Density Logging

The method of logging that determines the density of a formation based on the Compton effect of gamma rays with the formation is called density logging. Since the bombardment particles used in density logging and the objects detected are gamma photons, it is also known as gamma-gamma logging.

3.2.1 Nuclear Physics Basis for Density Logging

3.2.1.1 Interaction of Gamma Rays with Matter

Gamma rays emitted by the decay of a radioactive nucleus generally have energies of 0.5 MeV to 5.3 MeV, and the interaction of gamma photons with matter in this range of energies is characterized by photoelectric effect, Compton effect, and electron pair effect. .

(1) photoelectric effect

γ rays through the material and the atom in the collision of electrons, and its energy to the electrons, so that the electrons out of the atom and the movement of the γ photon itself is absorbed, was released by the electrons called photoelectrons, as shown in Figure 3.2.1 (a). This effect is called the photoelectric effect. Photoelectric effect and γ-ray energy and the atomic number of absorbing material has a close relationship with the increase in atomic number and rapid increase; but with the increase in γ-ray energy, the photoelectric effect decreases rapidly. The following formula can be used to express the probability of photoelectric effect τ:

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In the formula: τ is the probability of photoelectrons produced when a photon passes through 1cm of absorbing material, that is, the linear photoelectric absorption coefficient; λ is the wavelength of the photon in units of 10-8cm; n is the constant of the exponent, which equals to 3.05 for the elements N, C, and O; for sodium to iron it equals to 3.05, and for the elements sodium to iron it is equal to 2.85; A is the molar mass of the atom; Z is the atomic number; and ρ is the density, g-cm-3.

Figure 3.2.1 Three types of interactions of gamma rays with matter

(2) The Compton effect

When gamma rays are of intermediate energy value, gamma rays interact with the Atom's outer layer of electrons, the role of part of the energy to the electrons, so that the electrons from a certain direction, the electrons are called Compton electrons; loss of part of the energy of the rays to the other direction of the scattering out called scattering of gamma rays, as shown in Figure 3.2.1 (b). This effect is called the Compton effect.

Gamma rays through the material, the Compton effect caused by the intensity of gamma rays weakened, the degree of its weakening is usually expressed by the Compton absorption coefficient Σ. Σ and the atomic number of the absorber Z and the number of electrons per unit volume of the absorber is proportional to. The formula is:

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Equation:σe is the Compton scattering cross-section of each electron, when the energy of the γ photon is in the range of 0.25 to 2.5 MeV, it can be regarded as a constant; NA for is Avogadro's constant, is equal to 6.022045×1023mol-1. The rest of the symbols mean the same as the Eq. (3.2.1) is the same.

(3) electron pair effect

When the energy of the incident γ photon is greater than 1.022MeV, it acts with the material will make the photon is converted into an electron pair, i.e., a negative electron and a positron, which is absorbed. This is shown in Figure 3.2.1(c).

When γ-rays pass through a medium of unit thickness, the decrease in the intensity of γ-rays due to the occurrence of the electron-pair effect is expressed by the absorption coefficient κ, whose empirical formula is:

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In which:NA, ρ, A, Z symbols have the same significance as that of Eqn. (3.2.2); Eγ is the energy of the incident ray γ; and K is a constant.

The probability of these three roles of γ photon and matter is related to the energy of γ photon, low-energy γ photon and matter role is dominated by the photoelectric effect, medium-energy γ photon and matter occurs Compton effect has the highest probability, while the electron pair effect occurs in the case of γ photon energy is greater than 1.022MeV, Fig. 3.2.2 gives the absorption coefficient of the three roles of the γ photon and aluminum and γ photon energy.

