A modified version of Archie’s law to estimate effective diffusion coefficients of radionuclides in argillaceous rocks and its application in safety analysis studies

Loon, Luc R. Van; Mibus, J.

doi:10.1016/j.apgeochem.2015.04.002

Cited by 63 publications

(32 citation statements)

References 48 publications

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“…This leads to

D_{eff} = ϕ_{e} \frac{D_{italicaq}}{τ}

According to Archie's law (Archie, )

D_{eff} = D_{aq} {ϕ_{e}}^{m}

where m [−] is the cementation factor. The applicability of Archie's law to model diffusion has been described in Van Loon and Mibus (). Comparison of and leads to a relationship between tortuosity and porosity:

τ = {ϕ_{e}}^{1 - m}

The porosity follows from the scaling relationship between pore size and the grain volume fractal dimension as (Katz & Thompson, ):

ϕ_{e} = {(\frac{l_{1}}{l_{2}})}^{3 - D_{v}}

where l 1 is the lower limit of the self‐similar region, l 2 the upper limit, and D v the fractal dimension of the pore solid interface.…”

Section: Fractal Model For the Prediction Of Effective Diffusion Coefmentioning

confidence: 99%

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Predicting Effective Diffusion Coefficients in Mudrocks Using a Fractal Model and Small‐Angle Neutron Scattering Measurements

Busch

Kampman

Bertier

et al. 2018

Water Resources Research

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The determination of effective diffusion coefficients of gases or solutes in the water‐saturated pore space of mudrocks is time consuming and technically challenging. Yet reliable values of effective diffusion coefficients are important to predict migration of hydrocarbon gases in unconventional reservoirs, dissipation of (explosive) gases through clay barriers in radioactive waste repositories, mineral alteration of seals to geological CO2 storage reservoirs, and contaminant migration through aquitards. In this study, small‐angle and very small angle neutron scattering techniques have been utilized to determine a range of transport properties in mudrocks, including porosity, pore size distributions, and surface and volume fractal dimensions of pores and grains, from which diffusive transport parameters can be estimated. Using a fractal model derived from Archie's law, we calculate effective diffusion coefficients from these parameters and compare them to laboratory‐derived effective diffusion coefficients for CO2, H2, CH4, and HTO on either the same or related mudrock samples. The samples include Opalinus Shale from the underground laboratory in Mont Terri, Switzerland, Boom Clay from a core drilled in Mol, Belgium, and a marine claystone cored in Utah, USA. The predicted values were compared to laboratory diffusion measurements. The measured and modeled diffusion coefficients show good agreement, differing generally by less than factor 5. Neutron or X‐ray scattering analysis is therefore proposed as a novel method for fast, accurate estimation of effective diffusion coefficients in mudrocks, together with simultaneous measurement of multiple transport parameters including porosity, pore size distributions, and surface areas, important for (reactive) transport modeling.

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“…This leads to

D_{eff} = ϕ_{e} \frac{D_{italicaq}}{τ}

According to Archie's law (Archie, )

D_{eff} = D_{aq} {ϕ_{e}}^{m}

τ = {ϕ_{e}}^{1 - m}

The porosity follows from the scaling relationship between pore size and the grain volume fractal dimension as (Katz & Thompson, ):

ϕ_{e} = {(\frac{l_{1}}{l_{2}})}^{3 - D_{v}}

where l 1 is the lower limit of the self‐similar region, l 2 the upper limit, and D v the fractal dimension of the pore solid interface.…”

Section: Fractal Model For the Prediction Of Effective Diffusion Coefmentioning

confidence: 99%

“…where m [À] is the cementation factor. The applicability of Archie's law to model diffusion has been described in Van Loon and Mibus (2015). Comparison of (8) and (9) leads to a relationship between tortuosity and porosity:…”

Section: Fractal Model For the Prediction Of Effective Diffusion Coefmentioning

confidence: 99%

Predicting Effective Diffusion Coefficients in Mudrocks Using a Fractal Model and Small‐Angle Neutron Scattering Measurements

