1. Natural gamma radiation field in rocks
Nuclear characteristics of (1) uranium, radium, thorium and potassium
Uranium (U) is in the seventh cycle in the periodic table of elements, and it exists in asphalt mines and potassium vanadium uranium mines in nature. It has three natural isotopes, namely 238U, 235U and 234U, and their abundances are 99.27%, 0.0 1% and 0.72% respectively. Uranium is a typical oxygen-loving element with active chemical properties, and there are tetravalent and hexavalent compounds in it. The transformation between U6+ and U4+ in nature is the main feature of uranium geochemical process.
Radium (Ra) has four isotopes, of which 226Ra is the daughter of 238U. When uranium and radium are in balance, radium/uranium =3. 14× 10-7. The chemical properties of radium are similar to barium, showing obvious alkalinity, and its ionic radius is similar to Ca2+, Ba2+ and Pb2+. Radium can enter calcite (CaCO3), fluorite (CaF2), pyromorphite (Pb 10(PO4)3Cl2) and other minerals in isomorphic form. Radium is easily leached from minerals, which leads to the accumulation of radium in natural water. In the oxidation zone, leaching can sometimes make 85% radium in uranium ore leached by water, so that 226Ra can be separated from the parent material 238U and enriched in the circulating water in the oxidation zone. In oilfield water, the concentration of radium is sometimes as high as 7.5×10-9g/L. It is of great significance to study the redistribution of radium in oilfield development to observe the advancement of oilfield water and injected water.
Thorium (Th) has two long-lived isotopes and four short-lived isotopes, of which the abundance of 232Th is almost 100%. The valence is mainly tetravalent, and tetravalent thorium is closely related to tetravalent uranium, which is often isomorphic replacement. Thorium and uranium are often produced by * * *, and the ratio of thorium to uranium is considered as the basic ratio of the solar system. Indeed, for almost all meteorites, the Th/U ratio is equal to 3 ~ 4; In magmatic rocks, Th/U is almost constant, mostly around 4. In an oxidizing environment, uranium and thorium will be obviously separated. Thorium compounds have stable properties, and the migration is mainly mechanical weathering. The selective adsorption of thorium by clay minerals and the existence of thorium in stable minerals are the main factors to control the distribution of thorium in sedimentary rocks. Thorium is often used as an indicator of clay minerals, and the ratio of thorium to uranium can indicate sedimentary environment and lithology.
The main γ -ray radiator of thorium system is 208Tl, and the characteristic γ -ray energy is 2.62 MeV
There are three natural isotopes of potassium (K), which are 39K, 40K and 4 1K respectively. Among them, 40K is a radioactive isotope, emitting gamma photons of1.46mev.. The content of potassium in magmatic rocks increases with the increase of silica. Among sedimentary rocks, the potassium content of clay rock is higher than that of sandstone and limestone.
(2) Natural gamma radiation field in rocks
The natural gamma radiation field of rocks is mainly determined by the spatial distribution of potassium, uranium and thorium, followed by self-scattering and self-absorption of rocks.
The spatial distribution of natural gamma radiation field of rock is determined by the contents of potassium, uranium and thorium in rock per unit volume or mass. The stratum containing potassium, uranium and thorium is a gamma source distributed in a limited space.
The activity of each radionuclide is directly proportional to the number of photons emitted per unit time, but the number of photons emitted per unit time by two different nuclides with the same activity is not necessarily equal. The total number of photons emitted per unit time is called the source intensity of γ source, and the source intensity per unit volume is called the source intensity density. For large radiators, the spatial distribution of photon emissivity needs to be described by source intensity density. If natural gamma-ray spectrometry logging is carried out, it is necessary to study the energy distribution and angle distribution of photons.
The main parameter describing the natural gamma radiation field is the flux density, which is defined as follows: If the cross-sectional area of a sphere passing through the center of the sphere is α, and dφ is the photon flux number injected into the sphere in the time interval dt, then the flux density φr is defined as
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For parallel ray beams, the number of photons passing through the unit cross-sectional area perpendicular to the ray direction per unit time is called gamma ray intensity; For non-parallel rays, the flux density defined by formula (3- 1) can also be called intensity. The flux density is proportional to the counting rate of the instrument per unit time.
