Page 169 - Petrophysics
P. 169

142    PETROPHYSICS: RESERVOIR ROCK PROPERTIES


                    (2)  the cross-sectional area of each tube, Aa, is constant; and
                    (3) the  fluid  path  and  the  electric  current path  are  same  and  the
                       true conductivity, i.e., the reciprocal of  resistivity,  of  the bundle
                       of tubes is:





                    where C, is the water conductivity and m  is the cementation factor.
                    Because the apparent conductivity  Ca  of a block having a cross-sectional
                    area A and length L is related to the true conductivity C&  by the following
                    expression:



                                                                                 (3.71)


                    where A is the cross-sectional area of  all tubes, then


                                                                                 (3.72)


                    assuming  that  the  bundle-of-tubes  model  contains  n  tubes,  the
                    conductivity of the ith tube (Ci) can be defined as:



                                                                                 (3.73)


                    where  is the length of the ith tube.
                      The porosity of  the tube is unity. The apparent conductivity of  the
                    block is the sum of the individual conductivities of all the tubes. Thus:


                                                                                 (3.74)


                    From the assumption that A2 is constant:


                                                                                 (3.75)


                    By definition:



                                                                                 (3.76)
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