Monte Carlo Library Least-Squares Research Articles

Modeling and geometrization in PGNAA

Prompt Gamma Neutron Analysis Activation is a widely used technique for analyzing materials. This technique defines graphs (reference spectrum collection, or libraries) of spectral intensity as a function of energy (channels) for the elements inserted in a sample. The Monte Carlo Library Least Squares (MCLLS) is the dominant approach in the PGNAA technique. The main difficulties faced in the MCLLS domain are (1) numerical instabilities in the least-squares stage (Library Least Squares (LLS)); (2) overdetermination of the system of equations; (3) linear dependence in the libraries; (4) gamma radiation scattering; (5) high computational costs. The present work proposes optimizing the LLS module to face the abovementioned problems using the Greedy Randomized Adaptive Search Procedure (GRASP) and Continuous Greedy Randomized Adaptive Search Procedure (CGRASP) algorithms. The search for the spectral count peaks of the libraries leads to a partitioning of the data before applying the GRASP and CGRASP algorithms. The methodological procedures also address estimating the spectral counts of an unknown library possibly integrates the sample. The results show (1) efficient partitioning of the input data (2) evidence of suitable precision of the weight fractions of the libraries that make up the sample (average precision of the order of 3.16% against 8.8% of other methods); (3) success in the approximation and estimation of the unknown library (average precision of 4.25%) present in the sample. Our method proved to be promising in improving the determination of percentage count fractions by the least-squares module and showing the advantages of data partitioning.

Determination of boron content in Tinkal ore samples with Geant4 using MCLLS method

A new Monte Carlo-Library Least Squares (MCLLS) method was developed for the neutron inelastic-scattering and thermal-capture analysis (NITA) techniques in real-time online analysis systems to determine boron content in Tinkal ore samples. The Geant4 toolkit was used to simulate the Prompt Gamma-ray Neutron Activation Analysis (PGNAA) system for the NITA technique. Tinkal ore samples were bombarded with 14 MeV neutron beams in order to represent neutrons released from the Deuterium-Tritium (DT) neutron generator. After the simulation of shooting Tinkal ore samples with 14 MeV neutron beams was completed, histograms were obtained from Geant4. Once the histograms are broadened according to the shape calibration of the BGO scintillation detector, the spectrum (broadened histograms) are ready to be used in the MCLLS process. A single element library was created by broadened histograms of the nine Tinkal ore samples. In addition, set #10 was selected to be an unknown sample and was used for validating MCLLS. After analysing the unknown sample spectrum, boron content was estimated by the single element library created by the MCLLS method. The estimated value of the boron content by MCLLS was consistent with the laboratory result.

Angular distribution of scattered neutrons as a tool for soil moisture measurement: A feasibility study

The conceptual design of a soil-moisture measurement instrument using a rectangular soil sample and an almost collimated 241Am-9Be source was proposed. Unlike previous studies and in a different simulation approach, the soil moisture was determined using the angular distribution of thermal neutrons using MCNPX2.6 Monte Carlo code, where a cylindrical BF3 proportional counter located at different polar angles was responsible for thermal neutron detection. Both Monte Carlo library least-squares method (MCLLS) and artificial neural networks (ANN) were used to calculate the soil moisture based on BF3 count rates with small relative error, about 2% and 10% maximum relative errors, respectively.

Application of the Monte Carlo Library Least-Squares (MCLLS) approach for chromium quantitative analysis in aqueous solution

In the present work, a new in-situ prompt gamma-ray neutron activation analysis (PGNAA) setup was developed for the quantitative measurement of chromium (Cr) in aqueous solutions which consists of a 4" × 4″ inch Bismuth Germanate detector and a 300 mCi 241Americium-beryllium neutron source. A series of standard samples were prepared by dissolving Cr compounds in deionized water of analytical pure grade and measured using the in situ PGNAA setup. Quantitative spectrum analysis was conducted using Monte Carlo Library Least-Squares approach (MCLLS). Simulates of elemental library spectra were in silico modeled using the CEARCPG code, which was developed by Prof. Robin Gardner research group in North Carolina State University. The fitted spectra presented were in excellent agreement with the total experimental spectrum, and the correlation coefficients were all nearly 1. After applying the MCLLS approach, the minimum detectable concentration of Cr was 301.5 mg/L, better than that obtained with other setups, and the relative deviation of the Cr quantitative analysis accuracy was less than 4.09%.

