Effective gaseous diffusion coefficients of select ultra-fine, super-fine and medium grain nuclear graphite

Abstract

Understanding "Where?" and "How much?" oxidation has occurred in a nuclear graphite component is critical to predicting any deleterious effects to physical, mechanical, and thermal properties. A key factor in answering these questions is characterizing the effective mass transport rates of gas species in nuclear graphites. Effective gas diffusion coefficients were determined for twenty-six graphite specimens spanning six modern grades of nuclear graphite. A correlation was established for the majority of grades examined allowing a reasonable estimate of the effective diffusion coefficient to be determined purely from an estimate of total porosity.The importance of Knudsen diffusion to the measured diffusion coefficients is also shown for modern grades. Knudsen diffusion has not historically been considered to contribute to measured diffusion coefficients of nuclear graphite. Unitless9,10,13Open porosity of a porous material Unitless 9-11 A constriction factor for changing pore cross-section along the length of a pore. Unitless 9,11 Symbol Description Units Equation(s) Geodesic tortuosity. The ratio of the geodesic path length of a pore relative to the Euclidean distance traveled across the porous material. Unitless 9,11 〈 〉 Arithmetic mean gas molecule velocity assuming a Boltzmann energy distribution. / 12 Boltzmann constant ⁄ 12 Temperature 12 Knudsen diffusion coefficient for species A / 13

Validation of Wichner Predictive Model for Chronic Oxidation by Moisture of Nuclear Graphite

“…Thus, they argued, the higher D eff (or ) of grade 2114 suggests that Knudsen diffusion is less important for this graphite than for the other three grades. At the time of publication of their paper, Kane et al 44 did not have microstructural information in support of this assertion. Now, one can see from mercury porosimetry results ( Figure 3) and gas adsorption data (Figure 4) that the cumulated mesopore volumes (between 3 and 25 nm) increase in the order 2114 < NBG-17 < IG-110 < PCEA.…”

“…The increase of mean free path probably would not be significant for medium-fine grain graphites (PCEA, NBG-17); but for superfine grain graphites (2114, IG-110), the importance of Knudsen diffusion may increase significantly at the temperatures of chronic oxidation. 44 Further studies are needed to accurately quantify the Knudsen diffusion contribution at room temperature and at the oxidation temperatures.…”

“…This discovery was independently confirmed by our INL colleagues. 44 Because of reduced pore channels in higher-density modern graphites, the Knudsen diffusion may have a higher importance than previously thought because it slows down normal (viscous) diffusion in superfine grain grades. Knudsen diffusion is temperature dependent but in a different way from normal diffusion.…”

“…The porous media correction factor  depends on microstructure properties, such as porosity fraction, constriction factor in pore connectivity, and pore tortuosity. Several correlations, 41,44,45,46,47 not always in agreement with one another, have been proposed. Rather than analyzing them, which is not the scope of this report, we focused on measuring the effective diffusivity for H 2 O from H 2 O/He mixtures for each grade of graphite.…”

Diffusion in Porous Media: Phenomena and Mechanisms

“…Knudsen diffusion plays an important role in a large number of natural and engineered (nano)porous media. Examples include transport of various species in pharmaceutical tablets [37], in tubular sublimators utilized for purification of large organic molecules [57], in graphites designed for high-temperature gas-cooled reactor nuclear reactors [32], in membranes used for distillation desalination [23], and in hierarchical metamaterials tailored for energy-storage devices [69].…”