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244    PETROPHYSICS: RESERVOIR ROCK PROPERTIES


                         formation can be expressed as [21]:


                                                                                  (4.66)


                         where Vsh is the laminar shale volume estimated from:






                         hshi and ht are defined in Figure 4.29. Rsd  is the resistivity of  the
                         clean sand layers:


                                                                                  (4.68)


                         where Fsd is the formation resistivity factor of the sand beds. Using
                         Equation 4.35, F,d  is equal to:

                                                                                  (4.69)


                         where @sd is the sand-streak porosity:


                                                                                  (4.70)


                         and @ is the bulk-formation porosity. Thus, the general expression
                         for the  formation resistivity factor for sands laminated with thin
                         shale streaks is:

                                                                                  (4.71)


                         Combining equations 4.66-4.71 and solving explicitly for the water
                         saturation &, one obtains:


                                                                                  (4.72)


                           In practice, laminar shales are considered to have the same average
                         properties (such as Rsh)  as the closest thick shale body, because,
                         in all probability, they have been subjected to the same geological
                         process of deposition. The porous sand beds also are assumed to have
                         the  same effective porosities, permeability,  and water saturation.
                         Equation 4.72 can be  simplified by  assuming that the cementing
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