The Rw Problem

Sensitive, or Uncertain?

Two different things decide how much an input matters to the final saturation: how strongly $S_w$ responds to it, and how well we actually know it. They are not the same. In elasticity terms $\partial \ln S_w / \partial \ln R_w = 1/n \approx 0.5$, while for porosity $\partial \ln S_w / \partial \ln \phi = -m/n \approx -1$. So $S_w$ is actually only half as sensitive to the water resistivity as it is to porosity. On sensitivity alone, $R_w$ should be a minor worry.

Why Rw Still Wins

It wins on the other axis. Porosity we usually know to a couple of porosity units, Rt to perhaps fifteen percent, but $R_w$ can be wrong by a factor of two. The water sample may be contaminated by mud filtrate or have precipitated salts on the way to the lab, the SP may be muted in a fresh or shaly sand, the salinity may drift across the field, and $R_w$ itself swings with temperature. A modest sensitivity multiplied by a large uncertainty beats a large sensitivity multiplied by a small one, and the widget shows the $R_w$ bar opening far wider than the porosity or $R_t$ bars at realistic numbers.

Pinning Rw Down

Because of this, getting $R_w$ right is the highest-value half hour in a saturation job. Take it from a clean produced-water sample measured in the lab, cross-check it against an SP-derived value and a Pickett-plot intercept, scan an $R_{wa}$ minimum across the well, and compare with regional catalogs. Only once the three independent estimates agree is the computed pay worth trusting; until then the saturation is no better than its weakest input.

References

• Asquith, G. and Krygowski, D. (2004). Basic Well Log Analysis, 2nd ed. AAPG Methods in Exploration 16.
• Bateman, R. M. (2012). Openhole Log Analysis and Formation Evaluation, 2nd ed. SPE.