuation log from the new well to perform data analysis via the Gamma test, a mathematically nonparametric nonlinear smooth modeling tool, to choose the best input combination of well logs to train an artificial neural network (NN) for estimating Q−1. Then, the NN was applied to predict attenuation logs in the old wells. The Q−...

Transmission and detection of guided seismic waves in attenuating media

We can use guided seismic waves to map properties of reservoirs between wells, with the low-velocity layers acting as waveguides. When guided waves are detected, they are an indication of the continuity of the bed examined. Guided waveforms are characterized by time-frequency representations to study important physical properties of the beds acting as waveguides. We used full waveform seismic modeling in viscoelastic media to examine the required velocity contrasts and distances over which guided-wave signals can be used. In one set of models, sandstones are the central waveguide lithology; in another set, shales. We applied these models, referred to here collectively as shaly sandstone waveguides, to a range of geological circumstances where either the sands or the shales represent the low-velocity layers within a reservoir. To study the distances over which guided waves can be detected, we compared the amplitudes of the signals computed for the models, using a realistic source strength, to the signal levels determined from published borehole noise studies. In shaly sandstone waveguides, we find it is feasible to use particle velocity measurements to record guided waves above seismic noise levels in the frequency range of 60 to 800 Hz at well separations exceeding a distance of 800 m. However, pressure detectors such as hydrophones may only be useful up to distances of 400 m between wells. In addition to the issues of shaly sandstone waveguides and practical distances between wells, we present an application of guided waves using crosswell seismic data from the Gypsy test site in Oklahoma (a site originally established by British Petroleum). In this field example within a sandstone reservoir, we demonstrate the sensitivity of leaky mode amplitudes to source-receiver location. Another telltale characteristic of continuity in the type of reservoir studied at the Gypsy test site, where there is a low shear velocity contrast between the host medium and the waveguide, is the head wave followed by the leaky mode.

A parametric study of synthetic dipole logging data in azimuthally anisotropic formations

SUMMARY A parametric study of synthetic dipole sonic logs in formations with azimuthal anisotropy has been carried out using the integral transformed boundary integral equation (ITBIE) technique. The simulations are based on rock physical properties of a typical fracture zone containing vertical fractures. In low and mid frequencies and far field, in-line dipole waveforms can be interpreted by a combination of related isotropic models. Cross-line dipole waveforms have distinct azimuthal characteristics, which can be used to determine the orientation of the symmetry axis of the formation.

Interwell seismic transmission and reflection through a dipping low‐velocity layer

A dipping fractured layer zone has a characteristic seismic signature in interwell seismic data. A fracture zone is simulated as a dipping low‐velocity layer in an unbounded medium using the elastodynamic Green’s function for layered earth to include absorption and dispersion effects. The vector wave displacement solution is developed for a point force at an arbitrary angle with respect to the axis of symmetry of a horizontal layer. The source and detector boreholes are rotated such that the new boreholes are perpendicular to the force to form a new plane which contains a dipping layer and horizontal force. To simulate interwell seismic responses, a modified Clenshaw–Curtis quadrature method for wave‐number integrals of the Bessel function type is developed to evaluate the wave displacement vector in the frequency‐space domain. The model results demonstrate that the presence of a dipping low‐velocity layer produces seismic signatures associated with the attitude of the low‐velocity layer and the angle of ...

A model to relate P‐wave attenuation to fluid flow in fractured tight gas sands

An important issue in reservoir geophysics is to determine whether attenuation/dispersion measurements can be used to predict fluid filled fractures in tight gas sand reservoirs. To address this issue, we assume that fractures in a poroelastic medium can be represented by the permeability, squirt flow and stiffness constants tensors. We also assume that the principal axis of these tensors is aligned with the horizontal x-axis of symmetry. We construct models based on reservoir parameters from the Almond formation of the Siberia Ridge field, Wyoming. We predict attenuation responses by varying the permeability and squirt flow lengths in the plane of the cracks. We also vary the azimuthal and incident angles to predict the appropriate frequency range for detecting fractures. We analyze the sensitivity of the squirt flow length to attenuation and predict the contribution of fracture permeability in low permeability tight gas sands. The modeling results provide inside for detecting fluid filled fractures using acoustic/or seismic measurements in tight gas sand reservoir environments.

Effects of a vertical fluid‐filled fracture on borehole dipole logs

This paper examines the effects of a vertical fluid-filled fracture on borehole dipole logs through a parametric study using a recently developed full wave modeling method. The results indicate that the fracture generates significant flexural waves along the fracture as well as between the fracture and the borehole when they are separate. These new flexural waves are faster than the regular borehole flexural wave. Energy leakage to the fracture is observed. In addition, the fracture reduces direct S wave speed in the direction facing the fracture and reflects body waves. These characteristics are distinct from those of a uniform anisotropic formation.