Monte-Carlo Simulation of Response Functions for Natural Gamma-Rays in LaBr 3 Detector System with Complex Borehole Configurations WU Yongpeng ( ) 1,2, TANG Bin ( ) 2 1 Department of Engineering Physics, Tsinghua University, Beijing 100084, China 2 Key Laboratory of Radioactive Geology and Exploration Technology Fundamental Science for National Defense, East China Institute of Technology, Nanchang 344000, China Abstract Usually, there are several methods, e.g. experiment, interpolation experiment-based, analytic function, and Monte-Carlo simulation, to calculate the response functions in LaBr 3(Ce) detectors. In logging applications, the experiment-based methods cannot be adopted because of their limitations. Analytic function has the advantage of fast calculating speed, but it is very difficult to take into account many effects that occur in practical applications. On the contrary, Monte-Carlo simulation can deal with physical and geometric configurations very tactfully. It has a distinct advantage for calculating the functions with complex configurations in borehole. A new application of LaBr 3(Ce) detector is in natural gamma-rays borehole spectrometer for uranium well logging. Calculation of response functions must consider a series of physical and geometric factors under complex logging conditions, including earth formations and its relevant parameters, different energies, material and thickness of the casings, the fluid between the two tubes, and relative position of the LaBr 3(Ce) crystal to steel ingot at the front of logging tube. The present work establishes Monte-Carlo simulation models for the above-mentioned situations, and then performs calculations for main gamma-rays from natural radio-elements series. The response functions can offer experimental directions for the design of borehole detection system, and provide technique basis and basic data for spectral analysis of natural gamma-rays, and for sourceless calibration in uranium quantitative interpretation. Keywords: LaBr 3 (Ce) detector, complex borehole configurations, detector response function, Monte-Carlo simulation PACS: 29.40.Mc DOI: 10.1088/1009-0630/14/6/10 1 Introduction Uranium exploration is different from petroleum exploration. Uranium and its daughters can be detected from afar because they emit gamma-rays. Therefore, radiometric techniques are the most useful exploration methods. Logging techniques are very important in the evaluation of mine grade and reserve. Natural gammarays borehole logging is recognized as a feasible technique for evaluating uranium deposits. Borehole logging entails lowering a gamma-ray detecting system into a hole and measuring the radioactivity therein. It provides representative and objective borehole information required by the exploration in a rapid and economical way. In gross-count gamma-rays logging, the total gamma-rays intensity of earth formations is primarily the sum of contributions from potassium-40, uranium series and thorium series. Although DODD et al. suggested the use of natural gamma-rays spectralog in 1970, gross-count gamma logs are the only type used extensively in uranium exploration industry by China and world s main uranium producers including Kazakhstan. In recent years, however, borehole spectroscopy has been used to eliminate the effects of potassium-40 and thorium series. The borehole spectrometer based on NaI(Tl) detector is an advanced piece of radiometric equipment that can determine the particular energies of gamma-rays, and the relative equivalent concentrations of potassium, uranium and thorium can thus be determined. The cost required for the spectrometer is several times greater than for gross-count scintillometer. Because the comprehensive performances of NaI(Tl) detector is not excellent, spectral measurements require more time than gross-count surveys, the system is difficult to maintain in field, and frequent calibration is necessary [1]. The value of the results generally depends on the performances of the spectrometer, data processing and interpretation. High-resolution gammarays spectrometer probes are also being used to circumvent the problem of disequilibrium between uranium and its daughter products. A new technique to mea- supported by Key Laboratory of Radioactive Geology and Exploration Technology Fundamental Science for National Defense (No. 2011RGET04), East China Institute of Technology, and National Natural Science Foundation of China (No. 41074078)
sure and analyze natural gamma-rays spectra in borehole will be presented below. This technique combines a high-performance scintillation detector with full-spectrum data analysis. It uses the spectral shape changes and the so-called response functions to calculate the activity concentrations of potassium-40, thorium-232 and uranium-238 present in rocks. It is necessary to describe the full-spectrum and determine the response functions for the new technique. Response functions are constructed for various geometries and a comparison in intensity and shape will be made. Because the technique adopts an appropriate scintillator, the system does have advantages over a traditional one, consisting of a NaI(Tl) detector in combination with an energy windows analysis. For count rates typically encountered in borehole measurements, if the same accuracy is required, several times faster operation can be achieved by using the new technique. It costs shorter integration time, and thus achieves shorter measurements or a better energy resolution in borehole logging [2]. The future