For simplicity, it is assumed that only one radioactive element (such as potassium) emits single-energy photons in an infinite, uniform and isotropic stratum, and the density of stratum is ρ. Each gram of rock contains q grams of this radioactive element, and each gram of this radioactive element emits one photon per second on average, and the absorption coefficient of photon in stratum is μ. Then, the photon flux density of any point in stratum with initial energy is calculated. Therefore, take a volume element dV in the spherical coordinate system, and its flux density increment at point M with distance R is
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The flux density φr is obtained by integrating a sphere with radius r:
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If we integrate the infinite medium above, that is, r→∞, we get:
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Where φ0 is the photon flux density at any point in infinite medium; Micron is the mass attenuation coefficient, which decreases with the increase of photon energy; Aq is the number of photons emitted per second per unit mass of rock.
The micron of main minerals in sedimentary rocks has little change. For example, when the gamma photon energy is 1.5 MeV, the mass attenuation coefficients of pure water, timely and calcite are 0.0575 cm2/g, 0.0545 cm2/g and 0.05 18 cm2/g, respectively. The micron of concrete is 0.05 19cm2/g, and φ0∝q can be considered for frequently encountered strata.
Equation (3-3) can estimate the detection range of natural gamma logging. utilization ratio
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Do a calculation. When μr=4.605, this ratio is equal to 0.99. If μ is 0. 10/cm and 0. 15/cm respectively, the corresponding ball radii are 46.05 cm and 30.7 cm respectively. It can be considered that the detection range of natural gamma logging to strata is about a sphere with a diameter of1m.
2. Logging response of radioactive formation
(1) Photon flux density formed by radioactive stratum with finite thickness on well axis.
Figure 3- 1 Schematic diagram of radioactive stratum with limited thickness
Let the limited radioactive stratum thickness be h (Figure 3- 1), the well radius be r0, the well axis be perpendicular to the stratum, the m point be located on the well axis, and the distance from the stratum bottom be z 1. The physical properties in the stratum are uniform and isotropic, only containing a radioactive element (such as potassium) that emits single-energy photons, and the density of the stratum is ρ. Each gram of rock contains q grams of this radioactive element, and each gram of this radioactive element emits one photon per second on average. The photon absorption coefficient of Wainai stratum medium is μ, and the surrounding rock does not contain radioactive substances. Find the flux density of scattered photons at any point m on the well axis. Therefore, take the volume element dV=rdzdrdφ in the cylindrical coordinate system, and the flux density increment generated at point M is
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Firstly, φ is integrated in the range of 0 ~ 2π, and the flux density is obtained as follows:
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Replace this formula with a variable, so that h'= h/r', and
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Available:
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Move point m, that is, change the value of z 1, and numerically integrate equation (3-8) with the exponential integral function table to find out the photon flux density along the well axis caused by radioactive formation. For the variable z', the integrand has a maximum value at z'= 0 and is symmetrical about this point. Therefore, when the observation point m is located at the midpoint of the stratum, the integral has the maximum value:
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Let μ=0. 1/cm, r0= 15 cm, and make the formation thickness equal to 15 cm, 30 cm, 60 cm, 90 cm, 150 cm respectively. A set of curves can be obtained by using formula (3-9), as shown in Figure 3.
The curves measured by logging tools are different from those in Figure 3-2, or have different responses due to the influence of instrument parameters.
