Response functions for sodium iodide scintillation detectors

A comparative study of a traditional localization algorithm and a deep learning model for radioactive particle tracking application

Radioactive particle tracking is a nuclear technique that tracks a sealed radioactive particle inside a volume through a mathematical location algorithm, which is widely applied in many fields such as chemical and civil engineering in hydrodynamics flows. It is possible to reconstruct the trajectory of the radioactive particle using a traditional mathematical algorithm or artificial intelligence methods. In this paper, the traditional algorithm is based on solving a minimization problem between the simulated events and a calibration dataset, and it was written using C++ language. The artificial intelligence method is represented by a deep neural network, in which hyperparameters were defined using a Python optimization library called Optuna. This paper aims to compare the potentiality of both methods to evaluate the accuracy of the radioactive particle tracking technique. This study proposes a simplified model of a concrete mixer, six NaI(Tl) detectors, and a137Cs sealed radioactive particle. The simulated measurement geometry and the dataset (3615 patterns) were developed using the MCNPX code, which is a mathematical code based on the Monte Carlo Method. The results show a mean absolute percentage error (MAPE) of 20.81%, 10.33%, and 16.84% for x, y and z coordinates, respectively, for the traditional algorithm. For the deep neural network, MAPE is 6.87%, 2.70%, and 22.79% respectively for x, y and z coordinates. In addition, an investigation is carried out to analyze whether the size of the calibration dataset influences the performance of both methods.

Application of radioactive particle tracking and an artificial neural network to calculating the flow rate in a two-phase (oil-water) stratified flow regime

A multiphase flow is defined as the transport of two or more fluids with different properties flowing together inside a pipeline. After offshore oil production, it is necessary to control the amount of transported fluids based on flow rate measurements. Therefore, in this study, we developed a simulation method for predicting the volume fraction and calculating the superficial velocity for a two-phase flow based on radioactive particle tracking, which involves using a sealed radiation source inside the pipeline in order to obtain volume fraction measurements. The test section for the multiphase flow comprised oil and saltwater under a stratified flow regime, with a polyvinyl chloride pipe, four NaI(Tl) detectors, and a¹³⁷Cs radioactive particle that emitted gamma-rays at 662 keV. Simulations were conducted using the MCNP6 code, which is a mathematical code based on the Monte Carlo method. Volume fraction predictions were obtained using a multilayer perceptron neural network with a backpropagation algorithm. The novel feature of this method is the combination of radioactive particle tracking with an artificial neural network in order to predict volume fractions in multiphase flows. The results showed that 91.65% of the predicted patterns were within 5% of the relative error. In addition, the time delay was determined using the cross-correlation function to obtain the superficial velocity in three different volume fractions, which allowed each phase flow rate to be calculated in these cases.

Optimization of a flow regime identification system and prediction of volume fractions in three-phase systems using gamma-rays and artificial neural network

This study presents a method based on gamma-ray densitometry using only one multilayer perceptron artificial neural network (ANN) to identify flow regime and predict volume fraction of gas, water, and oil in multiphase flow, simultaneously, making the prediction independent of the flow regime. Two NaI(Tl) detectors to record the transmission and scattering beams and a source with two gamma-ray energies comprise the detection geometry. The spectra of gamma-ray recorded by both detectors were chosen as ANN input data. Stratified, homogeneous, and annular flow regimes with (5 to 95%) various volume fractions were simulated by the MCNP6 code, in order to obtain an adequate data set for training and assessing the generalization capacity of ANN. All three regimes were correctly distinguished for 98% of the investigated patterns and the volume fraction in multiphase systems was predicted with a relative error of less than 5% for the gas and water phases.

Comparison between codes MCNPX and Gate/Geant4 in volume fraction studies

Knowing the volume fraction in a multiphase flow is of fundamental importance in predicting the performance of many systems and processes, it has been possible to model an experimental apparatus for volume fraction studies using Monte Carlo codes. Artificial neural networks have been applied for the recognition of the pulse height distributions in order to obtain the prediction of the volume fractions of the flow. In this sense, some researchers are unsure of which Monte Carlo code to use for volume fractions studies in two-phase flows. This work aims to model a biphasic flow (water and air) experiment in a stratified regime in two Monte Carlo-based codes (MCNP-X and Gate/Geant4), and to verify which one has the greatest benefits for researchers, focusing on volume fractions studies.

