Page 168 - Petrophysics
P. 168

PERMEABILITY-POROSITY RELATIONSHIPS              141


                         in the outer layers of curved beds. Murray applied this approach to the
                         Spanish pool in McKenzie County, North Dakota, and demonstrated a
                         good coincidence between areas of  maximum curvature and areas of
                         best productivity.
                           The flow of  fluid through porous media is directly analogous to the
                         flow of  electricity. McGuire and Sikora used this analogy and showed
                         that the width of artificial fractures is much more important than their
                         length in affecting communication among natural fractures [41]. Stearns
                         and Friedman summarized that the permeability of a naturally fractured
                        formation can  be  expected  to  be  greatest  where  the  reservoir bed
                         contains wide, closely spaced, smooth fractures oriented parallel to the
                        fluid pressure gradient [42].
                           Fracture permeability cannot be  estimated directly from well logs.
                        The  modern  trend  is  to  combine  core-derived  parameters  with
                         computer-processed  log  data  to  establish  a  statistical  relationship
                         between  the  permeability  of  the  matrix-fracture system and various
                         parameters, such as porosity and irreducible water saturation. With such
                         a  relationship established,  the  formation’s petrophysical parameters,
                         including permeability distribution, can be deduced from log data alone
                         in wells or zones without core data. In carbonate formations, however,
                         where structural heterogeneity and textural changes are common, and
                         only a small number of  wells are cored because of  the difficulty and
                         cost of  the coring, the application of  statistically derived correlations
                         is extremely limited. Watfa and Youssef developed a sound theoretical
                         model that relates directly to the flow of path length (tortuosity), pore
                         radius changes, porosity, and cementation factor m  [43]. This model
                         assumes that:

                         (1) a porous medium can be represented by a bundle of tubes, as shown
                            in Figure 3.29;


                                                  Cube Length = L
                                           k                        J















                                         Figure 3.29. A bundle-oftubes model [43J.
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