Busch

Kampman

Bertier

et al. 2018

Water Resources Research

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“…5 Dissolved CH 4 , C 2 H 6 , and C 3 H 8 concentrations measured in BPC-C1 seepage water; logarithm scale; analytical uncertainty is included within the symbol size; water pressure of the test interval measured in the drift at a vertical distance of 9.6 and 12.9 m from the bottom and from the top of the test interval, respectively; the water pressure into the test interval is 1.0 to 1.3 bar lower than the measured one Fig. 6 d 13 C of CH 4 and C 2 H 6 measured in the gas circulating in BHT-1 and in BPC-C1 seepage water; analytical uncertainty is included within the symbol size diffusion coefficient D e of each dissolved gas is related to its diffusion coefficient D w in pure water by D e = eD w /G with e the porosity and G the geometric factor (see for example Van Loon and Mibus 2015). The porosity value is 0.16.…”

Section: Model Descriptionmentioning

confidence: 99%

Natural gas extraction and artificial gas injection experiments in Opalinus Clay, Mont Terri rock laboratory (Switzerland)

Vinsot

Appelo²,

Lundy

et al. 2017

Swiss J Geosci

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Two experiments have been installed at Mont Terri in 2004 and 2009 that allowed gas circulation within a borehole at a pressure between 1 and 2 bar. These experiments made it possible to observe the natural gases that were initially dissolved in pore-water degassing into the borehole and to monitor their content evolution in the borehole over several years. They also allowed for inert (He, Ne) and reactive (H 2 ) gases to be injected into the borehole with the aim either to determine their diffusion properties into the rock pore-water or to evaluate their removal reaction kinetics. The natural gases identified were CO 2 , light alkanes, He, and more importantly N 2 . The natural concentration of four gases in Opalinus Clay porewater was evaluated at the experiment location: N 2 2.2 mmol/L ± 25%, CH 4 0.30 mmol/L ± 25%, C 2 H 6 0.023 mmol/L ± 25%, C 3 H 8 0.012 mmol/L ± 25%.Retention properties of methane, ethane, and propane were estimated. Ne injection tests helped to characterize rock diffusion properties regarding the dissolved inert gases. These experimental results are highly relevant towards evaluating how the fluid composition could possibly evolve in the drifts of a radioactive waste disposal facility.

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“…Diffusion coefficients for Opalinus Clay were measured in the laboratory using 0.8-2 cm thick discs of rock, taking into account the effect of confining pressure, sample depth, sample orientation and temperature (Van Loon et al 2003;Van Loon 2014;Van Loon and Mibus 2015). Data are available for HTO (tritiated water = mainly ordinary H2O plus 3 HOH in trace amounts), 36 Cl -, 125 I -, 22 Na + , 85 Sr 2+ and 134 Cs + and relate mostly to transport perpendicular to bedding, with some information on transport parallel to bedding.…”

Section: Diffusion Properties Laboratory and Field Experimentsmentioning

confidence: 99%

Safety-relevant hydrogeological properties of the claystone barrier of a Swiss radioactive waste repository: An evaluation using multiple lines of evidence

Gautschi

2017

Grundwasser

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In Switzerland, the Opalinus Clay -a Jurassic (Aalenian) claystone formation -has been proposed as the first-priority host rock for a deep geological repository for both low-and intermediate-level and high-level radioactive wastes. An extensive site and host rock investigation programme has been carried out during the past 30 years in Northern Switzerland, comprising extensive 2D and 3D seismic surveys, a series of deep boreholes within and around potential geological siting regions, experiments in the international Mont Terri Rock Laboratory, compilations of data from Opalinus Clay in railway and motorway tunnels and comparisons with similar rocks.The hydrogeological properties of the Opalinus Clay that are relevant from the viewpoint of long-term safety are described and illustrated. The main conclusions are supported by multiple lines of evidence, demonstrating consistency of conclusions based on hydraulic properties, porewater chemistry, distribution of natural tracers across the Opalinus Clay as well as small-and large-scale diffusion models and the derived conceptual understanding of solute transport.

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A modified version of Archie’s law to estimate effective diffusion coefficients of radionuclides in argillaceous rocks and its application in safety analysis studies

Cited by 63 publications

References 48 publications

Predicting Effective Diffusion Coefficients in Mudrocks Using a Fractal Model and Small‐Angle Neutron Scattering Measurements

Predicting Effective Diffusion Coefficients in Mudrocks Using a Fractal Model and Small‐Angle Neutron Scattering Measurements

Natural gas extraction and artificial gas injection experiments in Opalinus Clay, Mont Terri rock laboratory (Switzerland)

Safety-relevant hydrogeological properties of the claystone barrier of a Swiss radioactive waste repository: An evaluation using multiple lines of evidence

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