# Density logging

Density logging
Well logging
Gamma ray logging
Spontaneous potential logging
Resistivity logging
Density logging
Sonic logging
Caliper logging
Mud logging
LWD/MWD

v · well logging tool determining rock bulk density along a wellbore. This is the overall density of a rock including solid matrix and the fluid enclosed in pores. Geologically, bulk density is a function of the density of the minerals forming a rock (i.e. matrix) and the enclosed volume of free fluids (porosity).

## General tool design

Modern density logging tools, generally shares the same design principles independent of manufacturer. Tool consist of housing with electronics catridges and a sonde part. Sonde part has a measuring pad, where radiactive source (CS-137 nowadays) is inserted and a number of detectors (Long Space, Short Space, and a "Backscattering" detector). Measuring pad is connected with a hydraulically operated caliper arm, which is used to measure borehole diameter, and on the same time apply pressure to the pad to ensure it's contact with the borehole. Density measurements are extremely sensitive to shape of the borehole - readings in large washouts are irrelevant due to very shallow depth of investigation of density tools.

## Principle

A radioactive source applied to the hole wall emits medium-energy gamma rays into the formation so these gamma rays may be thought of as high velocity particles which collide with the electrons in the formation. At each collision the gamma ray loses some of its energy to the electron, and then continues with diminished energy. This type of interaction is known as Compton scattering. The scattered gamma rays reaching the detector, at the fixed station from the source, are counted as an indication of formation density.

The number of Compton scattering collisions is related directly to the number of the electron density of the formation. Consequently, the electron density determines the response of the density tool. Electron density is related through equation

$\rho \dot{\epsilon}= \frac{2\rho B \sum Z_{1i}}{M}$

where $\textstyle \sum Z_{1i}$ is the atomic numbers of all the atoms making up the molecules in the compound, and M is them molecular weight of the compound.

## Inferring porosity from bulk density

Assuming that the measured bulk density (ρbulk) only depends on matrix density (ρmatrix) and fluid density (ρfluid), and that these values are known along the wellbore, porosity (ϕ) can be inferred by the formula

$\phi = \frac{\rho_\text{matrix} - \rho_\text{bulk}}{\rho_\text{matrix}-\rho_\text{fluid}}$

Common values of matrix density ρmatrix (in g/cm³) are:

Density of clay minerals is highly variable, and depends on depositional environment, overburden pressure, type of clay mineral and many other factors. It can vary from 2.1 (Montmorillonite) to 2.76 (Chlorite). A fluid bulk density ρfluid of 1 g/cm³ is appropriate where the water is fresh; highly saline water has a slightly higher density. For flushed gas or oil reservoirs, even lower ρfluid values should be assumed depending on the hydrocarbon density and residual saturation. In some applications hydrocarbons are indicated by the presence of abnormally high log porosities.

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