Rwa – Rw apparent
Rwa or Rw apparent is used to estimate the value of Rw, the resistivity of the waters filling the pores of a reservoir rock. Rwa is derived from the most basic concepts of well log analysis, the formation resistivity factor, F and water saturation, Sw.
Archie determined that for uniform porosity F = Ro/Rw = Ro’/Rw’. That is, for a given rock having pores filled with waters of resistivity Rw, the ratio of the rock resistivity Ro to Rw was a constant. If one changes Rw and re-measures Ro, the ratio of the new values would equal F. Ro is the total resistivity of the rock, 100% saturated with waters having resistivity of Rw.
Through subsequent experimentation, it was found that F = Ro/Rw = a / phi^m or that F is a function of porosity (phi in fractions) using constant ‘a’ and ‘m’ where ‘m’ is called the cementation exponent and ‘a’ is constant determined empirically.
It was also found that the apparent water saturation of a rock could be found from the following expression:
Water Saturation = Sw = (Ro / Rt)^1/n
where n=the saturation exponent, Ro is the total resistivity of the rock,100% filled with water and Rt is the measured resistivity of the target zone.
So by substitution, Sw = (Ro / Rt)^1/n = (F*Rw / Rt)^1/n = a*Rw /(phi^m)* Rt)^1/n
Or Sw = (Rw /Rwa)^1/n
where Rwa= a / (phi^m * Rt)
Determination of Rw from Rwa
For a given uniform porosity zone with an assumed water leg, calculate Rwa. In the water zone, the minimum Rwa will approach the actual Rw, which can then be used to calculate apparent water saturations for other intervals within the uniform porosity zone.
Typically, for first pass quick look calculations, n = 2.0, a = 1 and m = 2.0
If sands are being analyzed and pore geometry considerations are secondary to getting an ‘answer’ use a = 1.0 and m = 2.15
In sands, the rounder the grains and the better the sorting and the looser the packing of the grains the lower the value of ‘m’ with values from 1.5 to 2.0 not atypical.
In carbonates using a = 1.0 is not a bad assumption. ‘m’ will usually vary from 2.0 to 3.0
In the Western Canadian Sedimentary Basin (WCSB) typical ‘m’ would vary as follows:
Mississippian: m = 2.0
Wabamun: m = 2.10
Nisku: m = 2.2
Leduc: m = 2.3 – 2.4
Keg River: m = 2.2 – 3.2
Of course, there are exceptions to every rule.