Analysis of the compaction phenomena due to the water injection in reservoirs with a three-phase geomechanical model

In the coastal regions, the land subsidence due to the industrial pumping of underground fluids such as methane is documented by the means of in situ surveys. The laboratory characterization of the gas bearing formations has also been published, which complements the knowledge of the reservoir compaction due to the variation of fluid pressures. The withdrawal of gas is reproduced in the laboratory by injecting water under a constant uniaxial or hydrostatic load simulating the overburden. The water injection experiments provoke a plastic compaction of the samples. The paper proposes a new attempt to model the observed compaction of samples, as well as the changes in compressibility and size of the domain of elasticity during the process of water injection. The conceptual framework essentially relies on the mechanics of unsaturated weak rocks, provided that the subsidence phenomenon concerns a three-phase material with solid grains, liquid water and gas. The proposed constitutive model provides a description of the water retention capability of the studied soils that is coupled with the mechanical behaviour. Consequently, the elasto-plastic volumetric changes within the porous medium incorporate the effects of the water saturation and the capillary pressure, also called suction. The formulation of the yield locus is such that the shape of the yield limit depends on suction in order to model the apparent added stiffness brought by low water saturation. The modelling framework, based on the generalization of the effective stress principle to three-phase media, also provides an elasto-plastic comprehension of the well-known “wetting pore collapse” phenomenon. The ACMEG-s model shows consistent understanding of changes of compressibility with the quantity of retained water. The successive phases of isotropic compression and uniaxial mechanical compaction are used for the model calibration. Interestingly, the phases of plastic compression during the water injection are captured with accuracy, which evidence the applicability of such a model to the reservoir-related subsidence studies.