Effects of Anisotropic Permeability Evolution on Shale Gas Production: An Internal Swelling Factor Model

Considerable attention has been paid to the anisotropic permeability of shale gas reservoirs, but the impacts of heterogeneous internal swelling have rarely been studied. In this research, we propose a new definition of the internal swelling factor (ISF) as the ratio of the increment in the pore adsorption strain to the increment in the matrix adsorption strain. In particular, we pioneered the study of the influence of the boundary conditions on the ISF. A new shale gas production model that considers the anisotropic ISF is proposed. The validity of the model was verified using field data sets obtained from the Marcellus shale and Barnett shale. We examined the influence of the anisotropic ISF on the permeability in all directions. In particular, the influence of the ISF on gas exploitation was characterized. In addition, the sensitivity of the ISF to Langmuir pressure was also analyzed. We obtained the following results. First, under in situ stress boundary conditions, the horizontal ISF was constant as a result of the constant-stress boundary conditions, whereas the vertical ISF increased as a result of the constant-volume boundary conditions during gas depletion. Second, the horizontal permeability was determined by the competition between the effective stress-induced strain and the adsorption strain because of the constant-stress boundary conditions. The horizontal ISF mainly affects the middle and late stages of depletion, whereas the vertical ISF has little effect on both. Third, the large permeability enhances the gas production rate in the early stages of depletion but has relatively little effect on the cumulative gas production volume. The horizontal ISF value is also proportional to the horizontal permeability value. Finally, as the Langmuir pressure of the matrix increases, the ISF value also increases, which leads to an increase in the gas production rate of the inorganic pores, whereas the gas production rate of the matrix decreases because of the decrease in the gas adsorption capacity. As compared with the existing models, this model provides a more accurate way to estimate the impact of the ISF on the shale gas exploration process and to predict the gas depletion characteristics.