Hydraulic and acoustic properties as a function of porosity in Fontainebleau Sandstone

Laboratory measurements have been made of the permeability (k), free porosity (ϕL), compressional velocities (VP or VE), and compressional attenuations (QP or QE) in Fontainebleau sandstone over a continuous range of porosities ϕ from 3 to 28%. This large variation was achieved without any composition change: Fontainebleau sandstone is made of fine quartz grains with regular grain size (≈250 μm). Permeability was measured with a falling head permeameter. Velocities and attenuations were obtained either through an ultrasonic experiment for frequencies around 500 kHz or through a resonant bar technique experiment for frequencies around 5 kHz and in both cases with varying water saturation. The results show an excellent correlation between permeability k and total porosity ϕ for all our samples. For low porosities (ϕ = 3% to 9%), permeability (in millidarcies) is 2.75×10−5(ϕ)7.33, while for high porosities (ϕ = 9% to 28%), permeability k (in millidarcies) is given by 0.303(ϕ)3.05. The correlation is also excellent between free porosity and total porosity. On the other hand the correlation between acoustic properties and total porosity is not as clear as for hydraulic properties whatever the frequency (500 kHz or 5 kHz) or the water saturation. On the average, velocity decreases, and attenuation roughly increases with increasing total porosity. Velocity and attenuation values are related to the variation of grain contact structure, and two samples with the same porosity and permeability may exhibit different velocities and attenuations. The clear correlation between hydraulic properties and porosity is related to constant grain size, while the lack of correlation for acoustic properties emphasizes the importance of the microstructure.