1. Reference problem#

1.1. Geometry#

F

D

C

E

B

A

Coordinates of the points (\(m\)):

Point

\(X\)

\(Y\)

\(A\)

0.425

-10

\(B\)

1,1225

-10

\(C\)

1,1225

0

\(D\)

0.425

0

\(E\)

10

-10

\(F\)

10

0

The part delimited by \(\mathit{ABCD}\) will be called \(\mathit{BO}\) and the part \(\mathit{BEFC}\), \(\mathit{BG}\).

For the 3D version of the wtnv125 test, the geometry is extruded with a thickness of \(\mathrm{5,181}m\).

1.2. Material properties#

The properties of the material are shown in the table below.

Liquid water

Density (\({\mathit{kg.m}}^{\mathrm{-}3}\)) Heat at constant pressure (\({\mathit{J.K}}^{\mathrm{-}1}\)) Coefficient of thermal expansion of liquid (\({K}^{\mathrm{-}1}\)) Dynamic viscosity of liquid water (\(\mathit{Pa.s}\))

103 4180 10-4 10-3

Gaz

Specific heat (\({\mathit{J.K}}^{\mathrm{-}1}\)) Molar mass (\({\mathit{kg.mol}}^{\mathrm{-}1}\))

1000 0.02896 1.8. 10-5

Sturdy (\(\mathit{BO}\))

Density (\({\mathit{kg.m}}^{\mathrm{-}3}\)) Drained Young’s Modulus \(E\) (\(\mathit{Pa}\)) Poisson’s Ratio

2670 1.9.1020 0.2

Initial state (\(\mathit{BO}\))

Porosity Temperature (\(K\)) Gas Pressure (\(\mathit{Pa}\)) Vapor Pressure (\(\mathit{Pa}\)) Initial Capillary Pressure (\(\mathit{Pa}\))

0.35 293 1E5 2320 5.107 (\(S\mathrm{=}\mathrm{0,57}\))

Homogenized coefficients (\(\mathit{BO}\))

Homogenized density (\({\mathit{kg.m}}^{\mathrm{-}3}\)) Saturation Intrinsic permeability (\({m}^{2}\)) Relative liquid permeability () Relative liquid permeability Relative gas permeability (\({\mathit{J.K}}^{\mathrm{-}1}\)) Biot Thermal conductivities

\(2670\) \(S({P}_{c})\mathrm{=}0.99(1\mathrm{-}{6.10}^{\mathrm{-}9}{P}_{c})\) \({10}^{\mathrm{-}20}\) \({\mathit{kr}}_{w}(S)\mathrm{=}S\) \({\mathit{kr}}_{\mathit{gz}}(S)\mathrm{=}1\mathrm{-}S\) \(482\) \(1\) \(\begin{array}{c}{\lambda }_{S}^{T}(S)\mathrm{=}0.35\mathrm{\cdot }S\\ {\lambda }_{T}^{T}(S)\mathrm{=}0.6\\ {\lambda }_{\mathit{CT}}^{T}(S)\mathrm{=}0.728\end{array}\)

Solid (BG)

Density (\({\mathit{kg.m}}^{\mathrm{-}3}\)) Drained Young’s Modulus \(E\) (\(\mathit{Pa}\)) Poisson’s Ratio

\(2670\) \(\mathrm{1,9}{.10}^{20}\) \(0.2\)

Initial state (BG)

Porosity Temperature (\(K\)) Gas Pressure (\(\mathit{Pa}\)) Vapor Pressure (\(\mathit{Pa}\)) Initial Capillary Pressure (\(\mathit{Pa}\))

\(\mathrm{0,05}\) \(293\) \(1E5\) \(2320\) \({7.10}^{7}\) (\(S\mathrm{=}\mathrm{0,81}\))

Homogenized coefficients (BG)

Homogenized density (\({\mathit{kg.m}}^{\mathrm{-}3}\)) Saturation Intrinsic permeability (\({m}^{2}\)) Relative liquid permeability () Relative liquid permeability Relative gas permeability (\({\mathit{J.K}}^{\mathrm{-}1}\)) Biot Thermal conductivity

\(2670\) \(S({P}_{c})\mathrm{=}0.99(1\mathrm{-}{6.10}^{\mathrm{-}9}{P}_{c})\) \({10}^{\mathrm{-}19}\) \({\mathit{kr}}_{w}(S)\mathrm{=}S\) \({\mathit{kr}}_{\mathit{gz}}(S)\mathrm{=}1\mathrm{-}S\) \(706\) \(1\) \(\begin{array}{c}{\lambda }_{S}^{T}(S)\mathrm{=}0.05\mathrm{\cdot }S\\ {\lambda }_{T}^{T}(S)\mathrm{=}0.6\\ {\lambda }_{\mathit{CT}}^{T}(S)\mathrm{=}1.539\end{array}\)

1.3. Boundary conditions and loads#

On all edges: Zero hydraulic flow

The only driver here is the saturation of one medium by another.