INTRODUCTION
Shaly sandstones have a more complex structure of pore space because of clay minerals than pure sandstones. The rock can be seen as a composite material made of matrix and pore space. The shape, orientation, and connection of the two phases determine the anisotropic elastic properties of the rock. We develop an Anisotropic Dual Porosity (ADP) model to predict the effective elastic properties of shale sandstones. The ADP model is based on a combination of anisotropic formulations of the selfconsistent approximation (SCA), differential effectivemedium (DEM) and anisotropic Gassmann theory. The model divides the total pore spaces into two parts, one associated with sand grains and the other associated with clay minerals which tend to be characterized by smaller aspect-ratios than those associated with sand grains. The elastic moduli of clay-fluid mixture and sand-pore mixture are obtained by the combination of SCA and DEM respectively. Then we apply anisotropic DEM to calculate the elastic moduli of dry shaly sandstones. The P-wave and S-wave velocities of saturated rock are predicted by anisotropic Gassmann model. The model can be applied to predict P-and S-wave velocities of the rock using conventional logs such as density and gamma ray logs. Applied it to the field data, the predicted velocities are in good agreement with the well-log measurements, which indicates the ADP model has a greater value in processing the comprehensive data of shaly sandstones than isotropic dual porosity (IDP) model.
With the oil and gas exploration gradually extending to the complex areas, geological structures become more complex, which induces obvious anisotropic in elastic properties of rock. Establishing an anisotropic effective model for the shaly sandstones is very important. In the past, various empirical and theoretical models (Wyllie et al 1956; Han et al 1986; Marion et al.1992; Berryman et al 1991; Hornby et al 1994; Xu-White 1995) have been proposed to study the elastic properties for isotropic sandstones. However, all of them are used under limited conditions based on different assumptions for practical application. Among them, one very successful model, developed by Xu-White (1995), can be used to predict elastic properties of the clastic rock, but it is only restricted for the isotropic rock. Actually, clastic sediments exhibit transverse isotropic properties with the symmetric axis perpendicular to bedding. These anisotropic elastic properties of rocks are critical in seismic imaging, prestack seismic analysis, and reservoir characterization.
Brown and Korringa (1975) developed the dependence of the elastic properties of a porous material on the compressibility of the pore fluid. In general, the elastic properties of a container of arbitrary shape are related to the compressibility of the fluid filling the cavity in the container. If the material is homogeneous, this equation is similar to the well-known Gassmann equation. For the other elastic properties, Brown and Korringa derived their theory relating the effective elastic moduli of an anisotropic dry rock to the effective moduli of the same rock containing fluid, so that they are often called the anisotropic Gassmann equations.
