A shaly sand model is presented that combines the application of the bounds for dispersed clay modeling and Backus averaging technique for laminated clay modeling. The model produces anisotropic elastic moduli. The moduli are easily populated in 3D or along a proposed wellbore trajectory. Significant impact of the elastic anisotropy on 3D geo-mechanics modeling is shown. The model allows to overcome limitations of such popular anisotropic models as ANNIE and M-ANNIE.
Elastic anisotropy modelling has been discussed in a number of publications. The most common case and more easily solvable case is VTI or Vertical Transverse Isotropy case. The case requires five independent elastic constants to describe anisotropic media. The VTI concept has been introduced by Thomson at al. (1950). Recently more complex cases of anisotropy like orthorhombic and general anisotropy tensors modeling have been published (Thanoon et al. 2016). In general, these more complex anisotropic models can be described as a superposition of more simple VTI models with different symmetry axes.
The sources of sonic anisotropy can be stress anisotropy, presence of fractures, thin lamination or texture of the rocks, like grains shape, orientation or mineral intrinsic anisotropy. In the paper we will focus more on the thin lamination as a source of anisotropy, intrinsic anisotropy modeling will be briefly touched as well. The thin lamination is defined by the resolution of a method. The rocks, anisotropic for a sonic tool or seismic can be perfectly isotropic on a core sample scale. Thus, in order to model the anisotropy, the scale of a measurement must be always considered.
Anisotropy caused by thin lamination has been described by Backus (1962) and later reviewed by Berryman (1979, 2003). The paper takes the theory of Backus averaging as a basis and develops the model further, introducing complex clay structure where laminated and dispersed components are present. Techniques, applied in petrophysics, to evaluate dispersed and laminated clay volumes are well described in Thomas et al (1975) and are out of the paper scope.
