Modelling of the impact of stress concentration on permeability in porous medium based on machine learning method

The behavior of stress-dependent permeability has been an important research topic for oil/gas production. The majority of permeability models for porous media have been proposed based on porelasticity theory. The matrix is assumed to be thoroughly separated by pores in the models and the pore compressibility is used to represent the stress-dependent behavior of permeability. However, matrix could not be separated by pores thoroughly and the impact of stress concentration around pores on pore deformation and permeability should be considered. In this study, the impact of stress concentration on permeability was illustrated by numerical simulation. In addition, the mechanism of stress-dependent behavior of permeability was analyzed. Since it is difficult to establish theoretical permeability models involving stress concentration effect caused by the complex pore structure, machine learning was applied in this paper. One of the four capable machine learning methods was selected and the corresponding machine learning model was validated through both numerical and experimental data. Moreover, the different performance of permeability prediction between the conventional model and the proposed one was discussed. The results indicate that the stress-dependent behavior of permeability results from stress concentration rather than the pore bulk modulus. Therefore, the stress-dependent permeability model with the impact of stress concentration is more accurate, compared with the numerical results and experimental data. In addition, the stress concentration increases the pore deformation and induces strong stress-dependent behavior of permeability, which is sensitive to pore shapes and related to the pore shape complexity. Specifically, the impacts of pores with different shapes on permeability are similar if the complexity index of pore shape is under 0.6 or over 0.9 and distinct for the value in between. Furthermore, the alteration in the magnitude and orientation of the stress affects stress dependency of permeability, which increases with the pore shape complexity. If the complexity index of pore shape exceeds 0.96, the alteration of permeability induced by change in stress orientation can be over 64%.