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Open Access Publications from the University of California

Scholarly Works (5 results)

  • Thesis
  • Peer Reviewed
UC Berkeley Electronic Theses and Dissertations (2010)

The present work analyzes seismic attenuation due to wave-induced flow in complex poroelastic materials containing an arbitrary amount of

heterogeneity and fully or partially saturated with a mixture of fluids.

In the first part, two distinct finite-difference (FDTD) numerical schemes for solving Biot's poroelastic set of equations are introduced. The first

algorithm is designed to be used in the seismic band of frequencies; i.e., when the permeability of the medium doesn't depend on frequency. The

second algorithm accounts for viscous boundary layers that appear in the pores at high frequencies (in this case, the permeability depends on

frequency) and can be used across the entire band of frequencies.

An innovative numerical method is presented in the second part allowing computation of seismic attenuation due to wave-induced flow for any

poroelastic material. This method is applied to study the attenuation associated with different classes of materials saturated with a single

fluid (water). For a material having a self-affine (fractal) distribution of elastic properties, it is demonstrated that frequency

dependence in the attenuation is controlled by a single parameter that is directly related to the fractal dimension of the material. For

anisotropic materials, a relation is established between the attenuation levels associated with waves propagating in different directions and

the geometrical aspect ratio of the heterogeneities present within the material.

The third part concerns the study of attenuation associated with materials having a homogeneous solid skeleton

saturated with a mixture of immiscible fluids. The special case where the distribution of fluids is the result of an invasion-percolation process is

treated in detail.

Finally, the last part presents a novel experimental setup designed to measure fluctuations of the elastic properties in

real rock samples. This device performs automated micro-indentation tests at the surface of rock samples and produces maps of the spatial

distribution of Young's modulus. These maps are then used in combination with the aforementioned numerical methods to compute accurately the

attenuation as a function of frequency associated with real rock samples.

    Cover page: Computing the Seismic Attenuation in Complex Porous Materials
    • Article
    • Peer Reviewed
    UC Berkeley Previously Published Works (2014)
      Cover page: A Fast Algorithm for Invasion Percolation
      • Article
      • Peer Reviewed
      UC Berkeley Previously Published Works (2015)
      A microindentation scanner is constructed that measures the spatial fluctuation in the elastic properties of natural rocks. This novel instrument performs automated indentation tests on the surface of a rock slab and outputs 2-D maps of the indentation modulus at submillimeter resolution. Maps obtained for clean, well-consolidated, sandstone are presented and demonstrate the capabilities of the instrument. We observe that the elastic structure of sandstones correlates well with their visual appearance. Further, we show that the probability distribution of the indentation modulus fluctuations across the slab surfaces can be modeled using a lognormal probability density function. To illustrate possible use of the data obtained with the microindentation scanner, we use roughly 10 cm × 10 cm scans with millimeter resolution over four sandstone planar slabs to numerically compute the overall drained elastic moduli for each sandstone sample. We show that such numerically computed moduli are well modeled using the multicomponent form of the Hashin-Shtrikman lower bound that employs the observed lognormal probability distribution for the mesoscopic-scale moduli (the geometric mean works almost the same). We also compute the seismic attenuation versus frequency associated with wave-induced fluid flow between the heterogeneities in the scanned sandstones and observe relatively small values for the inverse quality factor (Q-1<10-2) in the seismic frequency band 102 Hz
        • Article
        • Peer Reviewed
        UC Berkeley Previously Published Works (2006)
          Cover page: Acoustic Attenuation in Self-Affine Porous Structures
          • Article
          • Peer Reviewed
          UC Berkeley Previously Published Works (2022)
          During drainage, as a voxel of porous material is being actively invaded prior to percolation, the invading nonwetting fluid cannot be transmitted to the neighboring downstream voxel until a critical nonwetting saturation (Snc) is reached. This occurs when the invading fluid forms a percolating path across the voxel. We present novel laboratory observations of gravitationally stable, air/water drainage in thin bead packs, with 2D saturation fields monitored at high spatial and temporal resolution using transmitted light. We also present Invasion Percolation simulations. Both show that Snc has a strong dependence on capillary number (Ca), Bond number (Bo), and voxel size (Lz). We propose a percolation model that describes the functional form of Snc(Bo,Ca,Lz). We also produce a new theoretical model for the macroscopic capillary pressure function Pc(Sw,Bo,Ca,Lz), where Sw is the saturation of wetting fluid in the voxel.
            Cover page: Stable drainage in a gravity field
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