of the method for uranium exploration will depend on development of more sophisticated data acquisition, processing and interpretation. On one hand, digital measurements are replacing the earlier analog measurements, and microprocessor-based logging systems have enabled new data processing techniques. On the other hand, new high density detector materials have been evaluated and have shown to yield considerable improvements for operation in the restricted borehole environment. Using the high resolution solid state detector has proceeded through a series of developments to its present availability as a commercial borehole logging service. A new scintillation crystal, Lanthanum bromide [LaBr 3 (5%Ce)] scintillator has excellent comprehensive performance. It presents an emission of light photon number higher than sodium iodide [NaI(Tl)], and it shows a scintillation decay time as short as 16 ns. Furthermore, the crystal shows an excellent energy resolution values (<3%@ 662 kev) and good radiation absorption properties [3 6]. Also, LaBr 3 (Ce) detector has a potential advantage in borehole logging application. In general, compared to NaI(Tl) detector, the LaBr 3 (Ce) detector is able to obtain more peaks and need shorter integration time under the same physical and geometric conditions. 2 Response functions for LaBr 3 (Ce) detector system in borehole Generally speaking, the response function (DRF) for LaBr 3 (Ce) detector is defined as the pulse height distribution for incident mono-energetic photons. The function is denoted as I(E, E i ), where E is the pulse-height energy with intensity I and E i is the incident photons energy. The DRF is a probability distribution function which has the properties that it is always larger than or equal to zero over its entire range and integrates over all E to unity [7]. 0 I(E i, E)dE = 1. (1) Usually, the DRF is denoted with histogram of relative counts rate and energy. They are needed for several reasons including the determination of detector efficiencies and its utilization with Monte Carlo simulation for generating detector spectral responses. Our interest includes both of them for uranium content analysis of natural gamma-rays spectralog. DRFs are becoming more and more useful in gammarays detecting for spectrometry purposes. Specifically, Monte Carlo modeling can predict incident photon spectra to a pulse-height spectra. They are receiving more and more attention as calculated LaBr 3 (Ce) detector spectral responses are becoming more and more important in such evolving diverse technologies as bulk material on-line analysis, and uranium well logging [8]. There are four basic approaches to obtaining LaBr 3 (Ce) detector response functions [9 12]. a. Experiment. This method obtains the response functions by multichannel spectrometer based on LaBr 3 (Ce) detector from various standard samples which radiate monoenergetic spectra. Its advantage is that the method can directly give the response. However, it is very difficult to determine the functions in the borehole of body source, and the number of mono-energetic gamma-ray sources is very limited. b. Interpolation. One can obtain the functions from many measured mono-energetic spectra and interpolate for other energies. They are more appropriately described as library spectra. This method is based on experiments and has the same limitation for the borehole of body source. c. Analytic functions. This method calculates the response functions from analytic functions. It first determines an analytic model for separable detector features and uses least-squares to fit a smaller number of mono-energetic results, and then generalizes these results with energy to provide a continuous calculating model. Its advantage is fast calculating speed, while it is very difficult to address many influential factors arising from complex conditions in practical applications. Besides, it does not give much insight into the physical processes which take place inside of LaBr 3 (Ce) crystal. d. Monte-Carlo simulation. Here, the functions are generated by Monte-Carlo simulation program. It not only minimizes the amount of experimental work required but also gives valuable insight into the actual physical processes which take place within the crystal. Monte-Carlo simulation has the potential to obtain the entire spectra. What s more, it can deal with the physical and geometric conditions 482
WU Yongpeng et al.: Monte-Carlo Simulation of Response Functions for Natural Gamma-Rays in LaBr3 very tactfully, including logging tube containing detector system, borehole tube and their specifications. Obviously, Monte-Carlo method has a distinct advantage for calculating the response functions under complex logging environment. 3 arrangement for spectra collection includes the highvoltage detector bias supply, signal-processing electronics and a remote RS-485 bus interface circuit for uploading spectra data and other information. The detector was produced by Saint-Gobain Crystals Company. Its inner structure is shown in Fig. 3(a). Monte-Carlo simulation of response functions The experiment Monte-Carlo simulating response functions for LaBr3 (Ce) detector in borehole has two aims: a. Determination of the resolution function and the pulse height vs. energy scale functions, which provides experimental direction for the borehole detection system design. b. Establishment of the technique basis and basic data for analyzing natural gamma-rays spectra measured in borehole. 