**Relationships between Porosity and Water Saturation: Methodology to Distinguish Mobile from Capillary Bound Water**

In 1965, Buckles proposed that porosity and irreducible water saturation are hyperbolically related:

Porosity×Irreducible Water Saturation=Constant

The magnitude of the constant was shown to be related to rock type, and indirectly to permeability. The lower the value of the constant, the better the quality of the rock -higher porosity for any given value of porosity.

Extensive analysis of both core data and petrophysical estimates of porosity and irreducible water saturation, from all types of reservoirs worldwide, suggests that Buckles relationship is a unique solution to a more general equation:

Porosity^Q×Irreducible Water Saturation=Constant

The value of the power function, Q, ranges from about 0.8 to about 1.3, with many reservoirs close to 1.0.

Values of Q and the constant are easily derived by plotting the log of porosity vs. log irreducible water saturation, resulting in a straight line of negative slope = Q. Projection of the straight line to a porosity of 1.0 gives the value of the constant.

The cross plot can be used to distinguish rock groupings with different values of Q and the constant. They also can be used to infer the presence of mobile water. Points that fall above the line suggest that the level is not at irreducible water saturation, or is of poorer rock quality.

By comparing, with depth, theoretical irreducible water saturation with petrophysical calculated water saturation, it is possible to categorize changing rock quality and /or presence of mobile water. This can be very useful in deciding which intervals to complete, and to rationalize water production. Examples from a number of reservoirs are presented, both core data and petrophysical calculations of porosity and water saturation.

AAPG Search and Discovery Article #90090©2009 AAPG Annual Convention and Exhibition, Denver, Colorado, June 7-10, 2009