| The vertical and horizontal mechanical properties of a VTI medium can be obtained from five stiffness coefficients (C33, C44, C66, C13, and C12) using velocities at different angles and density measurements. However, when using well log data for vertical wells, only three out of the five elastic constants can be calculated. The sonic tool cannot measure C13 and C12; thus, different empirical models have been proposed to determine them, making assumptions that do not provide completely accurate results. In this paper, a new empirical model is introduced to obtain the stiffness coefficients. Datasets of dynamic core measurements of shales from different parts of the world are compiled and later, analyzed. The method was based on establishing correlations for the stiffness coefficients, both for each formation and for all formations put together. There were two sets of correlations---those with C 33 as the dependent variable, and those with C44 as the dependent variable. M-ANNIE assumptions were also obtained. Because Stoneley slowness is difficult to measure and can cause errors in the calculations, it was not used.;Finally, isotropic and VTI minimum horizontal stresses are calculated and compared using well log data from the Bakken formation. VTI minimum horizontal stress calculations used the M-ANNIE model and the correlations determined for the Bakken formation core data. Generally, the new model provides results similar to M-ANNIE predictions, and better results than the isotropic and ANNIE models. Although the proposed method produces results similar to those of the M-ANNIE model, which is widely used as a reference model throughout the industry, the proposed method is different in that it can be used under a different set of circumstances when some inputs are available, and others are not. This method reduces the underestimation of minimum horizontal stress made by the isotropic and ANNIE models as well. |
