Pore geometry and elastic moduli in sandstones

John Jianlin Zhang, Laurence R. Bentley

Pore geometry is a difficult parameter to quantify, but it affects the elastic moduli in a fundamental way. The uncertainty in elastic moduli is to a large degree due to the uncertainty in pore geometry. The authors inverted the velocity measurements of ninety-seven sandstone samples for the pore aspect ratio spectra. It was found that the porosity of round pores is in direct proportion to total porosity, and that the porosity of cracks is small and varies randomly for a large set of samples from different geological backgrounds but may be linearly related to total porosity for a small subset from some specific area. This pore geometrical model is central to predicting the elastic properties in sandstones. The dry elastic moduli at a given porosity vary chiefly due to cracks and the variability increases with decreasing porosity. This causes the cross-plot of dry elastic moduli versus total porosity to scatter in a triangular form, and is also responsible for higher stress sensitivity of low-porosity sandstones. The linearity between total porosity and elastic moduli results from strong correlation between crack porosity and total porosity, and it becomes more pronounced at high effective pressure or at saturation with a less compressible fluid such as water. The Vp/Vs ratio in wet sandstones is affected by the Vp/Vs ratio of rock solid and pore geometry, but the former has far more influence, which may provide the rock physics basis for lithology identification using the Vp/Vs ratio. Vp and Vs are correlated very well for both dry and wet sandstones. The two straight lines are separate at low velocities but merging toward high velocities. In addition, clay content has been found with little relationship to pore geometry and with some connection to the elastic moduli of rock solid.