The Density Log

Counting What Comes Back

The density tool carries a gamma-ray source on one side of a pad and a detector a fixed distance away. The gammas stream into the rock, bounce off its electrons by Compton scattering, and a few wander back to the detector. The denser the rock, the more electrons there are to scatter the gammas away, so the fewer return. The tool turns that count rate straight into a bulk density, RHOB, in grams per cubic centimetre. Because electron density tracks bulk density almost exactly for ordinary minerals, the reading is a faithful measure of how heavy the rock is, pores and all.

The Mixing Law

What makes the density log so useful is that bulk density is a simple volume average. A unit of rock is part solid framework (the matrix, a fraction $1-\phi$ at density $\rho_{ma}$) and part pore fluid (a fraction $\phi$ at density $\rho_f$), so

The matrix density is a property of the mineral: about 2.65 for quartz sandstone, 2.71 for limestone, 2.87 for dolomite, 2.98 for anhydrite. The fluid density is near 1.0 for fresh mud filtrate, a little higher for salt water, and far lower (around 0.2) for gas. Heavier matrix and lighter fluid both widen the span the porosity has to work across.

RHOB on the Lever

Read the equation as a lever. With no porosity, $\rho_b=\rho_{ma}$; with all pore, $\rho_b=\rho_f$. In between, RHOB sits exactly $\phi$ of the way from the matrix point toward the fluid point. So measuring bulk density places you on the line between matrix and fluid, and the lever arm is the porosity. That is the whole idea behind reading porosity out of the density log, which is the next section. Switch the matrix and the fluid in the figure and watch the span change: the same RHOB means a different porosity once the endpoints move.

References

• Asquith, G. and Krygowski, D. (2004). Basic Well Log Analysis, 2nd ed. AAPG Methods in Exploration 16.
• Tiab, D. and Donaldson, E. (2015). Petrophysics, 4th ed. Gulf Professional Publishing.