- Email: [email protected]
Express measurement of solid fuel ash content by nuclear gamma-method
Applied Radiation and Isotopes 147 (2019) 54–58
Contents lists available at ScienceDirect
Applied Radiation and Isotopes journal homepage: www.elsevier.com/locate/apradiso
Express measurement of solid fuel ash content by nuclear gamma-method ∗
Yu Pak , D. Pak, М. Ponomaryova, М. Imanov, B. Balbekova
T
Karaganda State Technical University, Karaganda, Kazakhstan
A R T I C LE I N FO
A B S T R A C T .
Keywords: Coal ash Radioisotope control Scattered gamma radiation X-ray fluorescence Optimization of parameters Error of analysis
The methodological features of determining the ash content in coal using scattered gamma radiation are considered in the present study. Theoretical and experimental studies have shown that the integral intensity of secondary (scattered and fluorescent) radiation can serve as an instrumental signal depending on the quality of coal. To achieve a more unambiguous relationship between the integral radiation intensity and the ash content in coal of variable material composition, a compensation technique has been proposed consisting in artificial attenuating secondary radiation. The laws governing the integral intensity of radiation depending on the inverse thickness of the filter are studied, and the results are found to be invariant with variations in the ash composition. A model has been developed to optimize the filtering parameters of secondary radiation by considering the regularity of changes in the filter inversion thickness depending on the ash content.
1. Introduction The imperfection of the traditional (standard) thermo-weight method of determining the ash content of coal because of its destructiveness, low expressivity, and low representation, as well as the increasing need to obtain timely information about the quality of fuel during its extraction and processing, has actualized the development of more advanced instrumental physical methods using nuclear radiation [Klempner and Vasilyev, 1978; Starchik and Pak, 1985]. Among these methods, the method based on scattering gamma radiation has attracted increasing attention. Practical interest in this method is due to the relatively high sensitivity to ash, ease of hardware implementation, and efficiency of nondestructive analysis. However, the wide applicability of most modifications of the gamma method is hampered by the low accuracy of the ash content under conditions of significant variability in the elemental composition of the coal mineral part. The problem is aggravated by the increasing volume of mechanized coal mining in complex mining and geological conditions, which contribute to increasing the degree of contamination of coal by rock. Coal, as an object of nuclear-physical control, is a complex compound that includes an organic mass and a multicomponent mixture of mineral impurities represented by both light (Mg, Al, and Si) and heavy (K, Ca, and Fe) elements. Moreover, more than 95% of the total mineral mass of fossil coal accounts for compounds of aluminum, silicon, calcium, and iron. In most coal deposits, aluminosilicates constitute a significant (∼75%) and the most stable part of the mineral mass. By
∗
considering differences in the atomic numbers of the constituent components of the mineral (ash-forming) part and, consequently, in the values of the mass attenuation coefficients of gamma radiation, a conclusion can be drawn on the decisive effect of fluctuations in the content of heavy elements, in particular calcium and iron, on the accuracy of measuring the coal ash by the gamma method. The most integral characteristic of coal associated with its elemental composition is the effective atomic number Z , whose relationship with the coal ash determines the methodological basis of the gamma method based on scattering low-energy (< 80 keV) gamma radiation [Starchik and Pak, 1985]. The interconnection stability of the effective atomic number of coal and its ash content is determined by the elemental composition of the mineral part of coal and by the fluctuations due to the concentration of individual elements, especially the heavy ones. The study has shown that when the coal ash content changes by 10% (with the following average ash composition, %: Al2O3 – 20; SiO2 – 55; CaO – 15; and Fe2O3 – 10), the effective atomic number of coal changes by 0.85. When the natural Z fluctuation is only 0.15, the error in determining the ash content will be approximately 2% abs. [Pak, 1987; Pak and Pak, 2011]. 2. Simulation and computed dependences A more accurate assessment of the metrological characteristics and capabilities of the method can be made by analytical calculations of the intensities of scattered gamma radiation depending on the gammascattering and gamma-absorbing properties of the analyzed coal. A
Corresponding author. E-mail address: [email protected] (Y. Pak).
https://doi.org/10.1016/j.apradiso.2019.02.010 Received 20 November 2018; Received in revised form 14 January 2019; Accepted 11 February 2019 Available online 15 February 2019 0969-8043/ © 2019 Elsevier Ltd. All rights reserved.
Applied Radiation and Isotopes 147 (2019) 54–58
Y. Pak, et al.
variations in the iron content in ash by 3% (Fig. 2a, curves 2 and 3) will lead to errors in determining the ash content in the NS value by (1.7–2.2)% abs. With the same dispersion of the calcium content in ash (Fig. 2b, curves 2 and 3), the error in measuring the ash content will be 1.2–1.5% abs. Thus, the gamma method with registration of gamma radiation scattered by coal gives satisfactory results in cases of relatively stable composition of the coal mineral part.