(4)Absorption of gamma rays

When γ-rays pass through a substance, they will have the three effects with the substance as described above, and the γ-photons will be absorbed, so the intensity of the γ-rays will be weakened with the increase of the distance through the substance. Experiments have shown that the intensity of γ-rays passing through absorbing material has the following relationship with the thickness of the absorbing material:

Figure 3.2.2 Relationship between the absorption coefficient of aluminum and the gamma-ray energy

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In the formula:I0, I are the intensity of γ-rays when they do not pass through the absorbing material and when they pass through the absorbing material with thickness of L, respectively; μ is the absorption coefficient of material. absorption coefficient, determined by the photoelectric effect, Compton effect, and the electron pair effect of the three absorption coefficients, i.e., μ = τ + Σ + κ.

Absorption coefficient μ is approximately proportional to the density ρ of the absorbing body, and ρ varies with the physical state of the medium. In order to eliminate the effect of ρ, the mass absorption coefficient μm (μm = μ/ρ) is usually used, which has the unit of cm2/g. The mass absorption coefficient relation is:

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3.2.1.2 Density of Rocks

(1) True Density of Rock

The mass of the rock per cubic centimeter of volume of the rock is called true density of the rock. It is often expressed in logging as ρb, and its unit symbol is g/cm3. True density is also known as bulk density. The density is usually referred to as the true density. For example, the density of calcite is 2.71g/cm3, and the density of pure water is 1.00g/cm3. The density of pure limestone with a porosity of φ and saturated with fresh water can be calculated by the following formula:

ρb=2.71(1-φ)+1.00φ

Different minerals have different densities, as shown in Table 3.2.1. From these data, it can be seen:

1)Different rocks have different skeleton densities, so in the well profile according to the density can be differentiated between different lithological formations, especially other geophysical methods are difficult to distinguish between saline and hard gypsum, hard gypsum and dense chert, dense chert and dolomite, gypsum and high porosity chert and so on, according to the difference in the density between them can be differentiated.

2)Porosity stratum is equivalent to the dense stratum in the rock skeleton of a part of the water, crude oil or natural gas is less dense, so its density is less than the dense stratum. The larger the porosity, the smaller the density of the formation, so density logging data can be used to find the porosity of the formation. Density logging is one of the main methods of porosity logging.

Table 3.2.1 Density data for some minerals

(2) Electron density and electron density index of rocks

The number of electrons per unit volume of a rock is called the electron density of the rock, and is expressed as ne in electrons/cm3.

If a rock consists of one type of atom,

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For a rock consisting of a single compound molecule, the electron density is:

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Where:Zi is the atomic number of the ith atom in the molecule; ni is the atomic number of the ith atom; M is the molar mass of the compound.

For ease of use define a parameter proportional to ne, the electron density index ρe:

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Substances composed of a single element have an electron density index of:

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Substances composed of a single compound have an electron density index of:

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For most of the elements and compounds that make up the formation, the values in the parentheses at the right end of Eq. (3.2.9) and Eq. (3.2.10) are close to 1, which makes ρe ≈ ρb.

If you substitute the electron density exponent into Eq. (3.2.2), then you get:

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Eq.:K=σ e-NA/2, which can be approximated as a constant when the energy is in the range of 0.25 to 2.5 MeV.

(3)The apparent density of the rock

Setting the skeleton density of the rock as ρma, porosity as φ, and the pores are full of fresh water, according to the data in Table 3.2.1, the expression for ρb can be written:

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If the e-density exponent of its skeleton is ρme, then the e-density exponent of the rock is:

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For calcite, ρma = 2.7100 and ρme = 2.7075, which gives:

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The electron density index is measurable since it is proportional to the electron density and Compton absorption coefficient. The measured value of bulk density, on the other hand, is derived indirectly through its approximate relationship to the electron density index and can be affected by the scale factor. Typically, density logging instruments are scaled against a limestone saturated with fresh water and so follow equation (3.2.14). Logging, regardless of the measurement environment and the standard conditions of any difference, the output density value is obtained with this conversion, which is slightly different from the actual density of the measured medium, so it is called the apparent density.

