Why Clean Archie Fails

Part 8, Chapter 8: Shaly-Sand Saturation Models

Learning objectives

Explain how clay conducts in parallel with the formation water
Show that clay lowers Rt at a fixed water saturation
Recognize that clean Archie over-reads Sw in shaly sand
Quantify the pay clean Archie throws away as shale rises

Clay Carries Current

Clean Archie rests on one assumption: that the only thing conducting electricity in the rock is the salty formation water. In a clean sand that holds. In a shaly sand it breaks, because clay conducts too. The cations held loosely on clay surfaces, the cation exchange capacity, carry current in parallel with the brine, and the more clay the rock holds, the more this extra path matters. The total conductivity becomes the sand path plus a clay path that clean Archie does not know about:

C_t = \underbrace{\frac{\phi^{m} S_w^{n}}{a R_w}}_{\text{water path}} + \underbrace{C_{\text{clay}}}_{\text{ignored by clean Archie}}.

The Over-Read

The consequence is one-directional and dangerous. The clay path adds conductance, which drops the measured true resistivity at any given water saturation. Clean Archie reads that lower $R_t$ and, because low resistivity means high water in its world, computes a water saturation that is too high. The widget makes it concrete: hold the true saturation fixed, let the shale rise, and the clean-Archie curve climbs away from the truth, by a third shale it is several saturation units high, by half shale more than ten. Good pay gets called marginal, and the cleanest-looking dirty sand can be written off entirely.

Closing the Gap

The fix is to put the clay term back. Every shaly-sand model in this chapter, Simandoux, the Indonesia equation, Waxman-Smits, and Dual-Water, is a different way of writing $C_{\text{clay}}$ and solving for the saturation that the water path alone explains. They disagree in form and in the data they need, but they share one purpose: recover the pay that clean Archie throws away. The chapter builds them one at a time and ends by running them all on the Ogbon-1 well.

References

Worthington, P. F. (1985). The evolution of shaly-sand concepts in reservoir evaluation. The Log Analyst, 26(1).
Asquith, G. and Krygowski, D. (2004). Basic Well Log Analysis, 2nd ed. AAPG Methods in Exploration 16.