fairly accurate analytical expression for the intensity of scattered gamma radiation was obtained in a single scattering approximation [Starchik and Pak, 1985]:
Ns = NO σo (μo + μs )−1
(1)
where, NO is the intensity of primary gamma radiation; σO is the mass scattering coefficient of primary gamma radiation by coal; and μO and μS are the mass attenuation coefficients of primary and scattered radiation by coal, respectively. In computational studies, coal is represented by a three-component mixture of carbon and mineral (ash-forming) mass in the form of aluminosilicates and compounds of heavy components (FeS2.CaO). Following this model, the mass interaction coefficients (σO , μO , and μS ) are calculated according to the principle of additivity:
3. Ways of increasing accuracy The problem of increasing the accuracy of measuring the ash content of coal in terms of the intensity of scattered gamma radiation is solved by improving methodological approaches in the direction of minimizing the destabilizing effect of the variability of the material composition of the mineral part of the fuel. The use of the spectrometric modification of the gamma method, in which gamma radiation scattered forward (at small angles) is recorded, makes it possible to reduce the disturbing effect of iron in a small range of its fluctuations [Vasilyev et al., 1979]. The complexity of processing the results of spectrometric measurements associated with solving a system of nonlinear equations limits the applicability of the method to cases of instrumental analysis of coals with a small interval of variations in the material composition. The effect of inconstancy in iron content can be reduced by separately registering coherently and incoherently scattered gamma radiation [Pak and Pak, 2012]. The implementation of this technique is limited by its low sensitivity to the ash content of coal and the need to use highprecision spectrometric equipment with high-energy resolution. The problem of increasing the accuracy of measuring the coal ash content in terms of the intensity of scattered gamma radiation is solved by improving methodological approaches in the aspect of minimizing the destabilizing effect of variability of the material composition of the fuel mineral part. The use of spectrometric modification of the gamma method, in which gamma radiation scattered forward (at small angles) is recorded, makes it possible to reduce the disturbing effect of iron in a small range of its fluctuations [Vasilyev et al., 1979]. In the world practice, the gamma method has gained widespread modifications, in which the integral intensity of secondary radiation includes not only scattered gamma radiation but also X-ray fluorescence of the ash-forming element, in particular iron [Dijkstra and Sieswerda, 1958; Onishchenko and Grabov, 1979; Pak, 1980; V International coal enrichment congress. M., 1970; Transact. of the Society of Mining Engineers, 1976]. A characteristic feature of these modifications is
σO = σOC + A·Δσ + m ·Δσ / μO = μOC + A·ΔμO + m ·ΔμO/
μS = μSC + A·ΔμS + m ·ΔμS/ where, Δσ = σOH − σOC ; Δσ / = σOT − σOH ; Δμ = μOH − μOC ; Δμoi = μoT − μoH ; ΔμS = μSH − μSC ; Δ μS/ = μST − μSH ; and m is the content of the heavy ash-forming component. The C, T, and H indices are referred, respectively, to carbon, heavy ash-forming component, and ash filler (aluminosilicates). The individual effect of the coal ash content and the composition of the ash on the intensity of scattered gamma radiation of various energies is shown in Fig. 1. In general, the inverse dependence of the intensity of scattered gamma radiation on the ash content is confirmed. The higher the effective atomic number of the mineral component, the higher is the differentiation of the analytical parameter when the ash content changes. When using primary gamma radiation with energy of 5.9 keV (below the energy of the K-absorption edge of iron), the gamma-attenuating characteristics of iron are comparable to those of aluminum [Storm and Israel, 1973]. Computational studies of the intensity of scattered gamma radiation depending on the content of heavy components, in particular iron (Fig. 2a) and calcium (Fig. 2b), performed for various energies show the ambiguous intensity character depending on the ash composition. This is explained by the difference in the constituents of ash in the attenuation coefficients. When using primary gamma radiation with energy higher than the ionization potential of iron (ЕК = 7.11 keV),
Fig. 1. The effect of coal ash content A modeled by SiO2, CaO, and FeS2 on the intensity NS of scattered γ-radiation at various energies of primary radiation: a – 5.9 keV; b – 8 keV; and c – 22 keV. 55
Applied Radiation and Isotopes 147 (2019) 54–58
Y. Pak, et al.
Fig. 2. Dependences of the intensity NS of scattered γ-radiation on the iron content mFe (a) and calcium content mCa (b) in ash: 1 – Fe-55 (5.9 keV); 2 – H3eZr (∼8 keV); and 3 – Pu-238 (∼16 keV).
including calcium X-ray fluorescence is described in the work by [Pak, 1980]. The invariance of the total intensity of scattered gamma radiation from the Fe-55 radioisotope source (5.9 keV) and calcium fluorescent radiation (∼37 keV) with variations in the calcium content in ashes is provided by artificially reducing secondary radiation by a filter that selectively suppresses calcium X-ray fluorescence, the intensity of which can be estimated from the following expression [Starchik and Pak, 1985]:
measuring the integral intensity of secondary radiation attenuated by a filter made up of a light element. Selecting a certain thickness of the attenuating filter ensures the equality of the increments of scattered and fluorescent radiations by varying the iron content in ash. These modifications of the gamma method, implemented with primary gamma emitters with energies from 8 to 22 keV, make it possible to reduce partially the error due to fluctuations in the concentration of iron. However, there remains the destabilizing effect of the inconstancy of the calcium content, which is the second element after iron with a high gamma ray-absorbing ability. Methodological opportunities of the nuclear gamma method in terms of improving the analysis accuracy for coals of variable material composition are significantly expanded when using primary gamma radiation with energy below the K-absorption edge of iron. In this case, as it is noted earlier, iron is comparable in its gamma-absorbing properties to aluminum. Then, the ash-forming mass of fuel with a desirable approximation can be approximated by a binary mixture of aluminosilicates and calcium, and the task of the accurate analysis of the ash content in coal is reduced to searching for methodological approaches that reduce the error due to variations in the calcium content in ash. The ambiguity of the intensity of scattered gamma radiation depending on the ash content is caused by the redistribution of the ash composition (aluminosilicates and calcium oxide) uncorrelated with the ash content and the difference in their gamma ray-absorbing properties.
