Core Isotopic Depletion and Fuel Management

  • Paul J. Turinsky


This chapter discusses how core isotopic depletion and fuel management are completed for reactor cores of nuclear power plants. First, core isotopic depletion is discussed, in particular, how the Bateman equation is numerically solved, and the behaviors of the fissile, fertile, burnable poison and transient fission products isotopes. The concepts of breeding, conversion, and transmutation are introduced. Nuclear fuel management is discussed next, with a strong emphasis on the fuel management for light water reactors (LWRs), given their predominance. The discussion utilizes the components of design optimization, those being objectives, decision variables, and constraints. The fuel management discussion first addresses out-of-core fuel management, which involves such decisions as cycle length; stretch out operations; and feed fuel number, fissile enrichment, and burnable poison loading and partially burnt fuel to reinsert, for each cycle in the planning horizon. In-core fuel management is introduced by focusing on LWRs, with the basis of making decisions associated with determining the loading pattern, control rod program, lattice design, and assembly design presented. This presentation is followed by a brief review of in-core fuel management decisions for heavy water reactors, very high temperature gas-cooled reactors, and advanced recycle reactors. Mathematical optimization techniques appropriate for making nuclear fuel management decisions are next discussed, followed by their applications in out-of-core and in-core nuclear fuel management problems. Next presented is a review of the computations that are required to support nuclear fuel management decision making and the tools that are available to accomplish this. The chapter concludes with a summary of the current state of depletion and nuclear fuel management capabilities, and where further enhancements are required to increase capabilities in these areas.


