M. N. Toksoz

Experimental Study of Flexural Waves In a Fractured Or Cased Borehole Model

The ultrasonic logging is performed with dipole transducers in aluminum and lucite borehole models to study the propagation of flexural waves in a fractured or cased borehole. The experimental results show that the flexural wave is much more sensitive to a horizontal fracture than to a vertical one. The propagation of flexural waves in a borehole with an inclined fracture is related to both the polarization of the flexural wave and the direction of the fracture. The experimental results show that a very strong low-frequency flexural wave can be generated by a dipole source in a cased borehole and that it propagates with the shear wave velocity of the formation. High-frequency waves generated by a dipole source propagate with the compressional wave and flexural wave velocities of the casing. Dipole acoustic well logging could be an effective means for determining horizontal and declined fractures and measuring the formation shear wave velocity in a cased borehole.

Propagation of Flexural Waves in an Azimuthally Anisotropic Borehole Model

Flexural waves generated by a dipole source have been studied theoretically and used to estimate the shear parameters of a formation. The basic principles and main properties of flexural waves propagating in a borehole are reviewed in this paper. A mono/dipole transducer made of a PZT piezoelectric tube is used for laboratory experiments in borehole models. The radiation pattern of the dipole source is measured in a water tank. In order to simulate the hard and soft formations, measurements are performed in borehole models made of aluminum and IUcite, respectively. Experimental results are in good agreement with the theoretical dispersion characteristics. Measurements are also performed with the transducers in an azimuthally anisotropic borehole model made ofPhenolite XX-324. Both fast and slow flexural waves with different velocities are generated by a dipole source in the model. The flexural waves are related to the fast or slow shear waves in the anisotropic material. Experimental results show that the flexural wave splits into a fast and a slow component in an azimuthally anisotropic borehole; therefore, dipole acoustic well logging could be an effective means for estimating a formations anisotropy.

Acoustic Logging In Randomly Stratified Formations

The propagation of borehole acoustic waves in the presence of various types of heterogeneous formations is investigated by modeling them as stratified media with varying velocity depth distributions. Two types of formations are modeled using translational and cyclic random distributions, respectively. Borehole acoustic wavefields for the heterogeneity formation models were simulated using finite-difference techniques. The wavefield modeling results show that the borehole acoustic waves can be significantly affected by the formation heterogeneities. Specifically, the scattering due to heterogeneity can cause significant amplitude attenuation and travel time delay for the transmitted waves. The borehole guided waves are also sensitive to the formation heterogeneity. The effects of the random formation heterogeneity on the borehole acoustic waves are controlled by two factors: the degree of heterogeneity variation and the heterogeneity scale length relative to the wavelength.

Fourth-Order Finite-Difference Acoustic Logs In Transversely Isotropic Formation

In this paper we present a finite difference scheme for seismic wave propagation in a fluid-filled borehole in a transversely isotropic formation. The first-order hyperbolic differential equations are approximated explicitly on a staggered grid using an algorithm that is fourth-order accurate in space and second-order accurate in time. The grid dispersion and grid anisotropy are analyzed. Grid dispersion and anisotropy are well suppressed by a grid size of 10 points per wavelength. The stablility condition is also obtained from the dispersion analysis. This finite difference scheme is implemented on the nCUBE2 parallel computer with a grid decomposition algorithm. The finite difference synthetic waveforms are compared with those generated using the discrete wavenumber method. They are in good agreement. The damping layers effectively absorbed the boundary reflections. Four vertically heterogeneous borehole models: a horizontal layered formation, a borehole with a radius change, a semi-infinite borehole, and a semi-infinite borehole with a layer, are studied using the finite difference method. Snapshots from the finite difference results provide pictures of the radiating wavefields. INTRODUCTION Finite difference method is a very powerful technique in the modelling of seismic wave propagation in inhomogeneous media. There have been some applications of this method to acoustic logging problems. Stephen et al. (1985) directly applied the finite difference method to the second-order displacement formulation of the wave equation. The fluidsolid boundary at the borehole wall was treated explicitly. The velocity-stress finite difference method is widely used after Virieuxs (1986) work. Kostek (1990), using the first order hyperbolic wave equation formulation, discretized on the staggered grid to solve the logging problem with a transducer in the borehole. Randall et al. (1991) al-

Estimation of Reservoir Properties From Seismic Data By Regularized Neural Networks

Summary We present an approach to estimate the reservoir rock properties from seismic data through the use of regularized back propagation networks that have inherent smoothness characteristics, and that thus alleviate the non-monotonous generalization problem associated with traditional networks and help to avoid overfitting the data. We discuss two architectures for setting up the input/output network geometry, the columnar and serialized architectures, compare their merits, and comment on the optimal application of each. We apply the neural network method presented here to a 3D seismic survey in the Shedgum area of the Ghawar Field to estimate the reservoir porosity distribution of the Arab-D zone. The results of the crossvalidation tests indicate that the accuracy of the regularized back-propagation network remains consistent as the network parameters are varied, while that of the traditional network deteriorates as soon as deviations from the optimal parameters occur.