Ni = NO WK (SK − 1) SK−1 τmA (μO + μi )−1
(2)
where, WK is the coefficient of calcium fluorescence output; SK is the value of the К-jump of calcium absorption; τ is the mass coefficient of photoelectric absorption of primary gamma radiation by calcium; m is the calcium content in ash; А is the coal ash; and μ i is the mass attenuation coefficient of calcium radiation by coal. The μ i coefficient is calculated according to the principle of additivity, similar to μо. The studies have shown that when the calcium content in ash changes, regardless of the ash content of coal, the increment in the intensity of fluorescent calcium emission Ni compared to the increment in the intensity of the scattered radiation of NS is higher in value and has the reverse sign. The qualitatively different nature of changing the intensities of scattered NS and fluorescent Ni radiation with changing the calcium content in ash makes it possible to recommend the value of the total intensity of scattered and fluorescent radiation as an analytical signal for determining the ash content of coal. The intensity of secondary radiation is complexly dependent on the concentration of calcium in ash, the degree of filtration of secondary radiation (thickness of the attenuating filter), and the ash content in coal itself (Fig. 3).
4. Results For the first time, the idea of the compensation principle that consists in measuring the integral intensity of secondary radiation
Fig. 3. Dependences of the integral intensity N of secondary radiation on the CaO content in ash: a–d = 1 mg/cm2; b–d = 3 mg/cm2;and c–d = 5 mg/cm2; curves indicate ash content, %. 56
Applied Radiation and Isotopes 147 (2019) 54–58
Y. Pak, et al.
The compensation effect is not achieved with insufficient filtration of secondary radiation (Fig. 3a). Some invariance of the integral intensity, with variations in the CaO concentration, is observed at the filter thickness of 3 mg/cm2 in a limited range of the ash content (Fig. 3b). For high-ash coals (Fig. 3c), the independence of the integral analytical signal is achieved with a larger filter thickness. The insensitive regions for calcium vary depending on the ash content in coal and the degree of the secondary radiation attenuation. Increasing and decreasing the integral intensity of secondary radiation depending on the calcium concentration in ashes is caused by undercompensation of fluorescent radiation with a small thickness of the attenuating filter or overcompensation with a large thickness. The analytical expression for the optimal thickness of the attenuating filter is found from the condition of equality of the absolute increments of the intensities of scattered ∂NS and fluorescent ∂Ni radiation, with a single ∂m changing in the calcium content:
∂NS ∂N = − i, ∂m ∂m
(3)
Using equation (1) for intensity NS and equations (2) and (3) for intensity Ni and equality after simple transformations, we determine the ratio for the optimal thickness of the attenuating filter:
d = ln
i Ni⋅SCa (μ1 − μ 2 )−1 , S NS⋅SCa
(4)
where, μ1 and μ 2 are the mass attenuation coefficients of, respectively, fluorescent and scattered radiation by the filter; i S SCa and SCa are sensitivity to calcium on, respectively, fluorescent and scattered radiation. The resulting expression allows simulating coal of different qualities and different replacement schemes for the ash-forming mass. This simulation is close to real conditions because it includes the hardwarei s measured parameters (Ni, NS, SCa , and SCa ). The coefficients μ1 and μ 2 , with the selected energy of primary gamma radiation, are constants. The variable parameters affecting the choice of the optimal thickness of the attenuating filter are the ash content of coal and the concentration of calcium, depending on which the intensities Ni and NS vary, as well i S and SCa . In production conditions, as the values of the sensitivities SCa when various coals of variable material compositions are analyzed, it is difficult to have a priori the information about the ash content. In actual practice, the thickness of the weakening filter is as a rule selected from the average values of the ash content in coal. With an insignificant range of ash content fluctuations (2.5% abs.), the attenuating filter selected according to equation (4) for the average ash content can be considered optimal from the point of view of satisfactory accuracy for the entire range. If the ash content varies over a wide range (more than ± 5–6% abs.), the choice of the thickness of the attenuating filter according to the average ash content will be ineffective because of the significant error in measuring the ash content. To expand the methodological possibilities of the considered compensation gamma method as applied to coal with a highly varied ash content, patterns of variation in the integral intensity of secondary radiation depending on the thickness of the attenuating filter were studied experimentally. The inversion nature of the intensity of secondary gamma radiation has been observed on standard samples of coals with known ash content and different compositions (calcium concentration in ashes) depending on the calcium content. It means that with a certain filter thickness, the intensity is independent of varying the calcium content (Fig. 4). The area of intersection of dependences corresponding to the coals of the same ash content, but with different calcium contents, regularly shifts along the axis of the filter thickness, which is caused by the difference in throughput of the attenuating filter in relation to calcium X-ray fluorescence and scattered gamma radiation. In the preinversion region (to the left of the inversion), fluorescent radiation of calcium plays a prevailing role in the integral intensity. In the inversion region (to the right of the inversion), the opposite pattern is
Fig. 4. Dependences of the integral intensity N of secondary radiation on the thickness d of the filter for various ash content A in coal and calcium content mв in ash rel.un. (relative unit).