Implementation of the Monte Carlo Library Least-Squares (MCLLS) approach for quantification of the chlorine impurity in an on-line crude oil monitoring system

Prompt gamma-ray neutron activation analysis (PGNAA) has been widely used for elemental analysis of bulk samples as it provides an on-line, rapid and non-destructive means of performing such analysis. The Monte Carlo Library Least-Squares (MCLLS) approach is one of the methods for quantitative analysis providing elemental weight fractions via an assumption that the total prompt gamma-ray spectrum is a linear combination of the contributions from the individual prompt gamma-ray spectra of the sample constituents. For the generation of prompt gamma-ray libraries of each constituent, a specific purpose Monte Carlo code system called Center for Engineering Applications of Radioisotopes Coincidence Prompt Gamma-Ray (CEARCPG) is utilized. In this work, the focus was on detecting and measuring chlorine impurity in crude oil samples, i.e. trace amounts of chlorine. A preliminary study investigating the feasibility of PGNAA method in conjunction with the MCLLS approach for measuring trace amounts of chlorine in oil samples was performed. For this purpose, an extended version of the MCLLS approach, the so-called MCLLSX approach, was proposed and applied for the quantitative analysis. The results presented in this paper prove the feasibility of the proposed approach.

Study on the PGNAA measurement of heavy metals in aqueous solution by the Monte Carlo–Library Least-Squares (MCLLS) approach

In the present work, a prompt gamma neutron activation analysis (PGNAA) setup, which consists of a 300mCi 241Americium–Beryllium (Am–Be) neutron source and a 4 × 4-in. Bismuth germanium oxide (BGO) detector, was developed for heavy metal detection in aqueous solutions. A series of standard samples with analytical purity were prepared by dissolving heavy metals in deionized water. Quantitative spectrum analysis was performed by the Monte Carlo–Least-Squares (MCLLS) approach to measure the standard samples. The detector response functions of 4 × 4-in. BGO detector were generated by using the CEARDRF code. The element libraries were simulated in silico by the CEARCPG code, which was developed by Dr. Gardner. The simulation results presented were in very good agreement with the experimental results. The correlation coefficients were very close to 1 when the fitted spectrum was compared with the experimental spectrum. By applying the MCLLS approach, the relative deviation of the measurement accuracy was less than 2.27% for Ni, Mn, and Cu and up to 69.33% for Pb.

A Dual System for Monitoring the Positions of Multiple Radioactive Tracer Pebbles in Scaled Pebble Bed Reactors

A dual measurement system for monitoring the simultaneous positions of multiple radioactive tracer pebbles in scaled pebble bed reactors (PBRs) has been developed and benchmarked to the prototype stage. The first system (the collimated system) is an updated version of a previously developed system that is now a completely automatic system that uses three collimated directionally variable NaI detectors that are programed to continuously search for a maximum counting rate from a single radioactive pebble. This system can be used by itself when a single radioactive tracer pebble is of interest and the pebble is relatively slow moving. In the present case, its primary use is to provide an independent measurement of the position of a stationary tracer pebble that is used to provide a point for calibration of the second system. The second system (the uncollimated system) is a modified version of a multiple uncollimated NaI detector system commonly called CARPT. The modified version involves those changes necessary to allow for use of the entire gamma-ray spectra for the inverse problem instead of only the gamma-ray full energy peaks. This allows one to use multiple radioisotopes each in a different tracer pebble so that up to ten individual tracer pebbles can be followed simultaneously with the best possible accuracy. The inverse problem is treated with the Monte Carlo library least-squares approach in which Monte Carlo–generated library spectra for each radioisotope are made available for a complete range of reference positions within the scaled PBR. Then, any unknown total gamma-ray spectra can be analyzed in an iterative fashion with the radioisotope library spectra to yield the position of all the radioisotope tracer pebbles.The scaled PBR used was a 30-cm-high and 30-cm-diam circular cylindrical section on the top and a cone with a 25-deg angle on the bottom. The pebbles are 1.2-cm glass marbles. Results have been obtained with both single tracer radioisotope marbles and multiple tracer radioisotope marbles, simultaneously.

