Page 240 - Petrophysics 2E

FORMATION RESISTIVITY FACTOR 213

where: C, = concentration of NaCl solution, ppm.
ppm = mass of NaCl per lo6 mass units of solution.
p25 = density of NaCl solution at 25"C, g/cm3.
58,443 = molecular mass of NaCl, g.

The value of the density of the NaCl solution as a function of the
concentration Csm is given by:

p25 = 0.99708 + 0.040785 Csm - 9.5818 x lo-* C:m
+ 5.1208 x lop5 C&, (4.16)

To convert a given value of concentration in ppm to mol/L, and then
calculate the resistivity Rw25, one must employ Equations 4.15 and 4.16
in an iterative procedure:

Substitute C, and p25 = 1 into Equation 4.15, and calculate a value
of Csm.
Substitute this value of Csm into Equation 4.16, and calculate a new
density value.
Substitute this value of density into Equation 4.15, and calculate a new
value of Csm. Repeat these three steps until successive iterations yield
~ ~ < 2io-* g/cm3.
5
Select the correlation constants from Table 4.3 for the range
in concentration that includes the value of Csm calculated in
Step 3, and then calculate the concentration correlation function
X, (Equation 4.13).
Substitute this value of X, into Equation 4.12 and calculate the
resistivity Rw25.
Use Arp's Equation 4.14 to convert this resistivity at 25°C to
a resistivity at reservoir temperature Rw~.

An alternative method to Steps 1, 2, and 3 is to use the following
equation to convert Csp to Csm:

17.061
Csm = (4.17)
106
-- 0.69787
CSP

Equation 4.17 was obtained by combining Equations 4.15 and 4.16
and solving explicitly for Csm. This equation assumes the products
164 x Csm and 8.76 x Czm are negligible, For the maximum
value of Csm = 5.35 moVL these two terms are 8.77 x and