observed: scattered gamma radiation dominates in secondary radiation. A clear pattern has been established between the ash content and the inversion thickness of the attenuating filter, at which the compensation effect is achieved (with variations in the calcium content in ash, the integral intensity of secondary radiation remains unchanged). This allows obtaining the boundary dependence between the integral intensity of secondary radiation and the inversion thickness of the filter. To determine the optimal thickness of the attenuating filter when analyzing coal of unknown quality, it is recommended to measure the current dependence of the intensity of secondary radiation on the filter thickness and to select such dопт thickness as the optimum, at which the intensity of secondary radiation of the current dependence coincides with the intensity of the boundary dependence. This methodical approach allows optimizing the choice of the thickness of the attenuating filter under the condition that there is no a priori information about the ash content of the analyzed coal and the range of its fluctuations. Experimental thickness according to the boundary dependence of the integrated intensity of secondary radiation on the inversion thickness was performed using standard X-ray radiometric equipment including a radionuclide source of Fe-55 (∼5.9 keV) with 15 mCi activity and a proportional detector approbation of the proposed method with optimization of the attenuating filter SIe11P. In front of the entrance window of the detector, there was an attenuating filter made up of aluminum foil. The selected standard reflection geometry (source–sample–detector) provided the maximum measurement contrast, absence of edge interaction effects, and minimum level of background radiation. Coal samples of analytical size (∼0.1 mm) were analyzed and placed in a cylindrical cuvette of diameter 60 mm and height 4 mm. When measuring the integral intensity of secondary radiation within 120 s, the relative statistical measurement error was 0.2%. Table 1 presents metrological characteristics of various modifications of the 57
Applied Radiation and Isotopes 147 (2019) 54–58
Y. Pak, et al.
the integral intensity of secondary radiation (scattered and fluorescent) are considered. Theoretical and experimental studies of the gamma radiation albedo with energy below the ionization potential of iron have established the inversion nature of the intensity of secondary radiation from the calcium content in the ash. An analytical model has been developed that relates the optimal thickness of the attenuating filter to the hardware-measured parameters, thus making it possible to compensate for the disturbing effect of the inconstancy of the ash elemental composition. On the basis of the boundary dependence of the integral intensity on the inversion thickness of the filter associated with the ash of coal, a methodical approach is proposed that provides satisfactory accuracy in determining the ash content in coal of variable compositions within a large range of its variation.
Table 1 Metrological characteristics of the method modifications. The range of ash content changing range, %
7–11 7–18 18–32
The error of measuring the ash content, % abs. I
II
III
1.26 2.19 3.6
0.31 0.93 1.74
0.29 0.36 0.98
nuclear gamma method of controlling the ash content in coal of variable compositions. In coal samples, the calcium content varied within (1.8–10.2)%. The gamma method (I) based on the registration of gamma radiation scattered by coal because of its dependence on the ash composition, in particular the calcium content, is characterized by a significant error in measuring the ash content, regardless of the range of its fluctuations. The gamma method (II) in terms of the integral intensity of secondary radiation attenuated by a filter of finite thickness selected according to the average value of the ash content is effective from the point of view of accuracy of analysis with a slight dispersion of the ash content. With increasing ash content and the range of its fluctuations, the error in measuring the ash content naturally increases. The compensation gamma method (III) by the integral intensity of secondary radiation attenuated by a filter of variable thickness selected by the boundary dependence of the intensity on the inversion thickness of the filter, allows minimizing the error due to inconstancy of the ash composition in the absence of a priori information about the ash content. An increase in the analysis error observed for higher ash coals is caused by a regular decrease in sensitivity to the ash content for each modification of the method.
References Dijkstra, H., Sieswerda, B.S., 1958. Internat. Kongress Fur Steinkohlenaufbereitung, Luttich, Bercht F, vol. 9. pp. 126–129. Klempner, K.S., Vasilyev, A.G., 1978. Physical Methods for Controlling the Ash Content of Coal. M.: Nedra. pp. 176. Onishchenko, A.M., Grabov, P.I., 1979. Radioisotope methods and devices for controlling the ash content of coal. Coke Chem. 10, 7–15. Pak, YuN., 1980. To the Method of Increasing the Accuracy of the Radioisotope Analysis of the Ash Content of Coal, vol. 46. Zavodskaya Laboratory, pp. 743–744 No. 8. S. Pak, Yu, 1987. Possibility of accounting for inconsistency in elemental composition during radioisotopic control of coal ash content. Coke Chem. 6, 66–71. Pak, Y.N., Pak, D.Y., 2011. High-speed radioisotopic quality monitoring of coal of variable composition. Coke Chem. 54 (4), 108–113. Pak, YuN., Pak, D.Yu, 2012. Methods and Instruments for Nuclear Physical Analysis of Coal. Publishing house of KSTU, Karaganda, pp. 186. Starchik, L.P., Pak, YuN., 1985. Nuclear Physics Methods for Controlling the Quality of Solid Fuels. M.: Nedra. pp. 224. Storm, E., Israel, H., 1973. The Cross-Section of the Interaction of Gamma Radiation. M.: Atomizdat. pp. 256. Transact of the Society of Mining Engineers, 1976. V. 260. No. 4. P. 361-366. Vasilyev, A.G., Onishchenko, A.M., Kuznetsova, A.N., 1979. Physical and Technical Problems in the Development of Mineral Resources, vol. 12. pp. 89–94.
