The Indonesia Equation

A Different Form

Poupon and Leveaux built the Indonesia equation empirically in 1971 for the Indonesian basins, where the formation water is fresh and the clay is dispersed, and where Simandoux did not fit the core. Its shape is genuinely different: it adds the square roots of a shale term and a sand term, then scales the whole sum by the saturation:

The exponent $1-V_{sh}/2$ on the shale fraction is a cross term: it stops treating shale and sand as perfectly separate parallel paths as the clay grows, which is the real situation in a dispersed-clay sand where the two share one conducting network.

Less Aggressive Than Simandoux

Run the two models on the same logs and a pattern appears. They agree exactly in clean rock, but as the shale rises Indonesia corrects less hard than Simandoux, reading a slightly higher and more conservative saturation. That is usually the better answer in fresh-water, dispersed-clay systems, which is why Indonesia became the standard there. The fan that opens between clean Archie, Indonesia, and Simandoux is not noise: it is the model-choice uncertainty, and in a very shaly pay it can be several saturation units wide.

Choosing a Model

There is no universal shaly-sand model. The right choice depends on the clay type and the water salinity, and it should be calibrated against core or a known result: Simandoux tends to suit saline water and structural shale, Indonesia fresh water and dispersed clay. Both reduce to clean Archie when the rock is clean, so the choice only matters where it should, in the dirty intervals. The next two models, Waxman-Smits and Dual-Water, ground the same correction in the physics of the clay surface rather than in an empirical fit.

References

• Poupon, A. and Leveaux, J. (1971). Evaluation of water saturation in shaly formations. SPWLA 12th Annual Logging Symposium.
• Asquith, G. and Krygowski, D. (2004). Basic Well Log Analysis, 2nd ed. AAPG Methods in Exploration 16.