3.1 3.1.1 Modeling aspects Earth formations body source model Borehole logging techniques, in which instruments are lowered into boreholes, provide an excellent means for obtaining in-situ gamma-rays spectra. The instrument that measures in-situ radiation from natural earth formations must be calibrated in appropriate facilities to provide quantitative assessments of concentrations of radio-nuclides. For the instrument which is inserted into boreholes, these calibration facilities are typically special models having holes for probe insertion and having sufficient size to become radiometrically infinite in extent. They are concrete cylinders having a central borehole and containing known, enhanced amounts of potassium-40, uranium and thorium for spectral gamma-rays measurements. For borehole measurements, the calibration models are typically concrete cylinders having a hole for tool insertion and sufficient size to simulate actual earth formations containing known amounts of radio-nuclides. The size, 107.5 cm in diameter and 200 cm in height, is so big that the source of radiation appears infinite in extent to a detector detecting the rays inside the model. The extended dimensions, as opposed to point-size sources, enable calibration of instruments with body sources that simulate those actually encountered in field borehole measurements. Its structure is shown in Fig. 1. 3.1.2 LaBr3 (Ce) detector and its casings The system consists of a high-resolution LaBr3 (Ce) scintillator detector (a cylinder of 25.4 mm in diameter and 25.4 mm in length) with a higher efficiency, compared to a 25.4 mm 25.4 mm NaI(Tl) scintillator. The probe is mounted on the front of the logging tube. Their photo-graphs is shown in Fig. 2. Experimental Fig.1 Fig.2 Body source model with a borehole LaBr3 (Ce) detector and logging tube The analysis of natural gamma-rays spectra measured in boreholes has to take into account several parameters, such as the presence of steel casings and their thickness, geometry, tube component, and its inner structure in borehole. The logging tube is a stainlesssteel casing which contains the LaBr3 (Ce) detector system. The space between logging tube and LaBr3 (Ce) detector is filled with dry air. A longer stainless-steel casing must be pushed into the ground by applying a pulsating pressure on the casing because the boreholes are several hundred meters deep with unconsolidated sediments around the boreholes. This casing called borehole tube is different from the logging tube, and is around the logging tube. The space between the two tubes can be filled with dry air, water or fluid slurry. Further, there is a steel ingot at the front of logging tube. The relative position of the crystal to the steel ingot affects to some extent the gamma-rays entering the LaBr3 (Ce) crystal. Their structures are respectively shown in Fig. 3(b) (d). 483
3.2 3.2.1 Simulated parameters and configurations 3.2.2 Configurations for Monte-Carlo simulation The simulated configurations are listed in Table 2. The materials used in the simulations A list of the material properties is given in Table 1. Fig.3 Inner structure of LaBr3 (Ce) detector, logging tube and borehole tube Table 1. Parameters for Monte-Carlo simulation Component Size/Thickness (cm) Material Density (g/cm3 ) Body source Body: 107.5(D) 200(L) Mixture of many materials 2.01 Hole: 7.5(D) 200(L) Crystal 2.54(D) 2.54(L) LaBr3 (5%Ce) 5.08 Crystal shell 0.05 Aluminium 2.70 Dry air Oxygen[24.377%] 1.29 10 3 Nitrogen[75.623%] Logging tube Outside diameter: 5.55 Stainless steel 7.86 Stainless steel 7.86 Hydrogen[11.2%] 1.00 Length: 180 Thickness: 0.15, 0.275, 0.40 Borehole tube Outside diameter: 7.5 Length: 200 Thickness: 0.25, 0.35, 0.50 Water Determined by the parameters of the tubes Oxygen[88.8%] Fluid slurry Mixture of many Steel ingot To detector: 3.5, 9.5, 90 Stainless steel 1.20 materials included H2 O Table 2. Detector /Source LaBr3 (Ce) /Body source Simulations of different configurations Logging tube thickness (cm) 0.15 0.4 Borehole tube (cm) 0.25 0.35 0.275 0.5 484 7.86 Material between the two tubes Dry air Water Fluid slurry Material at the front of the logging tube Steel ingot no
WU Yongpeng et al.: Monte-Carlo Simulation of Response Functions for Natural Gamma-Rays in LaBr 3 3.3 Experimental spectra and simulated energies There are several hundred energies in natural gamma-rays spectra from potassium-40, uranium series and thorium series. Take measuring uranium ore for example, the LaBr 3 (Ce) detector was able to find some photoelectric peaks in low energy range as shown in Fig. 4. Therefore, more than twenty main energies are chosen, and their response functions are to be simulated in LaBr 3 (Ce) detector system with different configurations. 4 Results For each of the investigated parameters and configurations, an assessment includes the energy- and radionuclide-dependence, as well as the magnitude of the given. To know the effect of LaBr 3 (Ce) crystal internal radioactivity, the work simulates the energies from radionuclide. The effects are presented for the mono-energetic gamma-ray 0.609 MeV from radioisotope Bi-214. The same effects occur in the potassium- 40, thorium series and uranium series spectra for the design of detection system configurations [14]. Fig.4 Experimental spectra from uranium ore 3.4 Simulation considerations and approach In this project, only the photon mode was used in the body source. The detailed physics treatment for photon interaction is chosen for this geometry since the body size is saturated for natural gamma-rays 2.615 MeV, and the simulations