3.2.2 Density logging basic principles

Figure 3.2.3 is a commonly used density logging instrument schematic, which includes a gamma source, two detectors to receive gamma rays, that is, the long source distance detector and short source distance detector. They are mounted on a skid and are pushed against the wall of the well during logging. Auxiliary electronics are mounted on top of the downhole instruments.

137Cs is usually used as the gamma source, which emits gamma rays of moderate energy (0.661 MeV), and irradiation of material with it produces only Compton scattering and photoelectric effects. The different densities of the strata have different abilities to scatter and absorb gamma photons, and the count rates of the gamma photons received by the detectors are also different. It is known that the count rate N of a gamma photon passing through a distance of L is:

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Figure 3.2.3 Schematic diagram of density logging instrument

If there is only Compton scattering, then μ is the absorption coefficient of Compton scattering, so:

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Since the sedimentary rock's 2Z/A ≈ 1, the count rate of the gamma photons received by the detector will be different for the equation ( 3.2.4) is taken logarithmically on both sides, we get:

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Eq.:K=σe-NA/2 is a constant.

It can be seen that the count rate N recorded by the detector is linearly related to ρb and L on a semi-logarithmic coordinate system. Figure 3.2.4 shows the plot of ρb versus count rate N for two source distances.

After the source spacing is selected, the instrument is scaled to find this relationship between ρb and N. Then the density ρb of the formation can be measured by recording the scattered gamma photon count rate N.

When there is a mudcake present on the well wall and the density of the mudcake is different from the density of the formation, the mudcake has a certain effect on the measured value as shown in Figure 3.2.5. In the case where the formation density is greater than the mudcake density, if the mudcake thickness increases, the gamma photon count rate increases in the formation with the same density.

Figure 3.2.4 Response curves of count rate for the change of formation density without mudcake for two source spacings

Figure 3.2.5 Relationship curves of count rate with formation density for two source spacings with different mudcake thicknesses

In order to compensate for the effect of mudcake, two detectors are used in the density logging (long source spacing and short source spacing), and two count rates, NLS, NSS, are obtained. Using the long source distance count rate NLS to get an apparent formation density ρb, and then from NLS, NSS to get a mudcake influence correction value Δρ, then the formation density ρb = ρ'b + Δρ, the density logging at the same time to output ρb and Δρ two curves. Density logging also outputs limestone porosity logging curves, and the measurements are made using instruments that are scaled in a limestone formation saturated with fresh water. Figure 3.2.6 shows the density logging curve.

Figure 3.2.6 Density logging real-world curve 1in ≈ 2.54cm; API is American Petroleum Institute units

3.2.3 Density Logging Applications

The basic use of density logging is to determine the porosity of a formation, and it can also be used in conjunction with other logging to determine lithology, identify gas layers, and solve for porosity.

1) Determining formation porosity. The bulk density of rock is determined by the density of rock particles and the density of fluid in the pores. And the contribution of the fluid in the rock pores to the bulk density is related to the porosity of the rock. For pure rock, the relationship between porosity and bulk density is:

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So:

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Equation:φ is the porosity; ρb is the bulk density of the rock; ρma and ρf are the skeleton density and pore fluid density, respectively. Different lithology of the rock, its skeleton density ρma is different, sandstone is generally 2.61g/cm3; limestone is 2.71g/cm3; dolomite is 2.87g/cm3.

In the case of known lithology (known ρma) and pore fluid (known ρf), you can be measured by the density of the wells ρb to find the porosity φ of the pure rock.

Typical The density of mudstone and mudstone interlayer is 2.2~2.56g/cm3.Usually the density of mud in mudstone and reservoir is smaller than the density of rock skeleton, so the effect of mud should be taken into account when finding the porosity of mud-containing rock layer, otherwise the porosity will be large.

2)Overlaying density and neutron logging curves together for analysis can identify the gas layer and determine the lithology (see chapter seven).

3)Using density and neutron logging curves to make a rendezvous diagram, lithology can be determined to solve porosity (see Chapter Seven).