Page 78 - Geology of Carbonate Reservoirs

SATURATION, WETTABILITY, AND CAPILLARITY 59

Formation water resistivity, R w , is measured by the spontaneous potential (SP) log.
Resistivity and porosity values from logs are routinely used to calculate S w using

the Archie equation. Archie (1942) found that electric current flowing through a
porous rock 100% saturated with water follows a twisted path through pores and
pore throats such that

m
R o = F × R w ,where F = a/φ
or

F = R o = a
R w φ m
where R o is the resistivity of a porous rock at 100% water saturation, R w is the

resistivity of the water in the pores, F is the Archie formation factor, φ is reservoir
porosity, a is a tortuosity factor that varies from about 0.62 to 1.2, and m is Archie ’ s
cementation factor that can vary from 1.0 to as much as 4.0. The importance of using
an accurate m value is illustrated by the fact that a hydrocarbon saturation of 70%
calculated with an Archie cementation factor of m = 2 (a common choice) will
become zero if an m value of 4 is used (Figure 3.3 ). Values of 3 and 4 are realistic

100

90
m = 5.0 m = 4.0 m = 3.0 m = 2.5
80 m = 2.2 m = 2.0 m = 1.8
S W at varying m values 60 m = 1.6
70

50
40

30
20 Base Case
Porosity = 30%
10

10 20 30 40 50 60 70 80 90 100
S W values with m=2, a=1, and n=2
Figure 3.3 Water saturation ( S w ) at varying values of the Archie cementation exponent ( m )
as the vertical axis and S w at a fi xed value of m = 2, a = 1, and n = 2 in a sample with 30%

porosity. If m = 2, as in the base case, the values of S w are 30% on both the x and y axes.
However, if the true value of m were 4, as in the case of separate vug and moldic pores, the
corresponding S w value would be nearly 100%. In this case the use of m = 2 instead of 4
would cause an error in calculating S w by nearly 70% and would reduce the expected hydro-
carbon saturation from 70% to nearly 0. (Adapted from an illustration in Focke and Munn
(1987) .)