include deep penetration problems. If electron transport is turned off, a thick-target bremsstrahlung (TTB) model is used and the electroninduced bremsstrahlung photons were simulated. Significant difference was not found between the results with a TTB model and that with a detailed electron transport model. In LaBr 3 (Ce) crystal, electron transport is turned on, then all photon collisions except coherent scatter can create electrons that are banked for later transport. In order to model a realistic physical detector, pulse height tally was used. Pulse height tally provides the energy distribution of pulses created in the crystal cell. The output for pulse height tally is in counts versus energy. In the experiment, the gamma-rays spectroscopy output would be the counts that were recorded in the LaBr 3 (Ce) crystal. Additionally, real gamma-rays energy peaks in the spectroscopy output would be Gaussian shaped peaks. To model this, the Gaussian energy broadening (GEB) option was used with tally to better simulate a physical radiation detector. With the GEB option, the simulations can be treated as if they were real MCA and gamma-rays spectroscopy experiments [13]. 4.1 Effects of LaBr 3 (Ce) crystal internal radioactivity LaBr 3 (Ce) crystal has a drawback of its own, internal radioactivity due to naturally occurring radioisotopes La-138 and Ac-227. La-138, which makes up 0.09 percent of naturally occurring lanthanum, produces two energies: a 0.7887 MeV gamma-ray from beta decay (34%) to stable Ce-138 and a 1.4358 MeV gamma-ray from electron capture (66%) to stable Ba-138 [15]. The main energy response for the crystal internal radioactivity is shown in Fig. 5. The activity of high-purity LaBr 3 crystal per cubic centimeter is 1.8 Bq, so the total activity is 92 Bq for the cylinder crystal of 2.54 cm 2.54 cm in size. The radioisotope is well-distributed in the crystal. Fig.5 The main energy response for the crystal internal radioactivity 4.2 Effects of casings of the detector The effect of the casings and their thickness on incidence gamma-rays spectra is mainly intensities reduction as shown in Fig. 6(a) and (b). The reduction of relative intensities is largest at the photoelectric peak energy and at E i <0.15 MeV. This result can be qualitatively explained as follows: a. At the photoelectric-peak energy, the gammarays reach the crystal with interaction in either the formations or the casings, including the logging tube, borehole tube and the fluid between the two tubes. These materials and their thickness therefore enhance the chances for interaction and reduce the probability of photons entering into the crystal. The most likely 485
interaction between the gamma-ray and the ambient media it traverses is Compton Scattering, which gives rise to an event in the continuum part of the spectrum. The continuum part and the photoelectric-peak area are largely reduced. b. The photons at Ei <0.15 MeV are predominantly due to multiple scattering in the materials around the crystal. Moreover, the photoelectric cross-section for iron is higher than that of the formations in this energy range. c. The work simulates the effects of the fluid between the two tubes on gamma-rays, no matter it is dry air, water or fluid slurry. One notices that the reduction is little from the continuum part to the photoelectric-peak area because the thickness of the fluid layer is thin. Fig.7 The response functions for 0.609 MeV with different positions of steel ingot 4.4 Energy resolution for different configurations To determine the energy resolution of the detection system for different configurations, 0.662 MeV gammarays from point-size source Cs-137 are respectively simulated. The response functions of the system with different physical and geometric configurations are shown in Fig. 8. As the casings around LaBr3 (Ce) crystal become more and more complex, the spectra shape of the response functions has more and more complicated change in low energy region. Fig.8 The response functions for 0.662 MeV with different configurations Fig.6 The response functions for 0.609 MeV with different casings and casing thickness Energy resolution of the system is still excellent, 3.32% (@0.662 MeV, Cs-137) for different configurations is shown in Table 3. The casings have no effects on the energy resolution of the system. 4.3 5 Effects of the relative position of the crystal to steel ingot The project simulates the effects of the relative position of the crystal to steel ingot at the front of logging tube on gamma-rays spectra, including no steel ingot, the distance from surface 12 to surface 15 being 3.5 cm, 9.5 cm or 90 cm, as shown in Fig. 3(d). The response functions of the detection system with different position are shown in Fig. 7. With the configuration of no steel ingot, the distance of 9.5 cm or 90 cm, the effects is almost the same, but it is larger if the distance is less than 3.5 cm. 486 Discussion and conclusions The response functions of LaBr3 (Ce) detector system were simulated for various configurations and many natural gamma-rays at different energies. Analysis of their results showed that: a. There are several objectives in obtaining the response functions. The ideas presented above affect the design for fundamental components of detector response system. This work provides technique basis and basic data for spectral analysis of natural gamma-rays. In uranium quantitative interpretation, Monte-Carlo library spectra can be established based on the response functions for source-less calibration.