Comparative study for intermediate crystal size of NaI(Tl) scintillation detector

The distinctive features of a well-known NaI(Tl) scintillation detector, by virtue of its crystal size, are experimentally investigated by observing changes in parameters such as intrinsic efficiency (ε_i), photo-peak efficiency (ε_p), resolution, and response function to incident gamma photon energy. This study provides a better understanding for the choice of crystal size of the scintillation detector in Compton scattering experiments. The response function of the NaI(Tl) detector is in the form of an inverse matrix focusing on the retort of the crystal when gamma photons are incident upon it. The response function of the NaI(Tl) detector depends upon the distance between the source and the detector, composition of the material for the crystal itself, photo-fraction, solid angle, incident gamma energy, and geometry of the experimental setup. The factors responsible for broadening of full energy and backscattered peaks are discussed for present investigations. The observed results indicate that the resolution of the detector varies with the incident energy of gamma radiation, and it also depends upon the size of the crystal of the detector. Statistical fluctuations related with the scintillation mechanism are found to be responsible for broadening of instrumental line width (photo-peak). The signal-to-noise ratio and photo-fraction for different crystal sizes of the scintillation detector corrected for efficiency of the detector are also discussed.

The comparison of different multilayer perceptron and General Regression Neural Networks for volume fraction prediction using MCNPX code

This research presents a methodology for volume fraction predictions in water-gas-oil multiphase systems based on gamma-ray densitometry and artificial neural networks. The simulated geometry uses a dual-energy gamma-ray source and dual-modality (transmitted and scattered beams). The Am-241 and Cs-137 sources and two NaI(Tl) detectors have been used in this methodology. Different data from the pulse height distribution were used to train the artificial neural network to evaluate the volume fraction prediction. The MCNPX code has been used to develop the theoretical model for stratified regime and to provide data for the artificial neural network. 5-layers feed-forward multilayer perceptron using backpropagation training algorithm and General Regression Neural Networks has been used with different designs. The artificial neural network design that presented the best results of volume fraction prediction has a mean relative error below 2.0%.

Monitoring system of oil by-products interface in pipelines using the gamma radiation attenuation

This paper presents a methodology to precise identify the interface region, which is formed in the transport of petroleum by-products in polyducts, using gamma densitometry. The simulated geometry is compose for a collimated ¹³⁷Cs source and a NaI(Tl) detector to measure the transmitted beam. The modeling was validated experimentally on stratified flow regime using water and oil. The different volume fractions were calculated using the MCNPX code in order to determine the region interface with an accuracy of 1%.

Identification of Radioactive Isotopes Using Cholesky-Decomposition of Matrices

The process of identification of radioactive isotopes using gamma ray spectrum produced by scintillation detectors is a fundamental problem in physics. Military applications also require fast and efficient methods, especially in field conditions, for identifying unknown isotopes. The fundamental problem is the relationship between the observed gamma ray spectrum given by the detector and the real spectrum. This problem can be treated as a mathematical problem. The relationship between the real and the observed spectrum can be described by a linear algebraic equation system. In this article an efficient mathematical procedure is proposed to solve this linear system efficiently.

Density prediction for petroleum and derivatives by gamma-ray attenuation and artificial neural networks

This work presents a new methodology for density prediction of petroleum and derivatives for products' monitoring application. The approach is based on pulse height distribution pattern recognition by means of an artificial neural network (ANN). The detection system uses appropriate broad beam geometry, comprised of a (137)Cs gamma-ray source and a NaI(Tl) detector diametrically positioned on the other side of the pipe in order measure the transmitted beam. Theoretical models for different materials have been developed using MCNP-X code, which was also used to provide training, test and validation data for the ANN. 88 simulations have been carried out, with density ranging from 0.55 to 1.26gcm(-3) in order to cover the most practical situations. Validation tests have included different patterns from those used in the ANN training phase. The results show that the proposed approach may be successfully applied for prediction of density for these types of materials. The density can be automatically predicted without a prior knowledge of the actual material composition.

Implementation of a tree algorithm in MCNP code for nuclear well logging applications

The goal of this paper is to develop some modeling capabilities that are missing in the current MCNP code. Those missing capabilities can greatly help for some certain nuclear tools designs, such as a nuclear lithology/mineralogy spectroscopy tool. The new capabilities to be developed in this paper include the following: zone tally, neutron interaction tally, gamma rays index tally and enhanced pulse-height tally. The patched MCNP code also can be used to compute neutron slowing-down length and thermal neutron diffusion length.

Status of development of gamma-ray detector response function code or GAMDRF

The need for an accurate representation of the detector response functions (DRFs) for sodium iodide (NaI), bismuth germinate (BGO), etc., arises in the oilwell logging business, especially important for spectral logging tools such as a geochemical logging tool. While Monte Carlo models predict the photon spectra incidents on these detectors, the DRFs are used to generate the pulse-height spectra. A Monte Carlo-based γ-ray detector response function code (GAMDRF) was developed to meet the requirements based on complete photon physics.

