Page 174 - Petrophysics

PERMEABILITY-POROSITY RELATIONSHIPS 147

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4 ,-.. . .. - .- - .~~ . . . .- . . . . . . . . . ... .
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I
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3.5
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E I
‘ ~ , , , , ,
Potential Fracture
‘‘Zone
1 2 3 4 5 6 7 8 9 10
Secondary Porosity Index @PI%)
Figure 3.33. Estimation of the value of the inter-math Archie factor (mm) from
Archie factor (m) and seconday porosity index (i32) cross-plot [43J
where the coefficients a1 and a2 can be determined according to the
following procedure:

(a) Obtain values of m and 0 from well logs and k from core analysis.
(b) Determine the cementation factor of the matrix mm from:

(3.95)

where Is2 is the secondary porosity index, SPI, i.e., - @SL, where Qt
and QSL are, respectively, the total porosity and the sonic log porosity.
Figure 3.33 shows how to obtain mm from a plot of the cementation
factor m versus SPI. To compensate for the effects of fractures, data
points for Is2 < 1 % are not used to obtain m,. Inasmuch as the curve
is not linear, one needs to be careful when extrapolating the curve
to Is2 = 1 to obtain mm on the m axis.
(c) Determine the value of the effective pore radius rpe from
Equation 3.93.
(d) Calculate the tortuosity from Equation 3.78.
(e) Establish a data bank for rpe and z, and plot log rpe versus ,h.
(0 Draw the best-fit straight line. The general form of this line is given
by Equation 3.95.
(g) Determine the correlation coefficient a2 from the rpe log-axis at
,h=Oandal fromthe,haxisatrp,= 1.

DIRECTIONAL PERMEABILITY

In homogeneous reservoirs, permeability is assumed to be the same
in all directions. However, in heterogeneous reservoirs, permeability in