The RAPID code system is developed based on the Multi-stage Response function particle Transport (MRT) methodology for performing real-time simulation of complex nuclear systems. Thus far, it has been applied and benchmarked for the simulation of spent fuel pools, spent fuel casks, and reactor cores. RAPID can calculate system eigenvalue, subcritical multiplication, 3-D pin-wise fission neutron/gamma/antineutrino distributions, detector responses or surface radiation dose. When used in conjunction with measurements, e.g., for safeguards application, RAPID can identity potential fuel diversion or misplacement.

RAPID’s MRT methodology is based on the Fission Matrix method and the adjoint function methodology, and it is expressed as a linear system of equations with pre-calculated coefficients and response functions. These coefficients are determined via a proprietary MRT strategy for different assembly types, burnups, cooling times, and detector types and positions, and used for simulation of different system configurations and conditions.

RAPID is incorporated into a Web application that is referred to as the Virtual Reality System (VRS) for RAPID. VRS-RAPID provides a collaborative Virtual Reality environment for a user to build models, perform simulation, and view 3-D diagrams in an interactive mode. These simulation results can be projected into the virtual image of a system (e.g., a pool) for further analysis and training purposes. Additionally, VRS-RAPID outputs can be coupled with an immersive facility such as the VT’s HyberCube System.

RAPID is written in FORTRAN 95 and is capable of being run on any operating system. RAPID includes a Python software, pRAPID, for automatic pre-calculation of coefficients using a standard Monte Carlo code system for fixed-source and burnup calculations.

RAPID has been successfully benchmarked for reactor cores, spent fuel pools, and storage casks against traditional Monte Carlo predictions, and a subcritical facility. RAPID enables detailed neutronics calculations in real time (seconds/minutes) on a single computer core for design and inspection of nuclear systems.

Note that, as of October 2017, a patent is pending for the RAPID software

Before RAPID, calculations of neutronics took numerous days to complete; these calculations were not "real-time". RAPID, using a novel methodolgy, broke the barrier of non-real-time computations.

Methodology

Multi-stage Response-function Transport

RAPID is based on the MRT methodology, in which a problem is initially partitioned into a number of stages based on its physics, and each stage is represented by a response function or set of coefficients. These stages are combined into a linear system of equations which are solved iteratively using the pre-calculated functions and/or coefficients. The current version of RAPID is capable of simulating nuclear systems such as spent fuel pools, spent fuel casks, and reactor cores. RAPID solves for pin-wise, axially-dependent fission density, critical/subcritical multiplication, and detector response.

Fission Matrix Method

The FM method can take two forms, depending on the type of problem. For a sub-critical multiplication problem, in which the fission source is driven by an independent source in the spent fuel (i.e., spontaneous fission and (; n) reactions), the induced fission source in cell i is given by Equation (1):

where F_{j} is the induced fission source strength in fuel pin j, S_{j} is the intrinsic (or independent) source strength in fuel pin j, a_{i};j is the number of fission neutrons directly produced in fuel pin i due to a fission neutron born in fuel pin j, and b_{i};j is the same as a_{i};j except for intrinsic source neutrons. These values are different because S and F should have different spatial and energy distributions within each cell. N is the total number of computational cells.

We also consider the eigenvalue problem, as in Equation (2):

where k is the system eigenvalue.

The fission matrix method results in a set of N linear equations, which can be solved for F and k given the ai;j coefficients. The main difficulty is how to calculate the coefficients, and to decide on a computational cell size that is small enough to give detailed and accurate results, but not so large that the linear system becomes intractable. This can happen quickly as the matrix is of size N N.

RAPID Flowchart

Workshops and Seminars

October 24-25, 2017: "Virginia Tech Nuclear Engineering Program and MRT Methodology and the RAPID Code System for Neutronics Simulations," invited talk at Idaho National Lab, Idaho Falls, ID.

October 3, 2016: "MRT Methodologies for Real-Time Particle Transport Simulation of Nuclear Systems," workshop at the 13th ICRS & 19th RPSD , Paris, France.

April 6, 2016: "MRT Methodologies for Application to Nuclear Safeguards, Safety and Security," invited talk at the Energy Seminar Series, Colorado School of Mines, Golden, CO.

September 24, 2015: "MRT Methodologies for Spent Nuclear Fuel Pool Simulations," invited talk at the Mechanical and Aerospace Engineering Deptartment, University of Virginia, Charlottesville, VA.

May 18-22, 2015: "Using RAPID for Solving the VT3G-SNFP Benchmark," presentation at OECD Workshop on Benchmarks and Uncertainty Quantification at Universidad Politecnica de Madrid, Madrid, Spain.

