Page 248 - Petrophysics 2E

FORMATION RESISTIVITY FACTOR 22 1

CORRELATIONS BETWEEN FR AND CEMENTATION

The degree of cementation of sand particles depends on the nature,
amount, and distribution of numerous cementing materials including
silica, calcium carbonate and a variety of clays. The less-cemented
sands normally have higher porosities and, from Equation 4.37, lower
resistivity factors. As the sand becomes more cemented, @ decreases and,
therefore, FR increases. Archie derived, from laboratory measurements
of the formation resistivity factor FR with porosity, a relation between
these two variables, which seems to have survived the test of time and
usefulness [2]. The general form of this expression is:

1
FR = - (4.38)
om

The exponent m, which is referred to as the “cementation” factor, is a
function of the shape and distribution of pores. It is determined from
a plot of the formation resistivity factor FR versus porosity on a log-log
graph. Such a plot generally can be approximated by a straight line having
slope m. In chalky rocks and compacted formations, m is approximately
equal to 2. For compact limestones, which are very highly cemented
rocks, the value of m may be as high as 3. It is important to emphasize
that these empirical values of m very often differ from well to well in the
same or like formations. Where the value of m cannot be determined, the
following equation commonly referred to as the Humble formula, can be
used to estimate the formation factor:

0.62
FR = -
$2.15

or
FR = 7 (4.3913)
0.81

Whereas the Humble formula is satisfactory for many types of rocks,
better results can be obtained using the following generalized form of
the Humble formula:

(4.40)

where values of the constant a and the cementation factor m depend on
the types of rocks. The proper choices of a and m are best determined
by laboratory measurements.