59 2. Surface geophysical methods • The attenuation δ depends on the structure of the rock (i.e. pore geometry). • The attenuation δ can be expressed in terms of three structural parameters: porosity, permeability, and specific surface. A law which fits their experimental results has been established: δ ϕ π ρ µ = CS kf f 2 1/3 (2.3) with: δ: attenuation (dB/cm), f: frequency (Hz), ρf: fluid density, μ: fluid viscosity (centipoise), ϕ: porosity, S: Specific surface (cm2/cm3), C: calibration coefficient, k: permeability (mD, 1 mD = 10–15 m2). Figure 2.2 Permeability Kf versus granulometry and formation types. After Dominique Chapellier (2001a). Figure 2.3 is an example of laboratory measurements on sandstone core plugs. The upper part of the figure shows the results obtained on cores with a constant specific surface, the lower part on cores with a variable specific surface, the specific surface being estimated based on the average pore radius measurement. From equation (2.3), Mari et al. (2012) derived an indicator of permeability Ik-Seis, useable with seismic or acoustic data Ik-Seis = ( ) = ( ) ϕδ ϕ / / S f SQ f 3 3 (2.4) with f: P-wave frequency, Q: quality factor, δ: attenuation, S: specific surface, ϕ: porosity. It is necessary for computing the permeability from equations (2.3) or (2.4) to measure the attenuation of the formation and to calculate the effective specific surface of the formation.
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