By examining wireline data from Woodford and Wolfcamp gas shale, we find that the primary controls on the elastic-wave velocity are the total porosity, kerogen content, and mineralogy. At a fixed porosity, both Vp and Vs strongly depend on the clay content, as well as on the kerogen content. Both velocities are also strong functions of the sum of the above two components. Even better discrimination of the elastic properties at a fixed porosity is attained if we use the elastic-wave velocity of the solid matrix (including kerogen) of rock as the third variable. This finding, fairly obvious in retrospect, helps combine all mineralogical factors into only two variables, Vp and Vs of the solid phase. The constant-cement rock physics model, whose mathematical form is the modified lower Hashin-Shtrikman elastic bound, accurately describes the data. The inputs to this model include the elastic moduli and density of the solid component (minerals plus kerogen), those of the formation fluid, the differential pressure, and the critical porosity and coordination number (the average number of grain-to-grain contacts at the critical porosity). We show how this rock physics model can be used to predict the elastic properties from digital images of core, as well as 2D scanning electron microscope images of very small rock fragments.
The differential Kuster–Toksöz rock physics model for predicting S-wave velocity