Multiphase flow gas transport in a deep geological repository

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implemented into the finite element code OpenGeoSys-6 (OGS-6) [1].The permeability alteration in this model is a function of gas pressure.The laboratory experiments showed that the rate of permeability change are different at low and high gas pressures.Therefore, the permeability model employed a threshold pressure ( ℎ ) to categorize this behaviour.

𝑲 = {
(1 +  1   ) 0 ,   ≤  ℎ ((  −  ℎ ) 2 + 1 +  1  ℎ )  0 ,   >  ℎ  1 and  2 are empirical parameters.Moreover, two other permeability models were employed to study the hydro-mechanical behaviour of the host rock and permeability changes.In the strain-dependent permeability model, the permeability change was related to the elasto-plastic behaviour of the host rock, and in the embedded fracture model, it was related to the opening and closure of fractures [3] [4].Thus, volumetric elastic strain   and equivalent plastic strain   are employed to be the controlling variables.
The initial permeability of the intact rock samples were determined by applying a constant pressure at the upstream and downstream of the samples (i.e.constant pressure gradient).The imperical parameters were determined by matching experimental and numerical results.
Two types of gas injection tests carried out by the Institute for Rock Mechanics (IFG GmbH, See Figure 1) were used to investigate the gas transport through Opalinus Clay and to examine the permeability models [2].The first experiment demonstrates an advective-diffusiion gas transport through the sample and an elastic deformation.The second experiment highlights the formation of a tensile fracture (plastic deformation and preferred flow path).In both experiments the advective transport is the dominant transport mechanism.The strain-dependent permeability model was successfully applied to reproduce the hydro-mechanical behaviour of the host rock in both elastic deformation test and tensile fracture test (see Figures 2 and 3).The hydro-mechanical response of a saturated single phase flow model was compared with the behaviour of a saturated two-phase flow model.Both single phase and two-phase flow models were able to describe the hydraulic as well as mechanical behaviour of the experiments performed.
Therefore, one can conclude that in these experiments the water phase (wet-phase) was immobile.A gas injection test under triaxial conditions was performed by École Polytechnique Fédérale de Lausanne (EPFL) in saturated Opalinus Clay (Fig. 4).The numerical simulations reproduced the hydro-mechanical behaviour of the sample during the gas injection test.A two-phase flow model was applied to simulate the experiment.The relative permeabilities and capillary pressure functions followed Mualem approach and van Genuchten formulation, respectively.The outflow volume and mechanical response of the sample were measured.The experimental results were in good agreement with the numerical ones.The results of the modelling illustrated the penetration of gas into the sample and hence, the displacement water (see Figures 5 and 6).

Figure 1 :
Figure 1: Sketch of laboratory experiment (left) and mesh of numerical model (right).

Figure 2 :
Figure 2: Comparison of experimental and numerical results for the IfG first experiment (hydromechanical modelling).

Figure 3 :
Figure 3: Comparison of experimental and numerical results by BGE for the IfG second experiment.