On the treatment of ill-conditioned cases in the Monte Carlo library least-squares approach for inverse radiation analyzers

Prompt gamma-ray neutron activation analysis (PGNAA) has been and still is one of the major methods of choice for the elemental analysis of various bulk samples. This is mostly due to the fact that PGNAA offers a rapid, non-destructive and on-line means of sample interrogation. The quantitative analysis of the prompt gamma-ray data could, on the other hand, be performed either through the single peak analysis or the so-called Monte Carlo library least-squares (MCLLS) approach, of which the latter has been shown to be more sensitive and more accurate than the former. The MCLLS approach is based on the assumption that the total prompt gamma-ray spectrum of any sample is a linear combination of the contributions from the individual constituents or libraries. This assumption leads to, through the minimization of the chi-square value, a set of linear equations which has to be solved to obtain the library multipliers, a process that involves the inversion of the covariance matrix. The least-squares solution may be extremely uncertain due to the ill-conditioning of the covariance matrix. The covariance matrix will become ill-conditioned whenever, in the subsequent calculations, two or more libraries are highly correlated. The ill-conditioning will also be unavoidable whenever the sample contains trace amounts of certain elements or elements with significantly low thermal neutron capture cross-sections. In this work, a new iterative approach, which can handle the ill-conditioning of the covariance matrix, is proposed and applied to a hydrocarbon multiphase flow problem in which the parameters of interest are the separate amounts of the oil, gas, water and salt phases. The results of the proposed method are also compared with the results obtained through the implementation of a well-known regularization method, the truncated singular value decomposition. Final calculations indicate that the proposed approach would be able to treat ill-conditioned cases appropriately.

Produced water characterization by prompt gamma-ray neutron activation analysis

Multiphase gas/oil/water measurement has been and still is a challenging task within the petroleum industry. The requirements of measurement efficiency and accuracy have been continuously increasing at the same time as the trend is to use subsea installations. As a response, the design of the SOFA (Subsea Online Fluid Analyser) concept was initiated by Christian Michelsen Research in cooperation with the University of Bergen. The final design of the analyser is yet to be completed. The ultimate goal of this design is the development of a permanently installed subsea metering station which is capable of characterizing all of the components that can be found in multiphase flow. One of the key challenges in this design is the detailed characterization of produced water samples which includes the identification of salt ions in the sample and their weight percentages. In this work, use of prompt gamma-ray neutron activation analysis (PGNAA) in conjunction with the so-called Monte Carlo library least-squares (MCLLS) approach is considered for characterization of the produced water component. A relatively simple produced water sample was prepared and the prompt gamma-ray spectrum of the sample was recorded using a large 6" × 6" NaI(Tl) scintillation detector. A specific purpose Monte Carlo code named CEARCPG was used to generate the pertinent elemental libraries that are required in the MCLLS approach. The results of this feasibility study have shown that the PGNAA in conjunction with the MCLLS approach would be feasible for determining the amounts of salt ions that can be found in produced water samples.