WU Yongpeng et al.: Monte-Carlo Simulation of Response Functions for Natural Gamma-Rays in LaBr 3 Table 3. Energy resolution of the system with different configurations Detector Logging tube Borehole Material between Material at the front Energy /Source thickness (cm) tube (cm) the two tubes of the Logging tube resolution (%) LaBr 3(Ce) 3.32 /point-size 0.275 3.32 source 0.50 3.32 Cs-137, Fluid slurry no 3.32 0.662 MeV Steel ingot 3.32 b. Low-energy gamma-rays are absorbed in earth formations, casings around the LaBr 3 crystal and the borehole fluid before reaching the small detector. From comparing the response functions derived for different configurations, the thickness of surrounding layer of the detector affects the properties of transport medium of photons. One notices that the total intensity is reduced when more complex configurations are adopted, which is attributed to the interactions of rays with the casings. Moreover, a strong intensity reduction for E i <0.15 MeV is observed, which is attributed to the absorption of these low-energy gamma-rays in the materials surrounding the smaller detector. c. LaBr 3 (Ce) crystal internal radioactivity makes a small contribution to the spectral shape of low and medium energies. And the effects can be eliminated from the simulated response functions in quantitative analysis. d. To date, borehole radioisotope corrections for configuration were unknown for high performance LaBr 3 (Ce) detectors, which can employ full-spectrum data analysis. Based on Monte-Carlo simulations a series of corrections can be compiled. If no corrections for configuration are applied, the calculated results would exhibit unacceptable deviation. By using simulated response functions to describe the specific measurement configuration, the results can be independent of the specific measurement configuration and kept within the statistical and systematic uncertainties of the experiment. References 1 Burretto P M. 1981, International Atomic Energy Agency Bulletin, 23: 15 2 Hendriks P H G M, Limburg J, de Meijer R J. 2001, Journal of Environmental Radioactivity, 53: 365 3 Dorenbos P, de Haas J T M, van Eijk C W E. 2004, IEEE Trans. Nucl. Sci., 51: 1289 4 van Loef E V D, Dorenbos P, van Eijk C W E, et al. 2001, Appl. Phys. Lett., 79: 1573 5 Pani R, Cinti M N, de Notaratistefani F, et al. 2004, in: IEEE MIC Conference Proceeding, Rome 6 Pani R, Pellegrini R, Cinti M N. 2007, Nuclear Instruments and Methods in Physics Research A, 572: 268 7 Gardner Robin P, Sood Avneet. 2004, Nuclear Instruments and Methods in Physics Research B, 213: 87 8 Metwally W A, Gardner R P, Sood Avneet. 2004, Transactions of the American Nuclear Society, 91: 789 9 Sood Avneet, Gardner Robin P. 2004, Nuclear Instruments and Methods in Physics Research B, 213: 100 10 Gardner R P, Yacout A M, Zhang J, et al. 1986, Nucl. Instr. and Meth. A, 242: 399 11 Avneet Sood a, Robin P. Gardner. 2004, Nuclear Instruments and Methods in Physics Research B, 213: 100 12 Tavakoli-Anbaran H, Izadi-Najafabadi R, Miri- Hakimabad H. 2009, Journal of Applied Sciences, 9: 2168 13 Xu X George. Real Time Identification and Characterization of Asbestos and Concrete Materials with Radioactive Contamination. Final report U.S. department of energy (21), project ID: 65004 14 Maucec M, Hendriks P H G M, Limburg J, et al. 2009, Nuclear Instruments and Methods in Physics Research A, 609: 194 15 Shah K S, Glodo J, Klugerman M, et al. 2003, IEEE Trans. Nuclear Science, 50: 2410 (Manuscript received 17 May 2011) (Manuscript accepted 1 November 2011) E-mail address of WU Yongpeng: ypw213@yahoo.com.cn 487