Page 191 - Introduction to Petroleum Engineering

178 WELL LOGGING
where ϕ is porosity, A is area, h is net thickness, and S is hydrocarbon saturation.
h
The determination of porosity and saturation is often accompanied by the specifica-
tion of porosity and saturation cutoffs. The thickness of the rock interval that has
porosity or saturation values below the corresponding cutoffs is not included in the
net thickness of the pay interval.

9.8.3 Cross‐Plots
A cross‐plot is a plot of one well log parameter against another. For example, Archie’s
equation for wetting‐phase saturation can be written as

R = φ − m R S − n (9.15)
t
w w
where we assume the coefficient a = 1 in the empirical relationship for formation
resistivity factor F(a,m). Archie’s equation relates electrical conductivity of a sedi-
mentary rock to its porosity and brine saturation. The logarithm of both sides of
Archie’s equation gives
φ
log R =− m log + log R − n logS w (9.16)
w
t
We obtain the Pickett cross‐plot by plotting log R from a resistivity log versus log
t
ϕ from the density log. The Pickett cross‐plot is a visual representation of Archie’s
equation.
Another useful cross‐plot is the plot of sonic travel time from a sonic log versus
formation density from a density log. The resulting cross‐plot indicates lithology.

Example 9.6 Porosity–permeability Cross‐plot

The porosity–permeability (φ − K) cross‐plot relates porosity and permeability.
The φ − K cross‐plot for a well is obtained from core measurements to be
K = 0 0007exp (71 7. φ ) where K is in md and ϕ is a fraction. Use the φ − K
.
cross‐plot to find cutoff porosity for cutoff permeability = 1 md.
answer
×
Solve the φ − K cross‐plot for porosity: φ = 0 139 ln( 1428/K ). Substituting
.
×
.
/
.
cutoff permeability in the φ − K cross‐plot gives φ = 0 139 ln( 1428 1) = 0 10.
In this case, rock with less than 10% porosity would not be considered produc-
tive because the permeability would be too low.
9.8.4 Continuity of Formations between Wells
As shown in Figure 9.8, the continuity of formations between logged wells can be
illustrated with a fence diagram that displays two‐dimensional stratigraphic cross
sections in three dimensions. The fence diagram is prepared by first positioning
well logs in their correct spatial locations. Correlations are then drawn between