Fuel Assembly Fuel Cycle Pressurize Water Reactor Boiling Water Reactor Fuel Management 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. Anderson KA, Turinsky PJ, Keller PM (2007) Improvement of OCEON-P Optimization Capabilities. Trans Am Nucl Soc (96):201–202Google Scholar
  2. Bell MJ (1973) ORIGEN: the ORNL Isotope Generation and Depletion Code. Oak Ridge National Lab, Oak Ridge, doi:10.2172/4480214Google Scholar
  3. Beard CL (1978) FLAC, Unpublished Master of Science Thesis, Massachusetts Institute of Technology, CambridgeGoogle Scholar
  4. Casal JJ, Stamm’ler RJJ, Villarino E, Ferri A, (1991). “HELIOS: Geometric Capabilities of a New Fuel Assembly Program,” Proc. Int. Topl. Mtg Advances in Mathematics, Computations, and Reactor Physics, PittsburghGoogle Scholar
  5. Comes SA, Turinsky, PJ (1987). Out-of-core nuclear fuel cycle economic optimization for nonequillibrium cycles. Nucl Tech 83:31Google Scholar
  6. DeHart MD, Gauld IC, Williams ML (2007) High fidelity lattice physics capabilities of the SCALE code system using TRITON. Joint International Topical Meeting on Mathematics Computation and Supercomputing in Nuclear Applications, Monterey, pp 15–19Google Scholar
  7. Dixon B, Kim S, Shropshire D, Piet S, Matthern G, Halsey B (2008) Dynamic systems analysis report for nuclear fuel recycle. Idaho National Laboratory, doi: 10.2172/963737Google Scholar
  8. Driscoll MJ, Downar TJ and Pilat EE (1990) The linear reactivity model for nuclear fuel management. American Nuclear Society, La Grange ParkGoogle Scholar
  9. Du S, Turinsky PJ (2008) Implementation of genetic algorithms to the out of core economic optimization PWR (OCEON-P) code. Trans Am Nucl Soc (99):195–196Google Scholar
  10. Edenius M, Ekberg K, Forssen BH, Knott D (1995) CASMO-4: a fuel assembly burnup program, User’s Manual, SOA-95/1, Studsvik of AmericaGoogle Scholar
  11. Engrand P (1997) A multi-objective approach based on simulated annealing and its application to nuclear fuel management. Proceedings of 5th International Conference on Nuclear Engineering, Nice FranceGoogle Scholar
  12. Francois JL, Martin-del-Campo C, Morales LB, Palomera MA (2005) BWR fuel lattice optimization using scatter search. Trans Am Nucl Soc (92):615–617Google Scholar
  13. Goldberg DE (1989) Genetic algorithms in search, optimization, and machine learning. Addison-Wesley, New YorkMATHGoogle Scholar
  14. Greene NM, Lucius JL, Petrie LM, Ford WE III, White JE, Wright RQ (1976) AMPX: a modular code system for generating coupled multigroup neutron-gamma libraries from ENDF/B. Oak Ridge National Lab, Oak RidgeGoogle Scholar
  15. Halsall MJ (1996) WIMS7, an overview, Proc. Int. Conf Reactor Physics PHYSOR96 – breakthrough of nuclear energy by reactor physics, Mito, JAEIU, B-1Google Scholar
  16. Hernandez-Noyola H, Maldonado GI (2009) Added features and MPI-based parallelization of the FORMOSA-L lattice loading optimization code. Advances in Nuclear Fuel Management Fuel Management IV, Hilton HeadGoogle Scholar
  17. Hoffman A (1971) The Code APOLLO a general description. CEA Departement des Etudes de Piles, Service de Physique Mathematique, FranceGoogle Scholar
  18. Jessee MA, Kropaczek DJ (2005) Coupled bundle-core design using fuel rod optimization for boiling water reactors. Nucl Sci Eng (155): 378–385Google Scholar
  19. Jessee M, Turinsky PJ, Abdel-Khalik H (2009) Cross-section uncertainty propagation and adjustment algorithms for BWR core simulation. Advances in Nuclear Fuel Management Fuel Management IV, Hilton HeadGoogle Scholar
  20. Karve AA, Turinsky PJ (1999) FORMOSA-B: a boiling water reactor in-core fuel management optimization package II. Nucl Technol 131(1):48–68Google Scholar
  21. Karve AA, Turinsky PJ (2001) FORMOSA-B: a boiling water reactor in-core fuel management optimization package III. Nucl Technol 135(3):241–251Google Scholar
  22. Keller PM (2001) FORMOSA-P Constrained multiobjective simulated annealing methodology. Proc. Int. Mtg. Mathematical Methods for Nuclear Applications, Salt Lake City, UtahGoogle Scholar
  23. Keller PM, Turinsky PJ (2001) FORMOSA-P three- dimensional/two-dimensional geometry collapse methodology. Nucl Sci Eng 139(3):235–247Google Scholar
  24. Kim Y, Jo CK, Noh J (2007) Optimization of axial fuel shuffling strategy in a block-type VHTR. Trans Am Nucl Soc (97):406–407Google Scholar
  25. Kim Y, Venneri F (2007) Optimization of TRU burnup in modular helium reactor. ICAPP ’07, Niece, FranceGoogle Scholar
  26. Kirkpatrick S, Gelatt Jr. CD, Vecchi MP (1983) Optimization by simulated annealing. Science 220(4598):671–680MathSciNetMATHCrossRefGoogle Scholar
  27. Knott D, Mills VW, Wehlage E (2002) Validation of the GE lattice physics code LANCER 02. Trans Am Nucl Soc (92):505–507Google Scholar
  28. Kropaczek DJ (2009) COPERNICUS: a multi-cycle nuclear fuel optimization code based on coupled in-core constraints. Advances in Nuclear Fuel Management Fuel Management IV, Hilton HeadGoogle Scholar
  29. Kropaczek DJ, Turinsky PJ (1991) In-core nuclear fuel management optimization for pressurized water reactors utilizing simulated annealing. Nucl Technol 95(1):9–32Google Scholar
  30. MacFarlane RE, Muir DW, Boicourt RM (1982) The NJOY nuclear data processing system: Volume 1: user’s manual. Los Alamos National Laboratory, Los AlamosCrossRefGoogle Scholar
  31. Maldonado GI, Turinsky PJ (1995) Application of nonlinear nodal diffusion generalized perturbation theory to nuclear fuel reload optimization. Nucl Technol 110(2):198–219Google Scholar
  32. Martin-del-Campo C, Francois JL, Morales LB (2002) BWR fuel assembly axial design optimization using tabu search. Nucl Sci Eng 142: 107–115Google Scholar
  33. Metropolis N, Rosenbluth AW, Rosenbluth MN, Teller AH, Teller E (1953) Equation of state calculations by fast computing machines. J Chem Phys 21(6):1087–1092CrossRefGoogle Scholar
  34. Moler C, Van Loan CF (2003) Nineteen dubious ways to compute the exponential of a matrix, twenty-five years later. SIAM Rev 45(1):3–49MathSciNetMATHCrossRefGoogle Scholar
  35. Moore BR, Turinsky PJ, Karve AA (1998) FORMOSA-B: a boiling water reactor in-core fuel management optimization package. Nucl Technol 126(1):153–169Google Scholar
  36. Ouisloumen M et al (2001) PARAGON: the new Westinghouse lattice code. Proc ANS Int Meeting on Mathematical Methods for Nuclear ApplicationsGoogle Scholar
  37. Parks GT (1996) Multiobjective pressurized water reactor reload core design by nondominated genetic algorithm search. Nucl Sci Eng 124: 178–187Google Scholar
  38. Pincus M (1970) A Monte Carlo method for the approximate solution of certain types of constrained optimization problems. Operat Res 18(6):1225–1228MathSciNetMATHCrossRefGoogle Scholar
  39. Quist AJ, Van Geemert R, Hoogenboom JE, Illes T, De Klerk E, Roos C, Terlaky T (1999) Finding optimal nuclear reactor core reload patterns using nonlinear optimization and search heuristics. Eng Optimization 32(2):143–176, doi:10.1080/03052159908941295CrossRefGoogle Scholar
  40. Roque B et al (2002) “Experimental Validation of the Code System “DARWIN” for spent fuel isotopic predictions in fuel cycle applications,” PHYSOR 2002, Seoul KoreaGoogle Scholar
  41. Stewart CW, Cuta JM, Montgomery SD, Kelly JM, Basehore KL, George TL, Rowe DS (1989) VIPRE-01: a thermal-hydraulic code for reactor cores. Electric Power Research Institute (EPRI), Palo AltoGoogle Scholar
  42. Stewart CW, Wheeler CL, Cena RJ, McMonagle CA, Cuta JM, Trent DS (1977) COBRA-IV: the model and the method. Pacific Northwest Lab, Richland, doi: 10.2172/5358588Google Scholar
  43. Toppel BJ, Rago AL, O’Shea DM (1967). MC2, a code to calculate multigroup cross-sections. USAEC Report ANL-7318Google Scholar
  44. Vondy DR (1962) Development of a general method of explicit solution to the nuclide chain equations for digital machine calculations, ORNL/TM-361, Union Carbide Corporation, Nuclear Division, Oak Ridge National Laboratory, Oak RidgeGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  • Paul J. Turinsky
    • 1
  1. 1.Department of Nuclear EngineeringNorth Carolina State UniversityRaleighUSA

Personalised recommendations