April 21, 2015: "A Fission Matrix Approach to Calculate Pin-wise 3D Fission Density Distribution," paper presentation at Joint International Confernce on M&C, SNA, and MC, Nashville, TN.

April 19, 2015: "Real-time Analysis for Spent Fuel Pool In-situ Detection (RAPID)," workshop at Joint International Confernce on M&C, SNA, and MC, Nashville, TN.

December 8, 2014: "Multi-stage Response-function Transport (MRT) Methodologies for Real-Time Calculations," invited talk for the Global Leaders' Symposium on Reactor Physics at Korean Advanced Institute for Science and Technology (KAIST), Daejeon, Korea.

September 30, 2014: "Use of the Fission Matrix Method for Solution of the Eigenvalue Problem in a Spent Fuel Pool," paper presentation at PHYSOR 2014, Kyoto, Japan.

July 20, 2014: "Advanced Particle Transport Methodologies/Tools for Nuclear Safeguards and Nonproliferation," workshop at INMM 55th Anual Meeting, Atlanta, GA.

Lecutre

Virtual Reality System

Creation of a Collaborative Virtual Reality System

Goal

To develop and test a first-of-a-kind environment for the creation of a Virtual Reality System (VRS)

Development

The VT Transport Theory Group - VT^{3}G - collaborated with VT's Visionarium to create a Virtual Reality System through which to display spent nuclear fuel assemblies.

Publications

Journal Articles

V. Mascolino, A. Haghighat, and N. Roskoff, “Evaluation of RAPID for a UNF Cask Benchmark Problem,” EPJ Web of Conferences, EDP Sciences, 153, 05025, 2017. DOI: 10.1051/epjconf/201715305025

N. Roskoff, A. Haghighat, and V. Mascolino, “Experimental and Computational Validation of RAPID,” EPJ Web of Conferences, EDP Sciences, 2017, in press.

A. Haghighat, K. Royston, and W. Walters, “MRT Methodologies for Real-Time Simulation of Nonproliferation and Safeguards Problems,” Annals of Nuclear Energy, 87, pp.61-67, 2016.

N. Roskoff, W. Walters, and A. Haghighat, “Application of the subgroup decomposition method (SDM) for reactor simulation,” EPJ Web of Conferences, Vol. 106, EDP Sciences, 2016.

W. Walters, A. Haghighat, S. Sitaraman, and Y. Ham “Development of INSPCT-S for Inspection of Spent Fuel Pool,” Journal of ASTM International (JAI), 1550, pp. 690-705, 2012.

M. Wenner and A. Haghighat, “A Fission Matrix Based Methodology for Achieving an Unbiased Solution for Eigenvalue Monte Carlo Simulations,” Progress in Nuclear Science and Technology, 2, pp. 886-892, 2011.

Conference Proceedings

N. Roskoff, A. Haghighat, M. Millet, and C. Leidig, “Benchmarking of the RAPID Tool for a Subcritical Facility,” Proc. 57th INMM Annual Meeting, Atlanta, GA, July 24-28, 2016.

N. Roskoff, A. Haghighat, and V. Mascolino “Analysis of RAPID Accuracy for a Spent Fuel Pool with Variable Burnups and Cooling Times,” Proc. Advances in Nuclear Nonproliferation Technology and Policy Conference, Santa Fe, NM, September 25-30, 2016.

W. Walters, N. Roskoff, and A. Haghighat, “A Fission Matrix Approach to Calculate Pin-wise 3D Fission Density Distribution,” Proc. M&C 2015, Nashville, Tennessee, April 19-23, 2015.

W. Walters, N. Roskoff, and A. Haghighat, “Use of the Fission Matrix Method for Solution of the Eigenvalue Problem in a Spent Fuel Pool,” Proc. PHYSOR 2014, Kyoto, Japan, Sep. 28-Oct 3, 2014.

W. Walters, A. Haghighat, M. Wenner, S. Sitaraman, and Y. Ham “A Methodology for Determination of Detector Response for Inspection of a Spent Fuel Pool,” Proc. PHYSOR 2010, Pittsburgh, PA, May 9-14, 2010.

W. Walters, “Development of a Calculation Methodology to Determine Detector Response in a Spent Fuel Pool,” M.S. Thesis, University of Florida, 2009.

Contributors

Prof. Alireza Haghighat — Director Nuclear Science and Engineering Lab, Professor of Nuclear Engineering at Virginia Tech

Dr. William Walters — Assistant Professer of Nuclear Engineering at Penn State

Nathan Roskoff — PhD Candidate, Nuclear Engineering Program at Virginia Tech

Valerio Mascolino — PhD Candidate, Nuclear Engineering Program at Virginia Tech