1. Reference problem#
1.1. Presentation#
In this test case, we study the hydraulic behavior of an unsaturated porous medium consisting of two fluids: water in its liquid phase and dry air. In Code_Aster, this is a HHM model. The associated law of fluid behavior is of type LIQU_GAZ.
1.2. Geometry#
Coordinates of points \((m)\):
\(A:-\mathrm{0,5}-\mathrm{0,5}\text{}C:\text{}\mathrm{0,5}\mathrm{0,5}\)
\(B:\text{}\mathrm{0,5}-\mathrm{0,5}\text{}D:-\mathrm{0,5}\mathrm{0,5}\)
1.3. Material properties#
Fluid (liquid water) |
Density \(({\mathrm{kg.m}}^{-3})\) Compressibility of liquid \((\mathrm{Pa})\) Dynamic viscosity of liquid water \((\mathrm{Pa.s})\) Derived from the viscosity of the fluid with respect to temperature |
\({10}^{3}\) \({10}^{7}\) \({10}^{-3}\) \(0.\) |
Gas (dry air) |
Molar mass \(({\mathrm{kg.Pa.K}}^{-1})\) Gas viscosity \((\mathrm{Pa.s})\) Derivative of the viscosity of gas with respect to temperature |
\(1.8\times {10}^{-3}\) \({10}^{-5}\) \(0.\) |
Homogenization coefficients |
Coefficient of \(\mathrm{Biot}\) Porosity |
\(1.\) \(0.14\) |
Homogenized coefficients |
Ideal gas constant |
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Homogenized density \(({\mathrm{kg.m}}^{-3})\) |
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Saturation |
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Derivative of saturation with respect to pressure |
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Next gravity \(X\) |
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Next gravity \(Y\) |
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Next gravity \(Z\) |
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Intrinsic permeability \(({m}^{2})\) |
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Relative permeability to liquid \(({m}^{2})\) |
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Relative gas permeability \(({m}^{2})\) « |
\(1.6\times {10}^{3}\) \(0.5\) \(0.\) \(0.\) -10 in 2D, 0 in 3D -10 in 3D, 0 in 2D \({10}^{-18}\) \(1.\) \(1.\) |
1.4. Boundary conditions and loads#
Full item:
trips \({u}_{x}=0.0m,{u}_{y}=0.0m,{u}_{z}=0.0m\).
1.5. Initial conditions#
The displacement fields and capillary pressure fields are initially zero, the dry air pressure is equal to atmospheric pressure and the reference temperature is set to \({T}_{0}=273°K\)