Page 236 - Petrophysics 2E

FORMATION RESISTMTY FACTOR 209

resistivity, Arp's formula can be used:

(4.7)

where Rw~l and Rw~2 are, respectively, the water resistivities (ohm-m)
at formation temperature (OF) TI and T2. In freshwater, the constant 6.77
in Equation 4.7 is not necessary. The temperatures T1 and T2 are expres-
sed in OF. If 75°F is used as a reference temperature, Equation 4.7 can be
used to find water resistivity at any reservoir temperature T:

The value of Rw75 may be estimated from the following equation [4]

1
Rw75 = + 0.0123 (4.9)
2.74 x 10-4~::~~

Inasmuch as the slopes of the salinity lines in Figure 4.4 are not constant,
and these lines are not perfectly straight, the following equation may be
derived [ 31 :

(4.10)

where:

(4.11)

and

XH is a function of salinity and compensates for the change in slope
and accounts for the curving or deviation of the constant salinity lines
below 75°F and above 30O0F. Equation 4.10 yields more accurate values
of Rw than Equation 4.7, for all ranges of salinity and temperature (see
also Tables 4.1 and 4.2). Table 4.2 is very convenient for programming
purposes.

EXAMPLE

The chemical analysis of an oil reservoir brine yielded the following
ionic concentrations: 1 1,000 ppm Na+, 15,ooO ppm C1,8,000 ppm Mg2+,