A Modal Expansion Equilibrium Cycle Perturbation Method for Optimizing Fast Reactors

Touran, Nicholas W.; Lee, John C.

doi:10.13182/nse13-85

Cited by 3 publications

(8 citation statements)

References 53 publications

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“…Touran and Lee made plots similar to Figure 10.12, and they observed only the first cluster of dan/df coefficients [39]. This is because their primary test core is nearly homogeneous, and so the whole flux shift is a global shape -there are no localized patterns due to heterogeneity.…”

Section: Virdent-meptmentioning

confidence: 82%

“…Touran and Lee have already validated MEPT for material density perturbations, around which the whole history of modal expansion revolves [39,40]. Now we aim to validate our new…”

Section: Numeric Validation Of Virdent-meptmentioning

confidence: 89%

“…Touran derived a more general formula for the expansion coefficients and dubbed the process "modal expansion perturbation theory " (MEPT) [39,40]. Since computers sped up quite a bit from 1988 to 2012, Touran was able to compute hundreds of (real and adjoint) flux harmonics for the unperturbed flux distribution.…”

Section: Modal Expansion Perturbation Theory (Mept)mentioning

confidence: 99%

“…Mitani originally developed modal (or harmonic) expansion techniques in the 1970s [34]. In 2012, Touran and Lee revisited the topic and derived a new set of equations that allow for the contribution of each mode to be computed independently of the other modes, thus enabling convenient parallelization [39,40]. Let us now review the MEPT formalism of Touran and Lee.…”

Section: Modal Expansion Perturbation Theory (Mept) Formalismmentioning

confidence: 99%

“…The main demonstration case studied by Touran and Lee is a bare homogeneous sodium fast reactor in hexagonal-z geometry [39,40]. However, Touran's thesis does include modal analysis with a core that contains control and shield assemblies [39].…”

Section: A Large Asymmetric and Highly-heterogeneous Cartesian Corementioning

confidence: 99%

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The “virtual density” theory of neutronics

Reed¹,

Smith

Forget

2018

Annals of Nuclear Energy

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Sustainable nuclear energy will likely require fast reactors to complement the current light water reactor paradigm. In particular, breed-and-burn sodium fast reactors (SFRs) offer a unique combination of fuel cycle and power density features. Unfortunately, large breed-and-burn SFRs are plagued by positive sodium void worth. In order to mitigate this drawback, one must quantify various sources of negative reactivty feedback, among which geometry distortions (bowing and flowering of fuel assemblies) are often dominant. These distortions arise mainly from three distinct physical phenomena: irradiation swelling, thermal swelling, and seismic events.Distortions are notoriously difficult to model, because they break symmetry and periodicity. Currently, no efficient and fully generic method exists for computing neutronic effects of distortions. Computing them directly via diffusion would require construction of exotic hyperfine meshes with continuous re-meshing. Many deterministic transport methods are geometrically flexible but would require tedious, intricate re-meshing or re-tracking to capture distortion effects. Monte Carlo offers the only high-fidelity approach to arbitrary geometry, but resolving minute reactivities and flux shift tallies within large heterogeneous cores requires CPU years per case and is thus prohibitively expensive. Currently, the most widely-used methods consist of various approximations involving weighting the uniform radial swelling reactivity coefficient by the power distribution. These approximations agree fairly well with experimental data for flowering in some cores, but they are not fully generic and cannot be trusted for arbitrary distortions. Boundary perturbation theory, developed in the 1980s, is fully general and mathematically rigorous, but it is inaccurate for coarse mesh diffusion and has apparently never been applied in industry.Our solution is the "virtual density" theory of neutronics, which alters material density (isotropically or anisotropically) instead of explicitly changing geometry. While geometry is discretized, material densities occupy a continuous domain; this allows density changes to obviate the greatest computational challenges of geometry changes. Although primitive forms of this theory exist in Soviet literature, they are only applicable to cases in which entire cores swell uniformly. Thus, we conceive a much more general and pragmatic form of "virtual density" theory to model non-uniform and localized geometry distortions via perturbation theory.In order to efficiently validate "virtual density" perturbation theory, we conceive the "virtual mesh" method for diffusion theory. This new method involves constructing a slightly perturbed "fake" mesh that produces correct first-order reactivity and flux shifts due to anisotropic swelling or expansion of individual mesh cells. First order reactivities computed on a "virtual mesh" agree with continuous energy Monte Carlo to within 1-uncertainty.We validate "virtual density" theory via the "virtual mesh" me...