5. Conclusion The features of gamma-method modifications based on measuring
58
Contents lists available at ScienceDirect
Applied Radiation and Isotopes journal homepage: www.elsevier.com/locate/apradiso
Express measurement of solid fuel ash content by nuclear gamma-method ∗
Yu Pak , D. Pak, М. Ponomaryova, М. Imanov, B. Balbekova
T
Karaganda State Technical University, Karaganda, Kazakhstan
A R T I C LE I N FO
A B S T R A C T .
Keywords: Coal ash Radioisotope control Scattered gamma radiation X-ray fluorescence Optimization of parameters Error of analysis
The methodological features of determining the ash content in coal using scattered gamma radiation are considered in the present study. Theoretical and experimental studies have shown that the integral intensity of secondary (scattered and fluorescent) radiation can serve as an instrumental signal depending on the quality of coal. To achieve a more unambiguous relationship between the integral radiation intensity and the ash content in coal of variable material composition, a compensation technique has been proposed consisting in artificial attenuating secondary radiation. The laws governing the integral intensity of radiation depending on the inverse thickness of the filter are studied, and the results are found to be invariant with variations in the ash composition. A model has been developed to optimize the filtering parameters of secondary radiation by considering the regularity of changes in the filter inversion thickness depending on the ash content.
1. Introduction The imperfection of the traditional (standard) thermo-weight method of determining the ash content of coal because of its destructiveness, low expressivity, and low representation, as well as the increasing need to obtain timely information about the quality of fuel during its extraction and processing, has actualized the development of more advanced instrumental physical methods using nuclear radiation [Klempner and Vasilyev, 1978; Starchik and Pak, 1985]. Among these methods, the method based on scattering gamma radiation has attracted increasing attention. Practical interest in this method is due to the relatively high sensitivity to ash, ease of hardware implementation, and efficiency of nondestructive analysis. However, the wide applicability of most modifications of the gamma method is hampered by the low accuracy of the ash content under conditions of significant variability in the elemental composition of the coal mineral part. The problem is aggravated by the increasing volume of mechanized coal mining in complex mining and geological conditions, which contribute to increasing the degree of contamination of coal by rock. Coal, as an object of nuclear-physical control, is a complex compound that includes an organic mass and a multicomponent mixture of mineral impurities represented by both light (Mg, Al, and Si) and heavy (K, Ca, and Fe) elements. Moreover, more than 95% of the total mineral mass of fossil coal accounts for compounds of aluminum, silicon, calcium, and iron. In most coal deposits, aluminosilicates constitute a significant (∼75%) and the most stable part of the mineral mass. By
∗
considering differences in the atomic numbers of the constituent components of the mineral (ash-forming) part and, consequently, in the values of the mass attenuation coefficients of gamma radiation, a conclusion can be drawn on the decisive effect of fluctuations in the content of heavy elements, in particular calcium and iron, on the accuracy of measuring the coal ash by the gamma method. The most integral characteristic of coal associated with its elemental composition is the effective atomic number Z , whose relationship with the coal ash determines the methodological basis of the gamma method based on scattering low-energy (< 80 keV) gamma radiation [Starchik and Pak, 1985]. The interconnection stability of the effective atomic number of coal and its ash content is determined by the elemental composition of the mineral part of coal and by the fluctuations due to the concentration of individual elements, especially the heavy ones. The study has shown that when the coal ash content changes by 10% (with the following average ash composition, %: Al2O3 – 20; SiO2 – 55; CaO – 15; and Fe2O3 – 10), the effective atomic number of coal changes by 0.85. When the natural Z fluctuation is only 0.15, the error in determining the ash content will be approximately 2% abs. [Pak, 1987; Pak and Pak, 2011]. 2. Simulation and computed dependences A more accurate assessment of the metrological characteristics and capabilities of the method can be made by analytical calculations of the intensities of scattered gamma radiation depending on the gammascattering and gamma-absorbing properties of the analyzed coal. A
Corresponding author. E-mail address: [email protected] (Y. Pak).
https://doi.org/10.1016/j.apradiso.2019.02.010 Received 20 November 2018; Received in revised form 14 January 2019; Accepted 11 February 2019 Available online 15 February 2019 0969-8043/ © 2019 Elsevier Ltd. All rights reserved.
Applied Radiation and Isotopes 147 (2019) 54–58
Y. Pak, et al.
variations in the iron content in ash by 3% (Fig. 2a, curves 2 and 3) will lead to errors in determining the ash content in the NS value by (1.7–2.2)% abs. With the same dispersion of the calcium content in ash (Fig. 2b, curves 2 and 3), the error in measuring the ash content will be 1.2–1.5% abs. Thus, the gamma method with registration of gamma radiation scattered by coal gives satisfactory results in cases of relatively stable composition of the coal mineral part.