(2) instrument standardization and detection efficiency
The counting rate measured by natural gamma logging at each depth point is directly proportional to the flux density generated by the stratum at that point. The counting rate curve can directly reflect the distribution of flux density (or ray intensity) along the well profile. The detection efficiency of logging tools varies greatly. Even if the environmental conditions remain unchanged, the counting rate measured by different instruments at the same measuring point will be different. The so-called standardization of logging instruments is essentially efficiency calibration. The counting rate curve measured by the calibration instrument is expressed in standard units, which are international API units. Api unit is the natural gamma logging unit selected by API gravity. The regulations are as follows: A set of calibration wells consisting of three-layer concrete standard modules was built in the University of Houston, USA. Each standard module is a cylinder with a borehole with a diameter of1.219m and a height of 2.438m. The middle layer contains13mg/l of uranium, 24mg/l of thorium and 4. The reading difference between the high radioactive module and the low radioactive module measured by the instrument in the borehole is set to 200 API. Similar instruments calibrated in standard wells. It should have the same response, that is, the same amplitude (including statistical error) to the same thick stratum. In this way, the natural radioactivity distribution measured by different instruments can be compared.
Figure 3-2 Photon Flux Density along Well Axis of Limited Thickness Radioactive Formation
(2) The principle of natural gamma logging
1. Logging principle
There are many kinds of natural gamma logging tools, and their structures and specific lines are quite different, but their working principles are basically the same, and their structural block diagrams are basically the same (Figure 3-3).
Natural gamma logging tools are divided into two parts: surface tools and downhole tools. The basic components of downhole tools are gamma ray detector, amplifier and high voltage power supply. Gamma ray detector is a device that senses gamma rays and converts them into electric pulses. The amplifier amplifies these pulses for cable transmission.
Ground instruments include preamplifier, frequency discriminator, shaper and counter. The purpose of discriminator is to eliminate interference; The shaper can turn all pulse signals into rectangular waves with equal amplitude and width, so that the electric quantity of each rectangular wave band is the same; The counter changes a single rectangular pulse into a continuously changing voltage (or current), and the voltage (or current) reflects the number of gamma pulses. Then the voltage recorded by the logging tool forms a curve of gamma ray intensity changing with well depth-natural gamma logging curve.
The simplest counter is an integrating circuit composed of resistor and capacitor elements (Figure 3-4). The product RC=τ of resistance R and capacitance C is called time constant. The output voltage u of the RC integrator circuit has the following relationship with the number of input pulses n:
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Where: q is the amount of charge carried by each rectangular pulse; T is the elapsed time since the rectangular pulse was input.
Figure 3-4 shows that the output voltage cannot change synchronously with the input voltage, that is, the integrating circuit is inert. The magnitude of inertia is determined by the time constant. The calculation shows that when t=2τ, the output voltage can only reach 86% of the maximum output voltage; When t=3τ, the output voltage increases to 95% of the maximum output voltage. It can be seen that the use of integral circuit will have a great influence on the measurement results.
Figure 3-3 Schematic Diagram of Natural Gamma Logging Tool
Figure 3-4 Input and output characteristics of the integrating circuit
2. Detection radius
Because of the absorption of gamma rays by the formation and mud, the gamma rays emitted by radioactive elements in the formation can not reach and be detected by the detector, that is, the formation mainly detected by natural gamma logging is a limited formation close to the detector. Figure 3-5 is the apparent geometric factor distribution curve of natural gamma logging. It can be seen from the curve of integral geometric factor in the figure that the integral geometric factor changes exponentially with the increase of radial distance. The integral geometric factor can be used to study the detection range of natural gamma logging; However, the curve of contribution to the signal in the figure changes exponentially with the increase of radial distance, indicating that the farther the medium is from the detector, the smaller the contribution to the measurement signal, which can be used to study the detection range of natural gamma logging. In an infinitely uniform stratum, the detection range is a sphere centered on the probe, and the radius of the sphere is the detection radius. Assuming that the strata within the detection range produce 90% of the total natural gamma intensity, the calculated detection radius is less than 25 cm. In fact, its size is related to gamma ray energy, formation and mud density. When the energy decreases or the density increases, the detection radius decreases. In addition, the detection range is not strictly spherical. This is because the well exists and the detector has a certain volume.
