1. Reference problem#

1.1. Geometry#

The field studied represents a section of land around a storage cell.

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

\(A\)	0	-500	-500	\(C\)	10	-400
\(B\)	10	-500	-500	\(D\)	0	-400
\(O\)	0	-450

Cell radius: \(5.6m\)

Note:

The alveolus is not scaled on the diagram.

1.2. Material properties#

Only the properties on which the solution depends are given here. The command file contains other material data (temperatures,…) that play no role in solving the problem at hand.

Liquid water	Density ( \({\mathit{kg.m}}^{\mathrm{-}3}\) ) Viscosity	1000 1



Homogenized parameters	Permeability \(K\) Sorption isothermal Relative permeability Porosity Storage	\({10}^{\mathrm{-}18}{m}^{\mathrm{-}2}\) 0.14 \(4.{10}^{\mathrm{-}10}{m}^{\mathrm{-}1}\)

1.3. Initial conditions#

The problem has two phases:

A first phase of 15 years of desaturation corresponding to the operation of the underground structure.
A second phase of restoration after backfilling the cell corresponding to exploitation (the saturation of the cell is initialized to 0.7).

The initial conditions are as follows:

For phase 1

Cell \({P}_{c}\mathrm{=}\mathrm{9,4}{.10}^{7}\mathit{Pa}\) (\(S\mathrm{=}\mathrm{0,49}\))
Geological barrier \({P}_{c}\mathrm{=}{1.10}^{5}\mathit{Pa}\) (\(S\mathrm{=}\mathrm{0,999}\))

For phase 2 (\(t>15\mathit{ans}\))

Cell \({P}_{c}\mathrm{=}\mathrm{3,015}{.10}^{7}\mathit{Pa}\) (\(S\mathrm{=}\mathrm{0,7}\))

1.4. Boundary conditions#

They are expressed in capillary pressure.

Stage 1:

On \(\mathrm{[}\mathit{AB}\mathrm{]}\) \({P}_{c}\mathrm{=}{1.10}^{5}\mathit{Pa}\)

On \(\mathrm{[}\mathit{CB}\mathrm{]}\) Zero hydraulic flow

On \(\mathrm{[}\mathit{CD}\mathrm{]}\) \({P}_{c}\mathrm{=}{1.10}^{5}\mathit{Pa}\)

On \(\mathrm{[}\mathit{A01}\mathrm{]}\mathrm{\cup }\mathrm{[}\mathrm{02D}\mathrm{]}\) Zero hydraulic flow

On the whole cell \({P}_{c}\mathrm{=}\mathrm{9,4}{.10}^{7}\mathit{Pa}\) (\(S\mathrm{=}\mathrm{0,49}\)).

Stage 2:

On \(\mathrm{[}\mathit{AB}\mathrm{]}\) \({P}_{c}\mathrm{=}{1.10}^{5}\mathit{Pa}\)

On \(\mathrm{[}\mathit{CB}\mathrm{]}\) Zero hydraulic flow

On \(\mathrm{[}\mathit{CD}\mathrm{]}\) \({P}_{c}\mathrm{=}{1.10}^{5}\mathit{Pa}\)

On \(\mathrm{[}\mathit{AD}\mathrm{]}\) Zero hydraulic flow