An approximation for response function to gamma-rays of NaI(Tl) detectors up to 1.5 MeV

The response functions of a 7.62 x 7.62 cm NaI(Tl) scintillation detector to photons from point gamma-ray sources, 10 cm from the scintillator surface, in the energy up to 1.5 MeV, were calculated using the Monte Carlo method, applying simple approximations based on the peak to total ratio and the detector resolution. The Compton continuum of the detector response function was assumed as an isotropic (rectangular) region for the photon energies up to 1 MeV. In the energies between 1 and 1.5 MeV, the Compton continuum was obtained assuming a single Compton scattering with free electrons. The photopeak of the detector response function was assumed as a line. Each determined channel of the response function was distributed to Gaussian functions. The obtained response functions were compared with the experimental values and a good agreement was found.

Lithium target performance evaluation for low-energy accelerator-based in vivo measurements using gamma spectroscopy

The operating conditions at McMaster KN Van de Graaf accelerator have been optimized to produce neutrons via the (7)Li(p, n)(7)Be reaction for in vivo neutron activation analysis. In a number of earlier studies (development of an accelerator based system for in vivo neutron activation analysis measurements of manganese in humans, Ph.D. Thesis, McMaster University, Hamilton, ON, Canada; Appl. Radiat. Isot. 53 (2000) 657; in vivo measurement of some trace elements in human Bone, Ph.D. Thesis. McMaster University, Hamilton, ON, Canada), a significant discrepancy between the experimental and the calculated neutron doses has been pointed out. The hypotheses formulated in the above references to explain the deviation of the experimental results from analytical calculations, have been tested experimentally. The performance of the lithium target for neutron production has been evaluated by measuring the (7)Be activity produced as a result of (p, n) interaction with (7)Li. In contradiction to the formulated hypotheses, lithium target performance was found to be mainly affected by inefficient target cooling and the presence of oxides layer on target surface. An appropriate choice of these parameters resulted in neutron yields same as predicated by analytical calculations.

Precise Monte Carlo simulation of gamma-ray response functions for an NaI(Tl) detector

Three widely used methods to calculate the response functions for NaI(TI) detectors were investigated. The methods were Berger-Seltzer's method (Nucl. Instrum. Methods 104 (1972) 317), general Monte Carlo (MC) programs, such as EGS4 (The EGS4 code system, Stanford Linear Accelerator Center, 1985) and MCNP4B (MCNP-a general Monte Carlo N-particle transport code, Los Alamos National Laboratory Report, LA-12625-M, 1997), and special MC programs. The pulse height spectra in a 3" x 3" NaI(Tl) detector due to several gamma-ray sources have been measured to verify the calculated results of these methods. The energies of the sources ranged from 0.4118 to 7.11 MeV. The spectra generated by Berger-Seltzer's method and the general MC programs did not agree well with the experimental data. PETRANS 1.0, the special MC program developed in house, was fairly accurate since it also considered the scintillation efficiency and the single escape peak shift.

Relevance of accurate Monte Carlo modeling in nuclear medical imaging

Monte Carlo techniques have become popular in different areas of medical physics with advantage of powerful computing systems. In particular, they have been extensively applied to simulate processes involving random behavior and to quantify physical parameters that are difficult or even impossible to calculate by experimental measurements. Recent nuclear medical imaging innovations such as single-photon emission computed tomography (SPECT), positron emission tomography (PET), and multiple emission tomography (MET) are ideal for Monte Carlo modeling techniques because of the stochastic nature of radiation emission, transport and detection processes. Factors which have contributed to the wider use include improved models of radiation transport processes, the practicality of application with the development of acceleration schemes and the improved speed of computers. In this paper we present a derivation and methodological basis for this approach and critically review their areas of application in nuclear imaging. An overview of existing simulation programs is provided and illustrated with examples of some useful features of such sophisticated tools in connection with common computing facilities and more powerful multiple-processor parallel processing systems. Current and future trends in the field are also discussed.

Determination of effective bremsstrahlung spectra and electron contamination for photon dose calculations

A method is described for determining an effective, depth dose consistent bremsstrahlung spectra for high-energy photon beams using depth dose curves measured in water. A simple, analytical model with three parameters together with the nominal accelerating potential is used to characterise the bremsstrahlung spectra. The model is used to compute weights for depth dose curves from monoenergetic photons. These monoenergetic depth doses, calculated with the convolution method from Monte Carlo generated point spread functions (PSF), are added to yield the pure photon depth dose distribution. The parameters of the analytical spectrum model are determined using an iterative technique to minimise the difference between calculated and measured depth dose curves. The influence from contaminant electrons is determined from the difference between the calculated and the measured depth dose.