Using the change of radioactive strata within the detection range, radioactive logging curves can also be drawn approximately. We assume that the upper and lower surrounding rocks of radioactive strata with a thickness greater than twice the detection radius do not contain radioactivity (Figure 3-6). When the natural gamma logging tool is located below the radioactive formation, the natural gamma intensity is zero because there is no radioactivity in its detection range. As the instrument moves upward, the radioactivity in the detection range increases gradually, and the natural gamma intensity increases gradually. When the detection range of the instrument is all radioactive strata, the natural gamma intensity is the largest. If the formation is thick, there is a straight line segment on the natural gamma logging curve. Later, as the instrument moves upward until it enters the upper surrounding rock. Within the detection range, the radioactive stratum gradually decreases until it disappears completely, and the natural gamma intensity gradually decreases and approaches zero.
Figure 3-5 Apparent Geometric Factor Distribution Curve of Natural Gamma Logging
(3) Characteristics and influencing factors of natural gamma logging curve.
1. curve characteristics
The characteristics of natural gamma logging curve can be summarized as follows: when the radioactivity of surrounding rock is the same, the natural gamma logging curve is symmetrical with the midpoint of the formation; The natural gamma amplitude at the midpoint of the stratum is the largest, and its amplitude is related to the stratum thickness. When the formation is thin, the measured natural gamma amplitude Jγ and its natural gamma amplitude Jγmax at the midpoint of the formation meet the following requirements:
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Where: h is the stratum thickness; R is the detection radius.
When the stratum thickness is more than twice the detection radius (or more than three times the borehole diameter), the stratum interface is determined by using the half amplitude point.
2. Influencing factors
The actual natural gamma logging curve (Figure 3-7) is obviously different from the theoretical natural gamma logging curve, and the main reason for this difference is statistical fluctuation.
Figure 3-6 Detection Range of Natural Gamma Logging
Statistical fluctuation of radioactivity measurement leads to sawtooth change on natural gamma logging curve. This change may appear on the logging curve at the same time as the formation lithology change and instrument instability. Correctly identifying various changes on the curve is the premise of correctly using natural gamma logging curve.
Statistical fluctuation is measured by standard error. The standard error should be calculated by the average of many measurements. However, in natural gamma logging, it is usually only measured once. In this way, it is impossible to get the average value, so we can only take this measurement result as the average value. therefore
Figure 3-7 Actual Natural Gamma Logging Curve
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We know that the unit of logging results is "c/min, (c stands for counting)". So, N=nt. T is the residence time of logging tools in this formation, and n is the average counting rate of this formation. Therefore, the formula (3- 1 1) becomes
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The error of logging counting rate is:
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The formation thickness is h, and the tool running speed (penetration rate) is v, and the formula (3- 12) becomes
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σ 1 means that when logging readings are used instead of average values, errors will be brought, and the error size is σ 1. If the average value can be obtained through multiple measurements, the probability that the average value is within this range should be 68.3%.
It is generally considered that the output result of integral line natural gamma logging tool is the average value within 2τ before the output time. Therefore, the total reading of the formation n = 2 τ n-. Therefore, there are:
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The error of logging counting rate is:
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σ2 is defined as: if the average value can be determined from multiple measurements, the error between each measurement reading and the average value is σ2.
Obviously, due to the influence of statistical fluctuation, the relative error of natural gamma logging curve is σ 1+σ2, that is
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According to the size of ∑, evaluate the performance of logging tools and judge the reason of curve change.
In order to check the performance of the instrument, the usual practice is to put downhole tools in a certain position in the well and continuously measure the natural gamma intensity for a period of time. When the instrument performance is normal, the amplitude change on the curve should be caused by statistical fluctuation, that is, the relative error of measurement should conform to the statistical law. Otherwise, the instrument is unstable and needs maintenance and debugging. The following example illustrates the method of calculating the error.