fairly accurate analytical expression for the intensity of scattered gamma radiation was obtained in a single scattering approximation [Starchik and Pak, 1985]:
Ns = NO σo (μo + μs )−1
(1)
where, NO is the intensity of primary gamma radiation; σO is the mass scattering coefficient of primary gamma radiation by coal; and μO and μS are the mass attenuation coefficients of primary and scattered radiation by coal, respectively. In computational studies, coal is represented by a three-component mixture of carbon and mineral (ash-forming) mass in the form of aluminosilicates and compounds of heavy components (FeS2.CaO). Following this model, the mass interaction coefficients (σO , μO , and μS ) are calculated according to the principle of additivity:
3. Ways of increasing accuracy The problem of increasing the accuracy of measuring the ash content of coal in terms of the intensity of scattered gamma radiation is solved by improving methodological approaches in the direction of minimizing the destabilizing effect of the variability of the material composition of the mineral part of the fuel. The use of the spectrometric modification of the gamma method, in which gamma radiation scattered forward (at small angles) is recorded, makes it possible to reduce the disturbing effect of iron in a small range of its fluctuations [Vasilyev et al., 1979]. The complexity of processing the results of spectrometric measurements associated with solving a system of nonlinear equations limits the applicability of the method to cases of instrumental analysis of coals with a small interval of variations in the material composition. The effect of inconstancy in iron content can be reduced by separately registering coherently and incoherently scattered gamma radiation [Pak and Pak, 2012]. The implementation of this technique is limited by its low sensitivity to the ash content of coal and the need to use highprecision spectrometric equipment with high-energy resolution. The problem of increasing the accuracy of measuring the coal ash content in terms of the intensity of scattered gamma radiation is solved by improving methodological approaches in the aspect of minimizing the destabilizing effect of variability of the material composition of the fuel mineral part. The use of spectrometric modification of the gamma method, in which gamma radiation scattered forward (at small angles) is recorded, makes it possible to reduce the disturbing effect of iron in a small range of its fluctuations [Vasilyev et al., 1979]. In the world practice, the gamma method has gained widespread modifications, in which the integral intensity of secondary radiation includes not only scattered gamma radiation but also X-ray fluorescence of the ash-forming element, in particular iron [Dijkstra and Sieswerda, 1958; Onishchenko and Grabov, 1979; Pak, 1980; V International coal enrichment congress. M., 1970; Transact. of the Society of Mining Engineers, 1976]. A characteristic feature of these modifications is
σO = σOC + A·Δσ + m ·Δσ / μO = μOC + A·ΔμO + m ·ΔμO/
μS = μSC + A·ΔμS + m ·ΔμS/ where, Δσ = σOH − σOC ; Δσ / = σOT − σOH ; Δμ = μOH − μOC ; Δμoi = μoT − μoH ; ΔμS = μSH − μSC ; Δ μS/ = μST − μSH ; and m is the content of the heavy ash-forming component. The C, T, and H indices are referred, respectively, to carbon, heavy ash-forming component, and ash filler (aluminosilicates). The individual effect of the coal ash content and the composition of the ash on the intensity of scattered gamma radiation of various energies is shown in Fig. 1. In general, the inverse dependence of the intensity of scattered gamma radiation on the ash content is confirmed. The higher the effective atomic number of the mineral component, the higher is the differentiation of the analytical parameter when the ash content changes. When using primary gamma radiation with energy of 5.9 keV (below the energy of the K-absorption edge of iron), the gamma-attenuating characteristics of iron are comparable to those of aluminum [Storm and Israel, 1973]. Computational studies of the intensity of scattered gamma radiation depending on the content of heavy components, in particular iron (Fig. 2a) and calcium (Fig. 2b), performed for various energies show the ambiguous intensity character depending on the ash composition. This is explained by the difference in the constituents of ash in the attenuation coefficients. When using primary gamma radiation with energy higher than the ionization potential of iron (ЕК = 7.11 keV),
Fig. 1. The effect of coal ash content A modeled by SiO2, CaO, and FeS2 on the intensity NS of scattered γ-radiation at various energies of primary radiation: a – 5.9 keV; b – 8 keV; and c – 22 keV. 55
Applied Radiation and Isotopes 147 (2019) 54–58
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Fig. 2. Dependences of the intensity NS of scattered γ-radiation on the iron content mFe (a) and calcium content mCa (b) in ash: 1 – Fe-55 (5.9 keV); 2 – H3eZr (∼8 keV); and 3 – Pu-238 (∼16 keV).
including calcium X-ray fluorescence is described in the work by [Pak, 1980]. The invariance of the total intensity of scattered gamma radiation from the Fe-55 radioisotope source (5.9 keV) and calcium fluorescent radiation (∼37 keV) with variations in the calcium content in ashes is provided by artificially reducing secondary radiation by a filter that selectively suppresses calcium X-ray fluorescence, the intensity of which can be estimated from the following expression [Starchik and Pak, 1985]:
measuring the integral intensity of secondary radiation attenuated by a filter made up of a light element. Selecting a certain thickness of the attenuating filter ensures the equality of the increments of scattered and fluorescent radiations by varying the iron content in ash. These modifications of the gamma method, implemented with primary gamma emitters with energies from 8 to 22 keV, make it possible to reduce partially the error due to fluctuations in the concentration of iron. However, there remains the destabilizing effect of the inconstancy of the calcium content, which is the second element after iron with a high gamma ray-absorbing ability. Methodological opportunities of the nuclear gamma method in terms of improving the analysis accuracy for coals of variable material composition are significantly expanded when using primary gamma radiation with energy below the K-absorption edge of iron. In this case, as it is noted earlier, iron is comparable in its gamma-absorbing properties to aluminum. Then, the ash-forming mass of fuel with a desirable approximation can be approximated by a binary mixture of aluminosilicates and calcium, and the task of the accurate analysis of the ash content in coal is reduced to searching for methodological approaches that reduce the error due to variations in the calcium content in ash. The ambiguity of the intensity of scattered gamma radiation depending on the ash content is caused by the redistribution of the ash composition (aluminosilicates and calcium oxide) uncorrelated with the ash content and the difference in their gamma ray-absorbing properties.
