Prediction of sonic velocities in shales from well logs is important for seismic to log ties if the sonic log is absent for a shaly section, for pore pressure anomaly detection, and for data quality control. An anisotropic differential effective medium (DEM) was used to simulate elastic properties of shales from elastic properties and volume fractions of silt and wet clay (a hypothetical composite material that includes all clay minerals and water). Anisotropic elastic coefficients of the wet clay were assumed as a first-order approximation to be linearly dependent on wet clay porosity (WCP). Here, by WCP we mean a ratio of a pore volume occupied by water to a total volume of the wet clay. Effects of silt inclusions on elastic coefficients of shales were taken into account by using the anisotropic differential effective medium model. Silt inclusions were modeled as spherical quartz particles. Simulated elastic coefficients of shales were used to calculate compressional and shear velocities, and these were in a good agreement with the sonic velocities observed on a test data set from an offshore Mid-Norway well penetrating a 500-m vertical section of shale. To further study the elastic properties of wet clays, elastic coefficients calculated from compressional and sonic velocities measured in shales were inverted for vertical profiles of wet clay elastic coefficients. Analysis of these coefficients found that in the well considered, the increase in elastic coefficients of shales was controlled by the increase of silt fraction with depth. Elastic coefficients of wet clay found no increase with depth. The inverted elastic moduli of wet clay found much stronger correlation with WCP than do the moduli of shale. This confirmed the hypothesis that silt fraction is one of the key parameters for the modeling of elastic properties of shale.

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