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Contribution of the Dusty Gas Model to Permeability/Diffusion Tests on Partially Saturated Clay Rocks

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Abstract

Gas transfer experiments on claystone and numerical simulations have been conducted to enhance the knowledge of gas transport in nuclear waste repositories in the Callovo-Oxfordian clay formation in Bure, France. Laboratory Gas transfer experiments were performed with a specific device dedicated to very low permeability measurement (10−23 to 10−20 m2). Experiments were performed on both dry and close to saturation claystone. The Dusty Gas Model, based on multi-component gas transfer equations with Knudsen diffusion, was used to describe the experimental results. The parameters obtained are the effective permeability, the Knudsen diffusion (Klinkenberg effect) and molecular diffusion coefficients and the porosity accessible to gas. Numerical simulations were carried with various boundary conditions and for different gases (helium vs hydrogen) and were compared with experiments to test the reliability of the model parameters and to better understand the mechanisms involved in clays close to saturation. The numerical simulation fitted the experimental data well whereas simpler models cannot describe the complexity of the Knudsen/Klinkenberg effects. Permeabilities lie between 10−22 and 10−20 m2. Claystones close to saturation have an accessible porosity to gas transfer that is lower than 0.1–1% of the porosity. Analysis of the Klinkenberg effect suggests that this accessible pore network should be made of 50–200 nm diameter pores. It represents pore networks accessible at capillary pressure lower than 4 MPa.

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Abbreviations

b k :

Klinkenberg coefficient, Pa

c i :

Concentration of species i, mol/m3

\({D^{\rm e}_{i,M}}\) :

Effective Knudsen diffusion coefficient of species i, m2/s

\({D^{\rm e}_{i, j}}\) :

Effective molecular diffusion coefficient of species i with j, m2/s

\({\frac{D_{{\rm H}_2,N_2}}{D_{{\rm He},N_2}}}\) :

Diffusivity ratio hydrogen/helium

\({D^{\rm e}_{\rm app}}\) :

Apparent effective diffusion coefficient, m2/s

d :

Mean diameter of the porous media, m

e :

Sample length, m

k :

Permeability, m2

M :

Molecular weight, kg/mol

N D :

Diffusive flux, mol/m2/s

N μ :

Viscous flux, mol/m2/s

N T :

Total flux, mol/m2/s

P c :

Capillary pressure, MPa

P 0 :

Reference pressure, MPa

R :

Gas constant, J/K/mol

RH:

Relative humidity

s():

Confidence interval

S g :

Part of porosity accessible to gas transfer

S l :

Saturation to liquid obtained on the sample weight

T :

Temperature, K

P :

Pressure, Pa

x i :

Molar fraction of species i

λ m :

Mean free path, m

μ :

Dynamic viscosity, Pa s

\({\phi}\) :

Porosity

σ :

Superficial tension water/gas, N/m

τ :

Tortuosity

\({{\nabla}}\) :

Gradient operator

\({\nabla \cdot}\) :

Divergence operator

app:

Apparent

d :

Downstream

g :

Gas

u :

Upstream

1:

Permeant gas (hydrogen or helium)

2:

Vector gas (nitrogen)

M :

Porous medium

∞ :

Effective permeability

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Authors and Affiliations

  1. ANDRA, Chatenay Malabry, France

    P. F. Boulin & J. Talandier

  2. Université de Grenoble, LTHE/CNRS, Grenoble, France

    P. F. Boulin, R. Angulo-Jaramillo & J. F. Daian

  3. Liten/DTNM/L2T, CEA, Grenoble, France

    P. F. Boulin & P. Berne

  4. Université de Lyon, UMR 5023 Ecologie des Hydrosystemes Naturels et Anthropisés, Université Lyon 1, ENTPE, CNRS, 3, rue Maurice Audin, 69518, Vaulx-en-Velin, France

    R. Angulo-Jaramillo

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  1. P. F. Boulin
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  2. R. Angulo-Jaramillo
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  3. J. Talandier
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  4. P. Berne
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  5. J. F. Daian
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Correspondence to P. F. Boulin.

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Boulin, P.F., Angulo-Jaramillo, R., Talandier, J. et al. Contribution of the Dusty Gas Model to Permeability/Diffusion Tests on Partially Saturated Clay Rocks. Transp Porous Med 93, 609–634 (2012). https://doi.org/10.1007/s11242-012-9972-5

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