193 7. Integrated seismic study 7.7 Hydrogeological Study The impedance model (Ip block) can be converted into porosity using an empirical relationship between porosity and acoustic impedance established at well locations. To model porosities, another option is to use porosity at the well locations and interpolate between the wells by means of kriging. Partly due to the small number of wells, this outcome is very smooth and usually seems geologically consistent. More dense information can be integrated to improve the estimation of porosity. As porosity is linked to acoustic impedance, the use of dense seismic acoustic impedance information is relevant. A collocated co-kriging of porosity was thus conducted. The integration of the seismic information was performed using the normalized acoustic impedance as the secondary variable (Bourges et al., 2012). The use of a 3D cube makes it possible to provide 3D imaging of the connectivity of the porous bodies (Mari and Delay, 2011). Core analysis is usually carried out to establish porosity vs. permeability laws (Zinszner and Pellerin, 2007). It has been shown that it is possible to extract new attributes from seismic sections, leading to a better understanding of the distribution of the porous and permeable bodies (Mari and Guillemot, 2012). The attributes are also used to detect the impermeable layers. At well locations, porosity vs. impedance cross plots were used to define linear laws between the two. The cross plots were obtained using density, acoustic velocity, and porosity (NMR) logs recorded in the wells. Two empirical relationships between porosity and acoustic impedance were used to convert the Ip impedance into porosity j depending on the density ρ of the geological formation. The porosity is expressed in % and the acoustic impedance in (m/s).(g/cm3). The density sections with a threshold of 2.48 g/cm3 are used to select the law as follows (equation (7.10)): • for the carbonated formations: ρ ≥ 2.48 g/cm3, j = 45.1097 – 0.0028 Ip, • for the clayed formations: ρ < 2.48 g/cm3, j = 26.7678 – 0.0019 Ip (7.10) Laboratory experiments (Morlier and Sarda, 1971) have shown that the attenuation of a clean formation can be expressed in terms of three structural parameters: porosity, permeability and specific surface. Both theoretical and experimental studies have identified the relation between acoustic attenuation and petrophysical parameters: δ= ϕ π ρ µ ( ) ( ) C S k f f . . 2 . . . 1 3 (7.11) With δ: attenuation (dB/cm), f : frequency (Hz), ρf : fluid density, m: fluid viscosity (centipoise) j: porosity, S: Specific surface (cm2/cm3), C: calibration coefficient and k: permeability (mD). Fabricius et al. (2007) found that the specific surface with respect to grain volume (Sg) is apparently independent from porosity. In an attempt to remove the porosity
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