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Velocity and Attenuation Dispersion Relations for the Effective Biot Double Porosity Model: Total Field Formulation
- Publisher: European Association of Geoscientists & Engineers
- Source: Conference Proceedings, Near Surface 2010 - 16th EAGE European Meeting of Environmental and Engineering Geophysics, Sep 2010, cp-164-00137
- ISBN: 978-90-73781-88-7
Abstract
Two approaches – the host phase fields and the total fields - have been applied to formulate the effective Biot governing equations from the double-porosity, dual permeability model. The host phase formulation, given previously by Pride and Berryman (2003) is made under the assumption that the volume fraction of phase 2 (the inclusions) is very small. The total-field formulation is new and has no such limitation and gives rise to more general equations which cover the host phase field approach as a special case. We have computed the phase velocity and attenuation dispersion curves for the fast and slow Biot compressional waves using both approaches for a sample rock of water-saturated sandstone having sand as the inclusions. The curves are consistent across a wide frequency range for the fast P wave but deviate at higher frequencies and for large volume fractions of the inclusions .For the slow P wave there is a significantly increasing discrepancy in wavespeed as frequency increases, even for low inclusion concentrations