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Section: Virdent-meptmentioning

confidence: 82%

“…Touran and Lee have already validated MEPT for material density perturbations, around which the whole history of modal expansion revolves [39,40]. Now we aim to validate our new…”

Section: Numeric Validation Of Virdent-meptmentioning

confidence: 89%

Section: Modal Expansion Perturbation Theory (Mept)mentioning

confidence: 99%

Section: Modal Expansion Perturbation Theory (Mept) Formalismmentioning

confidence: 99%

Section: A Large Asymmetric and Highly-heterogeneous Cartesian Corementioning

confidence: 99%

See 3 more Smart Citations

The “virtual density” theory of neutronics

Reed¹,

Smith

Forget

2018

Annals of Nuclear Energy

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Strengths and weaknesses of the modal expansion method for perturbations calculations in nuclear reactor physics

Sauzedde

Archier

Nguyen

2023

Annals of Nuclear Energy

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Comparison between permeability estimates in a carbonate reservoir of Campos Basin using empirical and mathematical approaches

Carrasquilla

Mureb

2021

Braz J Geophys

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Abstract. The permeability estimate, using geophysical well logs, is an important and difficult task in a reservoir characterization, which is usually done with empirical models or statistical regression. Thus, logs were used to achieve this goal in two wells of a carbonate reservoir in Campos Basin, together with geological information and laboratory measurements on rock samples. The test Well A10 was zoned in electrofacies and models were built for each one. Next, the hydraulic flow units were defined and correlated to the logs and to the electrofacies. The same was done in a blind test in Well A3. The Principal Component Analysis, Cluster and Discriminant techniques, Multiple Linear Regression, Alternate Conditional Expectation and Hydraulic Flow Unit were used. The quality of the estimates was calculated using the Mean Absolute Error and the Coefficient of Determination. At Well A10, the Hydraulic Flow Unit was the most promising approach. The Alternate Conditional Expectation, without zoning, was the closest to experimental laboratory data in Well A3. These results indicate that all methods are feasible in inferring permeability, however, an inadequate classification of zones can lead to erroneous estimates.Keywords: carbonate reservoir, permeability estimates, multivariate statistics, well logs, laboratory measurements. Comparação entre estimativas da permeabilidade em um reservatório carbonático da Bacia de Campos usando abordagens empíricas e matemáticasResumo. A estimativa da permeabilidade, usando perfis de poços, é uma tarefa importante e difícil na caracterização de reservatórios, a qual é normalmente feita com modelos empíricos ou regressão estatística. Com esse fim, os perfis de poços juntamente com informações geológicas e medições de laboratório em amostras de rocha foram usados em dois poços de um reservatório carbonático da Bacia de Campos. O poço de teste A10 foi zoneado em eletrofácies e modelos foram construídos para cada uma. As unidades de fluxo hidráulico foram definidas e correlacionadas aos perfis a às eletrofácies. Isso foi feito num teste cego no poço A3. As técnicas Análise de Componentes Principais, de Cluster e Discriminante, Regressão Linear Múltipla, Expectativa Condicional Alternada e Unidade de Fluxo Hidráulico foram utilizadas. A qualidade das estimativas foi calculada com o Erro Médio Absoluto e o Coeficiente de Determinação. No Poço A10, a Unidade de Fluxo Hidráulico foi a abordagem mais promissora. A Expectativa Condicional Alternada, sem zoneamento, foi a técnica mais próxima dos dados experimentais de laboratório no poço A3. Esses resultados indicam que todos os métodos são viáveis na inferência da permeabilidade, porém, uma classificação inadequada das zonas pode levar a estimativas errôneas.Palavras-chave: reservatório carbonático, estimativas de permeabilidade, estatísticas multivariadas, perfis de poços, medições laboratoriais.

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A Modal Expansion Equilibrium Cycle Perturbation Method for Optimizing Fast Reactors

Cited by 3 publications

References 53 publications

The “virtual density” theory of neutronics

The “virtual density” theory of neutronics

Strengths and weaknesses of the modal expansion method for perturbations calculations in nuclear reactor physics

Comparison between permeability estimates in a carbonate reservoir of Campos Basin using empirical and mathematical approaches

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