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Application of Full Waveform Acoustic Logging Data to the Estimation of Reservoir Permeability
Frederic Mathieu
Submitted
to the Department of Earth, Atmospheric, and Planetary Sciences in May 1984
in partial fulfillment of the requirements for the degree of Doctor of Philosophy
Abstract
Development of borehole geophysics has recently focused on reservoir characterization. Within this effort, extensive full waveform acoustic surveys have demonstrated a correlation between the occurrence of open fractures and attenuation of Stoneley waves. A relationship is obtained here between fracture permeability and attenuation of Stoneley waves, on the basis of a physical mechanism. This mechanism involves an energy transfer under the form of a fluid flow inside permeable formations. It is applied to the cases of a single open fracture, a multiply-fractured medium and a homogeneous porous medium. In each case a diffusion equation is used to describe the flow inside the formation. Boundary conditions relate the different pressures in order to obtain an expression for the attenuation. Theoretical results show the effects of formation elastic parameters, fluid parameters, frequency, borehole radius, permeability, fracture density, and porosity on attenuation. The single fracture theory is applied to observed attenuation data due to isolated large open fractures in crystalline formations: the theoretical fracture apertures obtained compare favorably to values determined from packer tests.
