WELLOG             POROSITY FROM DENSITY LOGS

 

REVISED 07-16-2007

© 2003  - 2007 WELLOG

All Rights Reserved

 

PART II, PAGE 1

 

DENSITY TOOLS:

 

Density tools are designed to measure bulk density of the formations in a well. The tool is comprised of a “mandrel” made of very dense metal that allows collimation of backscattered gamma rays and a “caliper” that is used to assert side-ways pressure to force the density tool against the sidewall of the well. The caliper also provides information about hole diameter. The density measuring instrumentation in the tool usually consists of a gamma scintillation detector and pulse conditioning circuits.

 

 

HOW DENSITY TOOLS WORK:

 

A source of gamma radiation in the form of an encapsulated (sealed) gamma ray emitting source is used. The source is commonly made of Cesium 137 or other gamma ray emitter. Back-scattered gamma rays are collimated by a “window” in the side of the tool. The gamma rays are sensed by a scintillation detector.  A scintillation detector uses a scintillation crystal made of a material like thallium sodium Iodide. The crystal converts incoming gamma rays into photons of light using a process called “scintillation”.  The photons of light emitted by the scintillation crystal are detected by a photo-multiplier tube.  The photo-multiplier tube converts photons into millions of electrons thru a “photo-electric process”. Gamma ray photons remove electrons from a photo sensitive surface within the tube. Electron multiplication occurs as electrons are produced and successive stages of “dynode” electrodes within the photo-multiplier tube further amplify the photon “pulses”. The resulting output is in the form of electrical pulses representing the detected back-scattered gamma rays.  

 

COMPTON SCATTERING:

 

Gamma rays emitted by a density tool source undergo several possible interactions when they collide with matter. 

 

In the first interaction, at low energy, the photo-electric effect is the dominant interaction. When low energy gamma rays collide with an atom and it’s energy is absorbed by the atom, a photo-electron is emitted.

 

A second interaction, at intermediate energy, the Compton effect is the dominant interaction. The colliding gamma ray scatters (bounces) from an electron giving up part of it’s energy. The energy of the scattered gamma ray is a function of the angle of the collision. Each successive collision results in reduction of energy until the gamma ray is absorbed by a photo-electric interaction.

 

The third possible interaction, at high energies, greater than 1.02 Mev., the gamma ray is converted into an electron-positron pair. This interaction is called pair production. The positron represents anti-matter. When it interacts with an electron, they annihilate one another and produce two gamma rays. The two gamma rays travel in opposite directions with equal energies of 0.51 Mev.  These lower energy gamma-rays interact with other atoms and are eventually subjected to Compton scattering and finally absorbed by a photo-electric interaction.

 

Gamma ray sources containing Cesium 137 are low energy sources. The relatively low energy of this source excludes the possibility of counting the results of pair production making radiation intensity measurements only due to the effect of Compton scattering and the photo-electric effect.

 

BULK DENSITY:

 

The number of back-scattered gamma rays is directly related to the electron density of the surrounding materials. Fortunately, electron density is very closely proportional to bulk density for most low mass elements.  The ratio of electrons per atom to atomic weight is close to .500 . This ratio is referred to as the Z/A ratio.

 

 

                                    re =  rb (2 Z/A)

 

Where:            rb = bulk density

                        re = electron density

                        Z = Sum of the electrons

                        A = Total Atomic weight

 

The most common lithologies of commercial importance in oil and water wells are, sandstone, limestone, and dolomite.

 

 

Sandstone:      (SiO2)                          Z/A = .499

Limestone:     (CaCO3)                       Z/A = .500

Dolomite:         (CaMg(CO3)2)             Z/A = .499

 

Since the intensity of the gamma source may be considered constant, the geometry of the tool is also constant and the linear absorption coefficient for common rocks is constant for the energy levels involved, the validity of using gamma intensity as a method of measuring formation bulk density is established.

 

Counts are inversely related to formation bulk density.  High counts indicate low density, and lower counts indicate higher density.

 

BOREHOLE COMPENSATION:

 

Density logging tools have a relatively shallow depth of investigation.  The measurements are therefore subject to effects of mudcake and borehole rugosity (diameter). To compensate for these effects, a two detector density tool is used.  Two detectors having two spacings, short and long, with reference to the source have count rates based on their respective distances from the source.  In an ideal borehole, the count rates are known for a given tool design. A graph can be constructed having a straight line (referred to as a spine) that represents the ratio of count rates for various bulk densities. Additional lines referred to as ribs are plotted representing deviations from the spine due to various mudcake densities and thicknesses.  Borehole compensation is done thru computer calculation based on count rate deviation from the spine.

 

 

CALIBRATION:

 

Density tools are calibrated using three blocks having known density.

 

Typical materials used for calibration are, Aluminum (2.70 gm./cc), Magnesium (1.74 gm./cc), and Plexiglass plastic (1.1 gm./cc).

 

 

POROSITY FROM DENSITY:

 

Formation bulk density is directly related to porosity (f), fluid density and matrix density of the rock material.

 

Bulk density (rb) is the sum of the fluid density (rf) of the pore space and the density of the matrix (rma).

 

rb  =  f  x  rf + (1 – f) x rma

 

Rearranging the equation,

 

                        f =  (rma – rb) / (rma – rf)

 

 

Porosity (f) can be calculated given bulk density (rb), if fluid density (rf) and matrix density (rma) are known.

 

Typical matrix densities (rma) are as follows:

 

Anhydrite                    2.899 – 2.985 gm/cc

Dolomite                      2.8 – 2.9 gm/cc

Kaolinite                      2.6 – 2.63 gm/cc

Montmorillonite           2.2 – 2.7 gm/cc

Quartz                         2.653 – 2.660 gm/cc

 

Typical fluid density (rf) of water is 1.0 gm/cc.

 

Formation fluids containing oil and gas .7 gm/cc.

 

Formation fluids containing gas .3 gm/cc.

 

CORRECTION FOR FLUID DENSITY:

 

Formation fluid may be freshwater, salt water or other fluid. Because Density porosity is based on the assumption that the fluid density is 1.0 grams/cc, it is important to correct for the effect of temperature and pressure on fluid density.

 

Density versus temperature and pressure for water and salt water:

 

            Med. Resolution Chart

            High Resolution Chart

 

 

Density correction chart for Crude oil

           

Med. Resolution Chart

            High Resolution Chart

 

 

CORRECTION FOR SHALE OR GAS:

 

SHALE CORRECTION:

 

The physical properties of shale must be known in order to correct for the effect of shale or clay in a sandstone matrix. Shale densities vary according to depth.  The range of shale density may vary from 1.8 gm/cc near the surface to 2.60 gm/cc at 12,000 feet (US Gulf Coast).

 

Bulk density in a laminated shaly sand is based on; shale density, matrix density, and fluid density.

 

Laminated shale-sands are defined as having laminae that do not exceed .5 inch thickness.

 

The calculation is as follows: (not used in log interpretation)

 

                        rb =      rsh          +         rf               +       rma

                       

rb =  (Vsh x rsh) + (f x rf) + (1 - f - (Vsh x rsh)) x rma

 

            where Vsh = shale volume (percent shale)

 

The calculation for rma correction, rma(corr)  is:

 

                        rma(corr) = (Vsh rsh) + (1-Vsh) rma

 

GAS CORRECTION:

 

The fluid density of a gas reservoir will be composed of a liquid fraction (SL) and gas fraction (SG).

 

See a chart of gas density.

 

The corrected fluid density, rf(corr) is calculated as follows:

 

                        rf(corr) = SL x rL + SG x rG

 

See a chart of the effect of gas and shale.

 

 

 

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