Consolidated fuel reprocessing program: a mathematical model for liquid flow transients in a rotary dissolver

Lewis, B.E.; Weber, Fred

doi:10.2172/711374

Cited by 1 publication

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“…Compartment 9 is used for rinsing and is not relevant to this work. The time and spatial variation of the physical and chemical processes occurring within the dissolver's start‐up were originally developed by Weber and Lewis and subsequently modified by Cacuci et al , as follows:

V^{(k)} ((), t) \frac{d}{d t} ([], ρ_{a}^{(k)}) + ([], ρ_{a}^{((), k)} ((), t) - ρ_{a}^{((), k + 1)} ((), t)) C ([], V^{(k + 1)} ((), t)), k = 1, \dots, 7, 0 < t \leq t_{f},

V^{(8)} ((), t) \frac{d}{d t} ([], ρ_{a}^{(8)}) + ρ_{a}^{((), 8)} ((), t) f^{(italicin)} ((), t) = ρ_{a}^{in} ((), t) f^{(italicin)} ((), t), 0 < t \leq t_{f} .

\frac{d}{d t} ([], V^{(k)} ((), t)) = prefix- C ([], V^{(k)} ((), t)) + C ([], V^{(k + 1)} ((), t)), k = 1, \dots, 7, 0 < t \leq t_{f},

\frac{d}{d t} ([], V^{(8)} ((), t)) = prefix- C ([], V^{...})

…”

Section: Mathematical Modeling Of Rotary Dissolver Start‐upmentioning

confidence: 99%

“…The compatibility condition (Lewis and Weber ) for a fully developed initial flow implies that

\frac{d}{d t} V^{(k)} ((), 0) = 0, k = 1, \dots, 8

; in turn, this condition implies that

V_{0}^{((), k)} ≡ G {[f^{((), in)} (0)]}^{1 true/ p} + V_{0}, k = 1, \dots, 8 .

…”

Section: Mathematical Modeling Of Rotary Dissolver Start‐upmentioning

confidence: 99%

“…The nitric acid concentration in compartment #1,

ρ_{a}^{((), 1)} ((), t)

, was measured by Lewis and Weber at 307 time instances, t i , i = 1, …, I = 307, over a period of 10.5 h. The nominal values of these measurements are denoted as

ρ_{a, italicmeas}^{((), 1)} ((), t_{i})

and are depicted using blue circles in Figure . Notably, these experimental results are unique in the open literature for a rotary dissolver.…”

Section: Mathematical Modeling Of Rotary Dissolver Start‐upmentioning

confidence: 99%

“…This work aims at highlighting the efficiency of the ASAM introduced in by means of an illustrative application to a spent nuclear fuel dissolver model, originally developed by Lewis and Weber . The “dissolver” is a mechanical and chemical module that produces feed stock for the chemical separation processes employed in the “head end” segment of an aqueous nuclear fuel reprocessing facility.…”

Section: Introductionmentioning

confidence: 99%

“…The dissolver model comprises 16 time‐dependent state functions and 619 model parameters related to the model's equation of state and inflow conditions. In particular, the most important response for the dissolver model is the time‐dependent nitric acid in the compartment furthest away from the inlet, because this is the location where Lewis and Weber reported measurements (unique in the open literature) at 307 time instances, t i , i = 1, …, I = 307, over a period of 10.5 h.…”

Section: Introductionmentioning

confidence: 99%

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Efficient computation of operator‐type response sensitivities for uncertainty quantification and predictive modeling: illustrative application to a spent nuclear fuel dissolver model

