We propose an anisotropic model that provides independent moduli for the vertical transverse isotropy (VTI) case and can be rotated to the tilted transverse isotropy case (TTI). The model assumes that the anisotropy is caused by the sand and clay layers’ lamination or the lamination of contrasting elastic moduli of any other origin. The model calibration process includes stochastic inversion of the log based acoustic impedance, and Vp/Vs ratio to compute the porosity, laminated and dispersed clay volume.
Splitting the total clay volume into dispersed and laminated parts is the basis of the model. Dispersed clay modeling is done using a combination of the Upper and Lower Hashin-Shtrikman bounds, and Reuss bound. Laminated clay is incorporated using the Backus averaging technique. Once obtained, VTI elastic moduli matrix can be rotated to the borehole frame using the rotation matrix. Six plots model calibration and three implemented independent methods of laminated and dispersed clay volumes estimation techniques are presented and discussed. Stochastic inversion allows to estimate total porosity, dispersed and laminated clay volumes using log based acoustic impedance and Vp/Vs ratio as inputs. In hydrocarbon bearing intervals this technique estimates hydrocarbon effect and corrects acoustic impedance and Vp/Vs ratio for the hydrocarbon presence. The correction is done by gradually decreasing hydrocarbon saturation and estimating data point shift till convergence between the model and corrected data is achieved.
The model has been tested on datasets from wells located in different parts of the world and from different depositional environments. The calibration process involves model fitting using six cross-plots and three different methods of the dispersed and laminated clay volumes estimations. These three methods are Thomas-Stieber, shear moduli versus total clay volume, and inversion process. The model is sensitive to the total clay volume estimation and selection of the clay component elastic moduli. The hardness of the sand component can be adjusted by the cement in the pore space minimization process. The comparison of the three methods based on dispersed and laminated clay volumes allows to calibrate elastic moduli and total clay volume. A number of applications have been tested for the model. These applications include anisotropic elastic moduli estimates, Thomsen weak anisotropy parameters evaluation, inversion-based porosity and clay volume analysis, and saturation analysis. This paper presents a novel dispersed and laminated clay rock-physics model and its calibration technique. The model opens several opportunities for the acoustics anisotropy based petrophysical and geomechanical tasks, including new applications for the quantitative seismic inversion (QI seismic).
