Monte Carlo Library Least-Squares Approach Research Articles

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.

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.

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.

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.

The Monte Carlo—Library Least-Squares approach for energy-dispersive x-ray fluorescence analysis

A new analysis principle called Monte Carlo—Library Least-Squares (MCLLS) approach has been identified and investigated for quantitative energy dispersive x-ray fluorescence analyses. The feasibility of the MCLLS principle has been investigated with a radioisotope source excited EDXRF analytical system for several standard samples of known composition. With good initial elemental composition guesses, the MCLLS results showed excellent agreement with the elemental compositions in the standard samples. Furthermore, by taking the ratio of the photoelectric peak counts in the sample experimental spectra as approximate initial guesses, the proposed iterative MCLLS algorithm works quite well, converging to the correct elemental compositions. Only one iteration was needed for the analysis of all major elements. For trace elements a second iteration was needed in some cases. Other possible applications of the MCLLS approach and future work are also discussed.