Stoneley Wave Propagation In Heterogeneous Permeable Porous Formations

The propagation of borehole Stoneley waves is strongly correlated with permeability of the formation. Previous studies primarily focused on the situation where the permeability is homogeneously distributed in the formation. In many in-situ situations, however, the permeability distribution of the formation is heterogeneous, due to effects such as a damaged zone around the borehole, random variation of the formation permeability, and layering, etc. This study investigates the effects of formation permeability heterogeneity on Stoneley wave propagation. Using the theory of dynamic permeability and a finite difference technique in cylindrical coordinates, dynamic pore fluid flow in an arbitrarily heterogeneous porous medium surrounding the borehole is modeled. The effects of the flow on the borehole Stoneley waves are calculated. The calculations were performed on various types of permeability heterogeneities. For a formation having random permeability variation with various heterogeneity scale lengths (smaller than the scale of the borehole), the Stoneley wave attenuation and dispersion are only slightly higher than those calculated with a constant permeability (mean value of the random distributions). For a formation with permeability linearly increasing or decreasing away from the borehole, the Stoneley wave behaviors are also similar to those calculated with a constant permeability. Significant effects are found for a damaged zone case where the zone has much higher permeability than the virgin formation. The attenuation exhibits a peak and the Stoneley wave velocity is significantly decreased in the frequency range from 0 to 3 kHz. These features, if measured from the data, can be used as a diagnostic of the borehole condition.

Borehole Stoneley Wave Propagation Across Permeable Structures: Comparison Between Theory And Experiment

The attenuation of borehole Stoneley waves across a permeable structure (e.g., fractures or fracture zone) is correlated with the permeability of the structure. Using a simplified Biot theory, the structure can be modelled as a permeable porous layer intersecting the borehole. In order to study the effect of such a structure on Stoneley waves and to evaluate the theoretical model, we performed laboratory experiments using ultrasonic borehole models. The porous layer model is made of fine-grained sands with high permeability and porosity. The experiments are carried out with three saturant fluids: water, alcohol, and glycerol. The iso-offset Stoneley waveforms are recorded by moving the source and receiver across the porous layer. In this way, robust estimates of Stoneley wave transmission coefficients are obtalned. The experimental transmission coefficients are compared with the theoretical coefficients calculated using the borehole and permeable zone parameters. There is good agreement between theoretical results and experimental results. For low viscosity fluid water and ethyl alcohol, the agreement is very good. For high viscosity fluid, glycerol, the agreement is fair with the experimental Stoneley attenuation higher than the theoretical value.

Elastic Wave Diffraction of a Piston Source And Its Effect On Attenuation Measurements

The radiation of an elastic wave field from a plane piston source is formulated using the representation theorem, in which the Greens function for an elastic half space is employed. On the basis of this formulation, we derive the radiated elastic wave field for both compressional and shear wave sources. We study the diffraction of elastic waves incident on a receiver that is coaxially aligned with the source. We present a procedure in which both numerical and asymptotic techniques are employed to allow us to evaluate the diffraction effects in any frequency range of interest. We compare the elastic diffraction with the acoustic diffraction and find that they are different in the near field of the piston source due to the coupling between shear and com pressional components in the elastic case. In the far field, however, the elastic diffraction approaches the acoustic diffraction. With the help of ultrasonic laboratory measurements, we test the theoretical results and find that the theory and experiments agree well. An important result of this study is that in attenuation measurements with pulse propagation techniques where spectral ratio relative to a standard sample or ratio of samples of the same material but of different lengths is used, it is necessary to correct for diffraction effects. In the attenuation measurement using spectral ratio of a sample and a standard reference sample, the attenuation can be overestimated, while in the attenuation measurement using a spectral ratio of samples of different lengths, the attenuation can be significantly underestimated, if corrections for diffraction effects are not made.