Ni = NO WK (SK − 1) SK−1 τmA (μO + μi )−1
(2)
where, WK is the coefficient of calcium fluorescence output; SK is the value of the К-jump of calcium absorption; τ is the mass coefficient of photoelectric absorption of primary gamma radiation by calcium; m is the calcium content in ash; А is the coal ash; and μ i is the mass attenuation coefficient of calcium radiation by coal. The μ i coefficient is calculated according to the principle of additivity, similar to μо. The studies have shown that when the calcium content in ash changes, regardless of the ash content of coal, the increment in the intensity of fluorescent calcium emission Ni compared to the increment in the intensity of the scattered radiation of NS is higher in value and has the reverse sign. The qualitatively different nature of changing the intensities of scattered NS and fluorescent Ni radiation with changing the calcium content in ash makes it possible to recommend the value of the total intensity of scattered and fluorescent radiation as an analytical signal for determining the ash content of coal. The intensity of secondary radiation is complexly dependent on the concentration of calcium in ash, the degree of filtration of secondary radiation (thickness of the attenuating filter), and the ash content in coal itself (Fig. 3).
4. Results For the first time, the idea of the compensation principle that consists in measuring the integral intensity of secondary radiation
Fig. 3. Dependences of the integral intensity N of secondary radiation on the CaO content in ash: a–d = 1 mg/cm2; b–d = 3 mg/cm2;and c–d = 5 mg/cm2; curves indicate ash content, %. 56
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The compensation effect is not achieved with insufficient filtration of secondary radiation (Fig. 3a). Some invariance of the integral intensity, with variations in the CaO concentration, is observed at the filter thickness of 3 mg/cm2 in a limited range of the ash content (Fig. 3b). For high-ash coals (Fig. 3c), the independence of the integral analytical signal is achieved with a larger filter thickness. The insensitive regions for calcium vary depending on the ash content in coal and the degree of the secondary radiation attenuation. Increasing and decreasing the integral intensity of secondary radiation depending on the calcium concentration in ashes is caused by undercompensation of fluorescent radiation with a small thickness of the attenuating filter or overcompensation with a large thickness. The analytical expression for the optimal thickness of the attenuating filter is found from the condition of equality of the absolute increments of the intensities of scattered ∂NS and fluorescent ∂Ni radiation, with a single ∂m changing in the calcium content:
∂NS ∂N = − i, ∂m ∂m
(3)
Using equation (1) for intensity NS and equations (2) and (3) for intensity Ni and equality after simple transformations, we determine the ratio for the optimal thickness of the attenuating filter:
d = ln
i Ni⋅SCa (μ1 − μ 2 )−1 , S NS⋅SCa
(4)
where, μ1 and μ 2 are the mass attenuation coefficients of, respectively, fluorescent and scattered radiation by the filter; i S SCa and SCa are sensitivity to calcium on, respectively, fluorescent and scattered radiation. The resulting expression allows simulating coal of different qualities and different replacement schemes for the ash-forming mass. This simulation is close to real conditions because it includes the hardwarei s measured parameters (Ni, NS, SCa , and SCa ). The coefficients μ1 and μ 2 , with the selected energy of primary gamma radiation, are constants. The variable parameters affecting the choice of the optimal thickness of the attenuating filter are the ash content of coal and the concentration of calcium, depending on which the intensities Ni and NS vary, as well i S and SCa . In production conditions, as the values of the sensitivities SCa when various coals of variable material compositions are analyzed, it is difficult to have a priori the information about the ash content. In actual practice, the thickness of the weakening filter is as a rule selected from the average values of the ash content in coal. With an insignificant range of ash content fluctuations (2.5% abs.), the attenuating filter selected according to equation (4) for the average ash content can be considered optimal from the point of view of satisfactory accuracy for the entire range. If the ash content varies over a wide range (more than ± 5–6% abs.), the choice of the thickness of the attenuating filter according to the average ash content will be ineffective because of the significant error in measuring the ash content. To expand the methodological possibilities of the considered compensation gamma method as applied to coal with a highly varied ash content, patterns of variation in the integral intensity of secondary radiation depending on the thickness of the attenuating filter were studied experimentally. The inversion nature of the intensity of secondary gamma radiation has been observed on standard samples of coals with known ash content and different compositions (calcium concentration in ashes) depending on the calcium content. It means that with a certain filter thickness, the intensity is independent of varying the calcium content (Fig. 4). The area of intersection of dependences corresponding to the coals of the same ash content, but with different calcium contents, regularly shifts along the axis of the filter thickness, which is caused by the difference in throughput of the attenuating filter in relation to calcium X-ray fluorescence and scattered gamma radiation. In the preinversion region (to the left of the inversion), fluorescent radiation of calcium plays a prevailing role in the integral intensity. In the inversion region (to the right of the inversion), the opposite pattern is
Fig. 4. Dependences of the integral intensity N of secondary radiation on the thickness d of the filter for various ash content A in coal and calcium content mв in ash rel.un. (relative unit).
