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 \(\mathit{BEFC}\), \(\mathit{BG}\).

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 \(S({P}_{C})\mathrm{=}0.99(1\mathrm{-}{6.10}^{\mathrm{-}9}{P}_{C})\) 10-20
_images/Object_2.svg _images/Object_4.svg

482 1 \(\begin{array}{c}{\lambda }_{S}^{T}(S)\mathrm{=}\mathrm{0,35}\mathrm{\cdot }S\\ {\lambda }_{T}^{T}(S)\mathrm{=}\mathrm{0,6}\\ {\lambda }_{\mathit{CT}}^{T}(S)\mathrm{=}\mathrm{0,728}\end{array}\)

Solid (BG)

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

2670 1.9.1020 0.2

Initial state (BG)

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

0.05 293 1E5 2320 7.107 (S=0.81)

Homogenized coefficients (BG)

Homogenized density (\({\mathit{kg.m}}^{\mathrm{-}3}\)) Saturation Intrinsic permeability (\({m}^{2}\)) Relative liquid permeability () Relative liquid permeability () Saturation Intrinsic permeability () BioTthermal conductivity \({\mathit{J.K}}^{\mathrm{-}1}\)
2670 \(S({P}_{C})\mathrm{=}0.99(1\mathrm{-}{6.10}^{\mathrm{-}9}{P}_{C})\) 10-19
_images/Object_7.svg _images/Object_9.svg

706 1 \(\begin{array}{c}{\lambda }_{S}^{T}(S)\mathrm{=}\mathrm{0,05}\mathrm{\cdot }S\\ {\lambda }_{T}^{T}(S)\mathrm{=}\mathrm{0,06}\\ {\lambda }_{\mathit{CT}}^{T}(S)\mathrm{=}\mathrm{1,539}\end{array}\)

1.3. Boundary conditions and loads#

On all edges: Zero hydraulic flow

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