Water Saturation in the
Dual Porosity Model
This illustration, bottom left, shows a schematic of P vs cumulative frequency on probability paper for a water and hydrocarbon system. The 100 per cent water saturated zones form a straight line, and the hydrocarbon intervals deviate from this line and are thus easily recognized.
Bottom right shows the same type of plot for only the water bearing intervals. The mean value of P for water zone, Pmean, is determined from this graph at a cumulative frequency of 50 per cent. An arithmetic average of the P values from the water leg is usually satisfactory, so the probability plot is not necessary.
Having the mean value of P from the water zone allows us to calculate the water saturation of the dual porosity system from the following.
This long evaluation process requires the reading, plotting, and crossplotting of large volumes of data, and requires a large number of calculations. This makes it an ideal computer application and hand calculation is not recommended. A solution for a gas reservoir was never published. In many cases Swf is assumed to be 0.0 (because WOR = 0) so this assumption can be used for gas wells also.
NOTE: This is essentially an "Rwa type" saturation method and relies on the presence of a water zone. In the absence of a water zone, an rchie water saturation solution (Swa) will have to suffice, giving the equivalent of Swe. Swf is not derived from log data. If parameters are unknown, start with VISW =1.0, VISO = 2.0, WOR = 0.0, and Bo = 0.8. This makes Swf = 0.0 during production, which is close to the truth.
zone is fractured:
NOTE: The symbol M is used elsewhere in this book as the cementation exponent for the Archie equation. Mb is used here to indicate the use of Archie for the fractured reservoir case.
log shows the computed log results for a Williston Basin Mississippian
fractured zone. The contribution of fracture related porosity is about
1% porosity, but water saturation is 5 to 10% lower than the analysis
without the fractures. The partitioning coefficient varies and
was solved by iteration.
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