<p>The calculation of radionuclide transport in the subsurface is an important part of analyses to evaluate safety of nuclear waste disposal sites. Such calculations often emphasize on the solute breakthrough in space and time. In this context, unfractured low-permeability porous media represent effective radionuclide retention because diffusion becomes the dominant mode of transport. Under such conditions and for safe containment, diffusion is desired to be smallest, optimally in combination with large retardation by e.g. sorption. The present study investigates timescales and solute breakthrough distances for selected radionuclides in low-permeability porous media. The used mathematical model is the solute transport equation incorporating the processes of diffusion, sorption, and decay. Firstly, published physical through-diffusion experiments are recalculated in order to validate the transport parameters using a numerical simulator. Secondly, timescales and distances of radionuclide breakthrough are calculated using an analytical model. The simulation results indicate that solute breakthrough converges at a certain distance as decay becomes the dominant process limiting transport. For example, the migration of <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12665_2025_12182_Article_IEq1.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">$^{36}$</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mrow /> <mn>36</mn> </mmultiscripts> </math></EquationSource> </InlineEquation>Cl in Opalinus Clay converges at a solute breakthrough distance of approximately 162 m for timescales beyond 10 Mio years. Based on the results, an expression based on the <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12665_2025_12182_Article_IEq2.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="28" /> </InlineMediaObject> <EquationSource Format="TEX">$2{\text {nd}}$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>2</mn> <mtext>nd</mtext> </mrow> </math></EquationSource> </InlineEquation> Damköhler number is introduced and its accuracy is demonstrated. With this simple equation, maximum solute breakthrough distances can be calculated based solely on the input of a dimensionsless number, the effective diffusion coefficient, the effective porosity or capacity factor, and the physical half-life. That expression is accurate (<InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12665_2025_12182_Article_IEq3.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="71" /> </InlineMediaObject> <EquationSource Format="TEX">$R^2=1.00$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msup> <mi>R</mi> <mn>2</mn> </msup> <mo>=</mo> <mn>1.00</mn> </mrow> </math></EquationSource> </InlineEquation>) for non-sorbing radionuclides acting as inert tracers. For sorbing radionuclides, that equation deviates more from simulation results (<InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12665_2025_12182_Article_IEq4.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="71" /> </InlineMediaObject> <EquationSource Format="TEX">$R^2=0.77$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msup> <mi>R</mi> <mn>2</mn> </msup> <mo>=</mo> <mn>0.77</mn> </mrow> </math></EquationSource> </InlineEquation>). Results of the present study contribute to long term safety analyses of nuclear waste disposal sites.</p>

Timescales and solute breakthrough distances of diffusive radionuclide transport in low-permeability porous media

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2025年5月9日

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Aaron Peche,
Tuong Vi Tran,
Theresa Hennig,
Vinay Kumar,
Robert Kringel,
Sven Altfelder

摘要

The calculation of radionuclide transport in the subsurface is an important part of analyses to evaluate safety of nuclear waste disposal sites. Such calculations often emphasize on the solute breakthrough in space and time. In this context, unfractured low-permeability porous media represent effective radionuclide retention because diffusion becomes the dominant mode of transport. Under such conditions and for safe containment, diffusion is desired to be smallest, optimally in combination with large retardation by e.g. sorption. The present study investigates timescales and solute breakthrough distances for selected radionuclides in low-permeability porous media. The used mathematical model is the solute transport equation incorporating the processes of diffusion, sorption, and decay. Firstly, published physical through-diffusion experiments are recalculated in order to validate the transport parameters using a numerical simulator. Secondly, timescales and distances of radionuclide breakthrough are calculated using an analytical model. The simulation results indicate that solute breakthrough converges at a certain distance as decay becomes the dominant process limiting transport. For example, the migration of $^{36}$ $^{36}$ Cl in Opalinus Clay converges at a solute breakthrough distance of approximately 162 m for timescales beyond 10 Mio years. Based on the results, an expression based on the $2{\text {nd}}$ $2 nd$ Damköhler number is introduced and its accuracy is demonstrated. With this simple equation, maximum solute breakthrough distances can be calculated based solely on the input of a dimensionsless number, the effective diffusion coefficient, the effective porosity or capacity factor, and the physical half-life. That expression is accurate ( $R^2=1.00$ $R^{2} = 1.00$ ) for non-sorbing radionuclides acting as inert tracers. For sorbing radionuclides, that equation deviates more from simulation results ( $R^2=0.77$ $R^{2} = 0.77$ ). Results of the present study contribute to long term safety analyses of nuclear waste disposal sites.