observed: scattered gamma radiation dominates in secondary radiation. A clear pattern has been established between the ash content and the inversion thickness of the attenuating filter, at which the compensation effect is achieved (with variations in the calcium content in ash, the integral intensity of secondary radiation remains unchanged). This allows obtaining the boundary dependence between the integral intensity of secondary radiation and the inversion thickness of the filter. To determine the optimal thickness of the attenuating filter when analyzing coal of unknown quality, it is recommended to measure the current dependence of the intensity of secondary radiation on the filter thickness and to select such dопт thickness as the optimum, at which the intensity of secondary radiation of the current dependence coincides with the intensity of the boundary dependence. This methodical approach allows optimizing the choice of the thickness of the attenuating filter under the condition that there is no a priori information about the ash content of the analyzed coal and the range of its fluctuations. Experimental thickness according to the boundary dependence of the integrated intensity of secondary radiation on the inversion thickness was performed using standard X-ray radiometric equipment including a radionuclide source of Fe-55 (∼5.9 keV) with 15 mCi activity and a proportional detector approbation of the proposed method with optimization of the attenuating filter SIe11P. In front of the entrance window of the detector, there was an attenuating filter made up of aluminum foil. The selected standard reflection geometry (source–sample–detector) provided the maximum measurement contrast, absence of edge interaction effects, and minimum level of background radiation. Coal samples of analytical size (∼0.1 mm) were analyzed and placed in a cylindrical cuvette of diameter 60 mm and height 4 mm. When measuring the integral intensity of secondary radiation within 120 s, the relative statistical measurement error was 0.2%. Table 1 presents metrological characteristics of various modifications of the 57
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the integral intensity of secondary radiation (scattered and fluorescent) are considered. Theoretical and experimental studies of the gamma radiation albedo with energy below the ionization potential of iron have established the inversion nature of the intensity of secondary radiation from the calcium content in the ash. An analytical model has been developed that relates the optimal thickness of the attenuating filter to the hardware-measured parameters, thus making it possible to compensate for the disturbing effect of the inconstancy of the ash elemental composition. On the basis of the boundary dependence of the integral intensity on the inversion thickness of the filter associated with the ash of coal, a methodical approach is proposed that provides satisfactory accuracy in determining the ash content in coal of variable compositions within a large range of its variation.
Table 1 Metrological characteristics of the method modifications. The range of ash content changing range, %
7–11 7–18 18–32
The error of measuring the ash content, % abs. I
II
III
1.26 2.19 3.6
0.31 0.93 1.74
0.29 0.36 0.98
nuclear gamma method of controlling the ash content in coal of variable compositions. In coal samples, the calcium content varied within (1.8–10.2)%. The gamma method (I) based on the registration of gamma radiation scattered by coal because of its dependence on the ash composition, in particular the calcium content, is characterized by a significant error in measuring the ash content, regardless of the range of its fluctuations. The gamma method (II) in terms of the integral intensity of secondary radiation attenuated by a filter of finite thickness selected according to the average value of the ash content is effective from the point of view of accuracy of analysis with a slight dispersion of the ash content. With increasing ash content and the range of its fluctuations, the error in measuring the ash content naturally increases. The compensation gamma method (III) by the integral intensity of secondary radiation attenuated by a filter of variable thickness selected by the boundary dependence of the intensity on the inversion thickness of the filter, allows minimizing the error due to inconstancy of the ash composition in the absence of a priori information about the ash content. An increase in the analysis error observed for higher ash coals is caused by a regular decrease in sensitivity to the ash content for each modification of the method.
References Dijkstra, H., Sieswerda, B.S., 1958. Internat. Kongress Fur Steinkohlenaufbereitung, Luttich, Bercht F, vol. 9. pp. 126–129. Klempner, K.S., Vasilyev, A.G., 1978. Physical Methods for Controlling the Ash Content of Coal. M.: Nedra. pp. 176. Onishchenko, A.M., Grabov, P.I., 1979. Radioisotope methods and devices for controlling the ash content of coal. Coke Chem. 10, 7–15. Pak, YuN., 1980. To the Method of Increasing the Accuracy of the Radioisotope Analysis of the Ash Content of Coal, vol. 46. Zavodskaya Laboratory, pp. 743–744 No. 8. S. Pak, Yu, 1987. Possibility of accounting for inconsistency in elemental composition during radioisotopic control of coal ash content. Coke Chem. 6, 66–71. Pak, Y.N., Pak, D.Y., 2011. High-speed radioisotopic quality monitoring of coal of variable composition. Coke Chem. 54 (4), 108–113. Pak, YuN., Pak, D.Yu, 2012. Methods and Instruments for Nuclear Physical Analysis of Coal. Publishing house of KSTU, Karaganda, pp. 186. Starchik, L.P., Pak, YuN., 1985. Nuclear Physics Methods for Controlling the Quality of Solid Fuels. M.: Nedra. pp. 224. Storm, E., Israel, H., 1973. The Cross-Section of the Interaction of Gamma Radiation. M.: Atomizdat. pp. 256. Transact of the Society of Mining Engineers, 1976. V. 260. No. 4. P. 361-366. Vasilyev, A.G., Onishchenko, A.M., Kuznetsova, A.N., 1979. Physical and Technical Problems in the Development of Mineral Resources, vol. 12. pp. 89–94.
5. Conclusion The features of gamma-method modifications based on measuring
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