Let the average line determined by the curve be 5.5 cm away from the baseline (the baseline is not the zero line), and the baseline compensation is 10 cm (that is, moving the zero line10 cm); When the horizontal scale is 380 C/min. cm and the time constant is 4 s, then:
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and
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The distance of σ2 on the curve is:
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Draw two straight lines at 0.57 cm on both sides of the average value of natural gamma logging curve. The range covered by these two straight lines is the range where 68.3% of the measurement results should be distributed. The cumulative length of curves beyond this range is 3.9 cm according to their longitudinal length, and the total longitudinal length of curves is 12.3 cm. Accordingly, the ratio exceeding the error can be calculated as 100%=3 1.7%. This shows that the curve conforms to the statistical law and the logging tool has normal performance.
It is generally believed that only when the amplitude of the curve changes more than, the formation rock changes, and the interface should be determined by layers. It can be seen from the above that the fluctuation error of natural gamma logging is related to the time constant τ of the counter. A large τ means a large average range, and more measurement results are used for averaging. Obviously, this average value is close to the true value, and the error is very small. In order to make the measurement result close to the true value, a counter with large τ should be selected.
3. Environmental impact
Environmental impact refers to the influence of borehole environment on logging response. In open hole wells, the shielding effect of drilling fluid on gamma rays from the formation is the main factor, and the change of borehole diameter changes the thickness of drilling fluid between the instrument and the formation. Numerical integration method, Monte Carlo method or physical model experiment can be used to study environmental impact. When studying the environmental impact, a comprehensive correction coefficient Ap called "drilling fluid absorption function" is introduced, which takes the product of drilling fluid attenuation coefficient μp and well radius r as the parameter variable and the ratio of instrument radius Rs to well radius r as the variable, as shown in Figure 3-8. After finding the Ap, correct it with the following formula:
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Where: j is the measured value; Jc is the correction value.
For cased wells, the calibration formula or calibration curve can also be calculated or measured according to the actual model.
Figure 3-8 Absorption function of drilling fluid when the tool is centered.
Figure 3-9 api of natural gamma logging response curve is the unit specified by API specific gravity.
(4) Application of natural gamma logging curve
1) Lithology division. Different lithology can be distinguished mainly according to the amplitude change of natural gamma curve caused by the change of shale content in stratum. Figure 3-9 shows the response of natural gamma logging curves to different formations. For pure limestone, pure sandstone, dolomite, anhydrite, gypsum, coal seam and salt rock, natural gamma rays show low values. For volcanic ash and mudstone, it shows higher natural gamma value; However, the natural gamma ray display of argillaceous rocks is moderate, which changes with the increase or decrease of argillaceous content. Generally speaking, the natural gamma amplitude of mudstone is 75 ~ 15~20 API, with an average of 100 API, anhydrite and pure limestone are 15~20 API, and dolomite and pure sandstone are 20 ~ 30 API. For a certain area, the core analysis results should be compared with the natural gamma curve to find out the regional law, and then applied to the interpretation of the natural gamma curve.
2) Strata correlation. The natural gamma curve has nothing to do with the properties of the fluid contained in the formation, and the salinity of the formation water has no effect on it. Therefore, the amplitude of natural gamma curve mainly depends on the content of radioactive substances such as potassium, thorium and uranium in the stratum, which is usually stable for different lithology. In addition, the standard layer for comparison is also easy to choose. Usually, thick mudstone is used as the standard layer for stratigraphic correlation in oil fields or regions (Figure 3- 10).
3) Calculate the shale content of the formation. In order to calculate the shale content of the formation, firstly, the shale content index of the interpretation layer is calculated by using the natural gamma amplitude of the pure formation and pure mudstone in the interpretation interval:
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Among them, CGR, CGR, sh, CGR and clean are natural gamma logging values to explain strata, pure mudstone and pure strata respectively.
Obviously, the ish of pure mudstone is 1, and the ish of pure formation is 0. Use the following formula to convert Ish into shale content Vsh:
Figure 3- 10 determines the distribution of sandstone in the east/west profile of the oilfield 1 and class 2.
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Where g is the regional empirical coefficient, which can be obtained from the experimental data of this region (generally speaking, the tertiary stratum is 3.7 and the old stratum is 2).