Use of the CEARXRF GUI‐Based Monte Carlo–Library Least‐Squares (MCLLS) Code for the Micro‐Focused EDXRF analyzer

The CEARXRF GUI‐Based Monte Carlo–Library Least‐Squares (MCLLS) Code is demonstrated with results from a micro‐focused EDXRF analyzer, which can be used to calculate elemental weight fractions in metal alloys or rock samples accurately by library least‐squares regression of the measured X‐ray spectrum with computer‐generated elemental library spectra. An elemental stratified sampling variance reduction technique has been implemented in the CEARXRF5 code, which equalizes the statistical precision of the elemental libraries within the measured sample independent of the relative elemental amounts that are present. Also, an improved Si(Li) detector response function (DRF) has been obtained for micro‐focused X‐ray fluorescence (XRF) analyzers, and the DRF parameters are obtained based on regression from pure elemental experimental spectra. It is demonstrated that the resulting MCLLS approach can greatly improve the accuracy of elemental XRF analysis results. Copyright © 2011 John Wiley & Sons, Ltd.

Implementation of the elemental library stratified sampling technique on the GUI-based Monte Carlo library least squares (MCLLS) approach for EDXRF analysis

The Monte Carlo-based Energy Dispersive X-ray Fluorescence (MCXRF) elemental analyzer approach can be used to accurately calculate elemental weight fractions in rock formations or metal alloys, by least-squares regression of the measured X-ray spectrum with computer-generated elemental library spectra. The analog sampling scheme in a Monte Carlo simulation cannot generate satisfactory results for trace elements due to their low sampling probability. A stratified sampling variance-reduction technique is proposed and implemented to enable each element in the measured sample to have equal opportunity of being sampled with adjusted weights. Essentially, all computed elemental libraries have good statistical precision and improve the accuracy of the elemental analysis results.

Status of the Monte Carlo library least-squares (MCLLS) approach for non-linear radiation analyzer problems

The Center for Engineering Applications of Radioisotopes (CEAR) has been working for over a decade on the Monte Carlo library least-squares (MCLLS) approach for treating non-linear radiation analyzer problems including: (1) prompt gamma-ray neutron activation analysis (PGNAA) for bulk analysis, (2) energy-dispersive X-ray fluorescence (EDXRF) analyzers, and (3) carbon/oxygen tool analysis in oil well logging. This approach essentially consists of using Monte Carlo simulation to generate the libraries of all the elements to be analyzed plus any other required background libraries. These libraries are then used in the linear library least-squares (LLS) approach with unknown sample spectra to analyze for all elements in the sample. Iterations of this are used until the LLS values agree with the composition used to generate the libraries. The current status of the methods (and topics) necessary to implement the MCLLS approach is reported. This includes: (1) the Monte Carlo codes such as CEARXRF, CEARCPG, and CEARCO for forward generation of the necessary elemental library spectra for the LLS calculation for X-ray fluorescence, neutron capture prompt gamma-ray analyzers, and carbon/oxygen tools; (2) the correction of spectral pulse pile-up (PPU) distortion by Monte Carlo simulation with the code CEARIPPU; (3) generation of detector response functions (DRF) for detectors with linear and non-linear responses for Monte Carlo simulation of pulse-height spectra; and (4) the use of the differential operator (DO) technique to make the necessary iterations for non-linear responses practical. In addition to commonly analyzed single spectra, coincidence spectra or even two-dimensional (2-D) coincidence spectra can also be used in the MCLLS approach and may provide more accurate results.

On the use of prompt gamma-ray neutron activation analysis for determining phase amounts in multiphase flow

