Florian Karpfinger

Modeling of wave dispersion along cylindrical structures using the spectral method

Algorithm and code are presented that solve dispersion equations for cylindrically layered media consisting of an arbitrary number of elastic and fluid layers. The algorithm is based on the spectral method which discretizes the underlying wave equations with the help of spectral differentiation matrices and solves the corresponding equations as a generalized eigenvalue problem. For a given frequency the eigenvalues correspond to the wave numbers of different modes. The advantage of this technique is that it is easy to implement, especially for cases where traditional root-finding methods are strongly limited or hard to realize, i.e., for attenuative, anisotropic, and poroelastic media. The application of the new approach is illustrated using models of an elastic cylinder and a fluid-filled tube. The dispersion curves so produced are in good agreement with analytical results, which confirms the accuracy of the method. Particle displacement profiles of the fundamental mode in a free solid cylinder are computed for a range of frequencies.

Spectral-method algorithm for modeling dispersion of acoustic modes in elastic cylindrical structures

A new spectral-method algorithm can be used to study wave propagation in cylindrically layered fluid and elastic structures. The cylindrical structure is discretized with Chebyshev points in the radial direction, whereas differentiation matrices are used to approximate the differential operators. We express the problem of determining modal dispersions as a generalized eigenvalue problem that can be solved readily for all eigenvalues corresponding to various axial wavenumbers. Modal dispersions of guided modes can then be expressed in terms of axial wavenumbers as a function of frequency. The associated eigenvectors are related to the displacement potentials that can be used to calcu-late radial distributions of modal amplitudes as well as stress components at a given frequency. The workflow includes input parameters and the construction of differentiation matrices and boundary conditions that yield the generalized eigenvalue problem. Results from this algorithm for a fluid-filled borehole surrounded by an...

Modeling of axisymmetric wave modes in a poroelastic cylinder using spectral method

Algorithm and code are presented which solve the dispersion equation for cylindrical poroelastic structures. The algorithm is based on the spectral method, which discretizes the underlying wave equations with the help of spectral differentiation matrices and solves the corresponding equations as a generalized eigenvalue problem. The results are illustrated for the case of a fluid-saturated free cylinder with open- and closed-pore boundary conditions on its surface. The computed dispersion curves are in good agreement with analytical results, which confirms the accuracy of the method.

Understanding the acoustic response of deepwater completions

Deepwater production often hinges on the ability to safely complete and effectively draw down a small number of very challenging wells. Chances of success are greatly increased if surveillance tools are available to quickly diagnose downhole conditions and detect potential issues early on. Real-time completion monitoring with acoustic waves (RTCM) has great potential for diagnosing problems in sand-screened deepwater completions. RTCM uses tube waves to detect permeability changes and passive noises to characterize perforation flow. Interaction of a single tube wave with permeable formations in open boreholes is well explained by Biots theory of poroelasticity. However, experimental studies in laboratory models of sand-screened completions reveal that fast- and slow-tube waves behave differently. Further progress in acoustic surveillance requires better understanding on how signatures of fast- and slow-tube waves depend on completion properties. To this end, we simulate the dispersion and attenuation of ...

Computing borehold modes with spectral method

We present algorithm and code that solves dispersion equation for cylindrically layered media consisting of arbitrary number of solid elastic and fluid layers. The algorithm is based on the spectral method which discretises the underlying wave equations with the help of spectral differentiation matrices and solves the corresponding equations as an generalized eigenvalue problem. For a given frequency the eigenvalues correspond to the wavenumbers of different modes. The advantage of this technique is that it is easy to implement especially for cases where traditional root-finding methods are strongly limited or hard to realize, i.e. for attenuative, anisotropic and poroelastic media. We illustrate the application of the new approach using models of a free solid bar and a fluid-filled cylinder. The computed dispersion curves are in good agreement with analytical results, which confirms the accuracy of the new method.

Modeling acoustic response of deepwater completions using spectral method

Deepwater production often hinges on the ability to safely complete and effectively draw down a small number of very challenging wells. Chances of success are greatly increased if surveillance tools are available to quickly diagnose downhole conditions and detect potential issues early on. Real-time completion monitoring with acoustic waves (RTCM) has great potential for diagnosing problems in sand-screened deepwater completions. RTCM utilizes tube waves to detect permeability changes and passive noises to characterize perforation flow. Interaction of a single tube wave with permeable formations in open boreholes is well explained by Biot theory of poroelasticity. However experimental studies in laboratory models of sand-screened completions reveal presence of fast and slow tube waves that behave differently. In this paper, we simulate the dispersion and attenuation of the two tube waves by examining the solutions of Biot’s equations of poroelasticity in cylindrical structures using spectral method.

Spectral method for modeling waves in cylindrical poroelastic structures.

The modeling of propagating modes in poroelastic fluid‐saturated cylindrical structures is important for the interpretation of acoustic and seismic measurements in hydrocarbon wells as well as laboratory measurements on core samples. In order to obtain the velocities of different modes the roots of the appropriate dispersion equation have to be found. This is a very difficult task especially when some layers are represented by poroelastic materials with frequency‐dependent attenuation. A new technique is presented for modeling those modes, which adopts a spectral method to discretize the underlying partial differential equations using Chebyshev differentiation matrices. The corresponding system of linear equations can then be solved as a generalized eigenvalue problem. This means that, for a given frequency, the eigenvalues correspond to the slownesses of different modes. This approach is implemented for an arbitrary number of cylindrical fluid and solid layers as well as poroelastic layers. In addition t...

Modeling acoustic response of permeability variation in deepwater wells using spectral method.

Petroleum production in deepwater oil fields often hinges on the ability to safely complete and effectively draw down a small number of very challenging wells. The success of this operation requires regular completion monitoring, which is most effectively achieved using real‐time surveillance tools. Real‐time completion monitoring with acoustic waves (RTCM) has great potential for diagnosing problems in sand‐screened deepwater completions. RTCM uses tube waves to detect permeability changes and passive noises to characterize perforation flow. Interaction of a single tube wave with permeable formations in open boreholes is well explained by Biot’s theory of poroelasticity. However, experimental studies in laboratory models of sand‐screened completions reveal existence of two tube wave modes: fast and slow, supported by completion and sand screen, respectively. Development of quantitative monitoring methodology of acoustic surveillance requires better understanding on how signatures of fast and slow tube wa...

Modeling of borehold modes using the spectral method

P095 Modeling of Borehole Modes Using the Spectral Method F. Karpfinger* (Curtin University of Technology) B. Gurevich (Curtin University of Technology Australia) & A. Bakulin (Shell International E & P USA) SUMMARY We present algorithm and code that solves the dispersion equation for cylindrically layered media consisting of arbitrary number of solid elastic and fluid layers. The algorithm is based on the spectral method which discretises the underlying wave equations with the help of spectral differentiation matrices and solves the corresponding equations as an generalized eigenvalue problem. For a given frequency the eigenvalues correspond to the wavenumbers of different modes.

Radiation Characteristics of Seismic Waves in Poroelastic Structures

Excitation and radiation of seismic waves in poroelastic media are analyzed. Based on the Fourier transform method we derive the fundamental solutions (Green’s functions) of dynamic poroelasticity. In analogy to the elastodynamic problem, the representation of the results allows identification of near- and farfield terms. It is shown that seismic sources in poroelastic media can be consistently described with moment tensors. The results are illustrated with help of radiation patterns for various source types. Synthetic seismograms of the slow P-wave mode demonstrate the importance of viscous dissipation in seismic modeling of poroelastic structures.