Pore structure model for elastic wave velocities in fluid‐saturated sandstones

Abstract

[1] During hydrostatic compression conducted within the elastic regime, P and S-wave velocities measured on porous rock samples generally increase with pressure and reach asymptotic values at high pressures. The increase in velocities can be attributed to the gradual closure of compliant cracks, in which case the high-pressure velocities reflect only the influence of the stiff, non-closable pores. A procedure is presented to extract the complete pore aspect ratio distribution from the pressure dependence of dry velocities, assuming that the rock contains a distribution of cracks with different aspect ratios, and one family of stiff pores having an aspect ratio that generally will lie between 0.01 and 1. The model is able to invert successfully many sets of experimental data on dry sandstones taken from the literature. The pore aspect ratio distribution inverted from dry data can then be used to predict saturated velocities as functions of pressure, by introducing fluid into the pores. For ultrasonic velocity measurements that are performed at high frequencies in the laboratory ($ MHz), the predictions of saturated velocities using effective medium theories match well the experimental data for a good number of sandstone data sets. The saturated velocities thus predicted are always more accurate than those predicted from the Gassmann relations, which underpredict the saturated velocities by a large amount. These results are only weakly dependent on the choice of the effective medium theory.Citation: David, E. C., and R. W. Zimmerman (2012), Pore structure model for elastic wave velocities in fluid-saturated sandstones,

Dynamic bulk and shear moduli due to grain-scale local fluid flow in fluid-saturated cracked poroelastic rocks: Theoretical model

“…Each crack is characterized by individual porosity ϕ c i , aspect ratio γ i and volume v c i . Stiff pores are assumed to be spheroidal pores but with aspect ratios greater than 0.01 (Walsh, 1965;David and Zimmerman, 2012). For simplicity, we assume that stiff pores have the uniform aspect ratio γ p and the uniform volume v p i , but can vary in orientation.…”

“…Following David and Zimmerman (2012), we assume that the pore space of the rock consists of a distribution of cracks (compliant/soft pores) with different aspect ratios and one family of stiff pores having uniform aspect ratio. The stiff pores and cracks form the whole interconnected pore space.…”

“…It is more appropriate to estimate the unrelaxed effective elastic moduli using effective medium theory. Recently, David and Zimmerman (2012) developed a procedure to extract the pore aspect ratio distribution from the dry velocities. Their results showed that for ultrasonic velocity measurements, the predictions of saturated velocities using Mori-Tanaka (MT) scheme (Mori and Tanaka, 1973;Benveniste, 1987) and differential effective medium (LeRavalec and Guéguen, 1996) matched well the experimental data for a good number of sandstone data sets.…”

A Poroelastic Description of Permeability Evolution

“…That is, a few long cracks may strongly affect the rock behavior. David and Zimmerman (2012) reported an order of magnitudes higher aspect ratios for Vosgas and Fontainbleau sandstone, albeit the samples were subjected to a high confining pressure of 280 MPa.…”

Clay squirt: Local flow dispersion in shale-bearing sandstones

“…Several authors have ascribed the dispersion in sandstone to "squirt flow": pore-pressure gradients caused by deformation of compliant pores embedded in the stiffer framework of the sandstone (i.e., microcracks, grain boundaries, etc.) (Mayr and Burkhardt, 2006;Gurevich et al, 2010;Paula and Peruvhina, 2012), and according to this concept, the stress dependency of the elastic moduli of dry sandstone should delimit the possible dispersion in the water-saturated state (Mavko and Jizba, 1991;Shapiro, 2003;Gurevich et al, 2010;David and Zimmerman, 2012). In spite of this theory, dispersion in shaly sandstones has been frequently found to exceed the bounds for dispersion based on the measured stress dependency (Marketos and Best, 2010;Paula and Peruvkhina, 2012).…”