Prompt gamma-ray neutron activation analysis (PGNAA) is considered for the measurement of the in situ multiphase flow amounts of oil, gas, water and salt in a deep sea oil well. PGNAA has the advantages for this application that: (1) useful characteristic prompt gamma rays are produced by neutron interactions with almost all elements, (2) it is a rapid non-destructive measurement method, (3) a large sample volume is measured and (4) it can be used under the relatively extreme conditions present for undersea oil recovery. Feasibility calculations have been made with the previously developed Monte Carlo–library least-squares (MCLLS) measurement approach used with the specific purpose Monte Carlo code named CEARCPG that was previously developed at CEAR for PGNAA bulk material analysis. A slight modification of the MCLLS measurement approach previously developed for the nonlinear PGNAA and energy dispersive x-ray analysis (EDXRF) measurement applications is used for the present application. This modification allows the use of the very accurate forward Monte Carlo calculation of the PGNAA response and consists of using first the three components oil plus gas, water and salt as library spectra rather than the normal use of individual elemental libraries. Then the gamma-ray transmission density gauge response from the Cs-137 source is used to obtain the amount of gas. This approach allows one to determine the four parameters of primary interest directly. The arrangement considered is the use of a Cf-252 neutron source and a Cs-137 gamma-ray source with a large NaI detector placed on the opposite side of a right circular cylindrical sample holder for an assumed homogeneous mixture of oil, gas and seawater. A background that was previously obtained experimentally in bulk analysis applications was added in various amounts to the response here to make the calculations more reasonable. More experimental results for benchmarking will be taken in the future. Results indicate that this approach would be accurate and is feasible.

CEARPGA II: A Monte Carlo Simulation Code for Prompt-Gamma-Ray Neutron Activation Analysis

A Monte Carlo simulation code, CEARPGA II, has been developed to generate the complete set of library spectra that are required for the application of the Monte Carlo–Library Least-Squares approach in prompt-gamma-ray neutron activation analysis. Compared to the previous version, the CEARPGA I code, several important improvements have been made including eliminating the “big weight” problem by implementing the Analog Linear Interpolation technique, generating the appropriate detector response functions using improved simulation models that account for NaI detector nonlinearity and flat continua, generating the neutron activation backgrounds by directly sampling detector-activated gamma-ray energies, generating the natural background libraries by interpolating the energy-score tables, and tracking the annihilation gamma rays from the pair production interaction that occurs outside the detector. The coal sample spectrum calculated with the CEARPGA II code is benchmarked against those calculated from the CEARPGA I code, the MCNP code, and experimentally measured data.

Development of a Monte Carlo—Library Least-Squares code package for the EDXRF inverse problem

The Monte Carlo – Library Least-Squares (MCLLS) approach has now been developed, im plemented, and tested for solving the inverse problem of EDXRF sample analysis. It consists of a linear library least-squares (LLS) code and a comprehensive Monte Carlo code named CEARXRF that is capable of calculating the unknown sample spectrum, all the elemental library spectra in the sample, and the differential operators for each library spectrum with respect to each element. Two codes with Graphical User Interface (GUI) have been designed to implement the MCLLS approach and benchmark results are presented for the two stainless steel samples; SS304 and SS316. The results are accurate, the system is easy to use, and all indications are that this approach will be very useful for the EDXRF practitioner.

F01 Use of the Monte Carlo Simulation Code CEARXRF for the EDXRF Inverse Problem

The EDXRF inverse problem is solved by first correcting (if necessary) the sample pulseheight spectrum for pulse pile-up with the Monte Carlo code CEARPPU. Then the Monte Carlo - Library Least-Squares (MCLLS) approach is used. This approach consists of using a forward Monte Carlo code (CEARXRF) that is capable of simulating the complete non-linear pulse-height spectral response of any EDXRF system. Using an original estimate of the unknown sample elemental composition, the CEARXRF code is used to simulate the total and individual library spectral responses of all elements. These libraries are then used with the linear Library Least-Squares (LLS) approach to calculate the elemental amounts. Iterations of these steps are made until the estimated and calculated amounts are within prescribed limits so that the measurement non-linearity is accounted for. The two additional features of Differential Operators and all necessary fundamental parameters have been added to the CEARXRF code and a Graphical User Interface (GUI), respectively, that now allows complete automation of this inverse analysis from qualitative to quantitative. The first of these allows iterations without additional Monte Carlo simulation while the second allows initial qualitative as well as quantitative analysis. Benchmark experimental results are given for a series of aluminum alloy samples for a prototype system that employs the radioisotope source 109 Cd and a Si(Li) detector. These results indicate that the approach is accurate and should be very useful to the EDXRF analyst.

