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30    Applied Petroleum Geomechanics


             2.7.3 Empirical methods for Biot’s coefficient               76
             2.7.4 Biot’s coefficient estimate from well logs             78
          References                                                     80

          Abstract
             Rock physical and mechanical properties are introduced, and methods to obtain these
             properties are discussed. Rock properties, including bulk density, porosity, perme-
             ability, sonic velocity, transit time, Young’s modulus, Poisson’s ratio, and Biot’s coeffi-
             cient are the fundamental inputs for geomechanical modeling and geological
             engineering design. The anisotropy and stress-dependent behaviors in rock properties
             are addressed to better characterize the rock, and these are particularly important for
             hydraulic fracturing design in unconventional plays. The fluid impact on sonic ve-
             locities is also investigated, and the slowdown of the compressional velocity by gas-
             bearing formation is studied. Empirical equations and new correlations for obtaining
             rock properties are examined with considerations of anisotropy for both conventional
             and unconventional reservoirs. Dynamic and static properties and their relationships
             are also evaluated.

          Keywords: Anisotropy; Biot’s coefficient; Bulk density; Dynamic and static relationship;
          Poisson’s ratio; Porosity and permeability; Rock properties; Sonic velocity; Young’s
          modulus.


          2.1 Rock density

          2.1.1 Bulk and matrix densities
          Rock density, or bulk density, is a measure of mass of the rock contained in
          a given unit volume. It is a very important parameter for obtaining the
          overburden stress. Rock bulk density is controlled by densities and volu-
          metric fractions of components of which the rock is composed. For a
          porous rock it is dependent on not only the density of each solid matrix but
          also the density of each pore fluid as well as fluid saturation. Therefore, bulk
          density has a strong correlation with minerals, fluids, and porosity, which
          can be obtained from the following equation:
                                 r ¼ð1   fÞr þ fr   f                  (2.1)
                                  b
                                             m
          where r b is the bulk density of the rock; r m is the matrix or mineral density;
          f is the porosity of the rock; r f is the fluid (water, oil, or gas, etc.) density in
          the rock. If the fluid is water, r f is the density of formation water.
             The density of formation water is a function of water salinity, tem-
          perature, and content of dissolved gases. Normally, it varies from 1.0 to
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