Cacuci

Badea

et al. 2016

Numerical Methods in Fluids

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SUMMARYThis work honors the 75th birthday of Professor Ionel Michael Navon by presenting original results highlighting the computational efficiency of the adjoint sensitivity analysis methodology for functionvalued operator responses by means of an illustrative paradigm dissolver model. The dissolver model analyzed in this work has been selected because of its applicability to material separations and its potential role in diversion activities associated with proliferation and international safeguards. This dissolver model comprises eight active compartments in which the 16 time-dependent nonlinear differential equations modeling the physical and chemical processes comprise 619 scalar and time-dependent model parameters, related to the model's equation of state and inflow conditions. The most important response for the dissolver model is the time-dependent nitric acid in the compartment furthest away from the inlet, where measurements are available at 307 time instances over the transient's duration of 10.5 h. The sensitivities to all model parameters of the acid concentrations at each of these instances in time are computed efficiently by applying the adjoint sensitivity analysis methodology for operator-valued responses.The uncertainties in the model parameters are propagated using the above-mentioned sensitivities to compute the uncertainties in the computed responses. A predictive modeling formalism is subsequently used to combine the computational results with the experimental information measured in the compartment furthest from the inlet and then predict optimal values and uncertainties throughout the dissolver. This predictive modeling methodology uses the maximum entropy principle to construct an optimal approximation of the unknown a priori distribution for the a priori known mean values and uncertainties characterizing the model parameters and the computed and experimentally measured model responses. This approximate a priori distribution is subsequently combined using Bayes' theorem with the "likelihood" provided by the multiphysics computational models. Finally, the posterior distribution is evaluated using the saddle-point method to obtain analytical expressions for the optimally predicted values for the parameters and responses of both multi-physics models, along with corresponding reduced uncertainties. This work shows that even though the experimental data pertains solely to the compartment furthest from the inlet (where the data were measured), the predictive modeling procedure used herein actually improves the predictions and reduces the predicted uncertainties for the entire dissolver, including the compartment furthest from the measurements, because this predictive modeling methodology combines and transmits information simultaneously over the entire phase-space, comprising all time steps and spatial locations.

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V^{(k)} ((), t) \frac{d}{d t} ([], ρ_{a}^{(k)}) + ([], ρ_{a}^{((), k)} ((), t) - ρ_{a}^{((), k + 1)} ((), t)) C ([], V^{(k + 1)} ((), t)), k = 1, \dots, 7, 0 < t \leq t_{f},

V^{(8)} ((), t) \frac{d}{d t} ([], ρ_{a}^{(8)}) + ρ_{a}^{((), 8)} ((), t) f^{(italicin)} ((), t) = ρ_{a}^{in} ((), t) f^{(italicin)} ((), t), 0 < t \leq t_{f} .

\frac{d}{d t} ([], V^{(k)} ((), t)) = prefix- C ([], V^{(k)} ((), t)) + C ([], V^{(k + 1)} ((), t)), k = 1, \dots, 7, 0 < t \leq t_{f},

\frac{d}{d t} ([], V^{(8)} ((), t)) = prefix- C ([], V^{...})

…”

Section: Mathematical Modeling Of Rotary Dissolver Start‐upmentioning

confidence: 99%

“…The compatibility condition (Lewis and Weber ) for a fully developed initial flow implies that

\frac{d}{d t} V^{(k)} ((), 0) = 0, k = 1, \dots, 8

; in turn, this condition implies that

V_{0}^{((), k)} ≡ G {[f^{((), in)} (0)]}^{1 true/ p} + V_{0}, k = 1, \dots, 8 .

…”

Section: Mathematical Modeling Of Rotary Dissolver Start‐upmentioning

confidence: 99%

“…The nitric acid concentration in compartment #1,

ρ_{a}^{((), 1)} ((), t)

, was measured by Lewis and Weber at 307 time instances, t i , i = 1, …, I = 307, over a period of 10.5 h. The nominal values of these measurements are denoted as

ρ_{a, italicmeas}^{((), 1)} ((), t_{i})

and are depicted using blue circles in Figure . Notably, these experimental results are unique in the open literature for a rotary dissolver.…”

Section: Mathematical Modeling Of Rotary Dissolver Start‐upmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Efficient computation of operator‐type response sensitivities for uncertainty quantification and predictive modeling: illustrative application to a spent nuclear fuel dissolver model

Cacuci

Badea

et al. 2016

Numerical Methods in Fluids

View full text Add to dashboard Cite

show abstract

Consolidated fuel reprocessing program: a mathematical model for liquid flow transients in a rotary dissolver

Cited by 1 publication

References 0 publications

Efficient computation of operator‐type response sensitivities for uncertainty quantification and predictive modeling: illustrative application to a spent nuclear fuel dissolver model

Efficient computation of operator‐type response sensitivities for uncertainty quantification and predictive modeling: illustrative application to a spent nuclear fuel dissolver model

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