{\rtf1\ansi\ansicpg1250\deff0\deflang1038\deflangfe1038\deftab708{\fonttbl{\f0\froman\fprq2\fcharset238{\*\fname Times New Roman;}Times New Roman CE;}} \viewkind4\uc1\pard\f0\fs24 Status of software for PGNAA bulk analysis by the Monte Carlo - Library Least-Squares (MCLLS) approach \par }

{\rtf1\ansi\ansicpg1250\deff0\deflang1038\deflangfe1038\deftab708{\fonttbl{\f0\froman\fprq2\fcharset238{\*\fname Times New Roman;}Times New Roman CE;}} \viewkind4\uc1\pard\f0\fs24 The Center for Engineering Applications of Radioisotopes (CEAR) has been working for about ten years on the Monte Carlo - Library Least-Squares (MCLLS) approach for treating the nonlinear inverse analysis problem for PGNAA bulk analysis. This approach consists essentially of using Monte Carlo simulation to generate the libraries of all the elements to be analyzed plus any other required libraries. These libraries are then used in the linear Library Least-Squares (LLS) approach with unknown sample spectra to analyze for all elements in the sample. The other libraries include all sources of background which includes: (1) gamma-rays emitted by the neutron source, (2) prompt gamma-rays produced in the analyzer construction materials, (3) natural gamma-rays from K-40 and the uranium and thorium decay chains, and (4) prompt and decay gamma-rays produced in the NaI detector by neutron activation. A number of unforeseen problems have arisen in pursuing this approach including: (1) the neutron activation of the most common detector (NaI) used in bulk analysis PGNAA systems, (2) the nonlinearity of this detector, and (3) difficulties in obtaining detector response functions for this (and other) detectors. These problems have been addressed by CEAR recently and have either been solved or are almost solved at the present time. We have now finished the development of Monte Carlo simulation for all of the libraries except the prompt gamma-ray library from the activation of the NaI detector. We must first determine a treatment for the coincidence schemes for Na and particularly I to complete the Monte Carlo simulation of this last library. \par }

F-19 Development of a Monte Carlo—Library Least-Squares (MCLLS) Code Package for the EDXRF Inverse Problem—Invited

F-19 Development of a Monte Carlo—Library Least-Squares (MCLLS) Code Package for the EDXRF Inverse Problem—<i>Invited</i>

Using the Monte Carlo – Library Least-Squares (MCLLS) approach for the in vivo XRF measurement of lead in bone

The Monte Carlo – Library Least-Squares (MCLLS) method has been developed by the Center for Engineering Applications of Radioisotopes for various XRF applications of multi-elemental composition analysis and implemented with the CEARXRF code. In the present work, it is successfully applied to the in vivo XRF measurement of lead in bone and benchmarked by the measurement of a plaster of Paris phantom of known lead concentration. It is implicitly assumed that if the approach works for this sample that closely approximates the real problem of interest, it will also work for the real in vivo case when the proper description of the real case is used. Traditional techniques for XRF analysis are reviewed briefly and the full advantages of the MCLLS method are discussed. Simulation results are presented that are in good agreement with experimental results. The applicability of the MCLLS method to the lead in bone measurement is supported by the good fitting results obtained with simulated Monte Carlo elemental library spectra and close agreement between simulated and experimental spectra from a calcium-rich matrix-based calibration standard in a test geometrical configuration.

Preliminary studies on K and L coincidence spectroscopy for optimizing the in vivo XRF measurement of lead in bone

Previous studies treated the optimal combined K and L XRF system which consists of a Cd-109 point source, a low energy Ge detector (LEGe) and a Si(Li) detector. The Monte-Carlo library least-squares (MCLLS) approach and differential operator approach were treated separately. In this work, an approach for combining the MCLLS approach with the differential operator approach (MCDOLLS) is presented and an optimal configuration for coincidence spectroscopy of K and L X-rays is proposed based on preliminary experimental data.