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.

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As a new type of waterless technology, supercritical carbon dioxide fracturing has been widely studied by scholars in recent years, and the migration characteristics of the corresponding proppant in supercritical carbon dioxide still need further research. In this paper, the Eulerian–Eulerian computational fluid dynamics method was used to study the transport capacity of supercritical carbon dioxide, and the UDF method was used to simulate the physical parameters of supercritical carbon dioxide. In view of the deficiencies of previous studies, the special cases of wedge-shaped fractures and bypass fractures are considered, and the influence of large-span pressure and temperature on migration is first analyzed in plane fractures, which makes this study more complete. The results show that: (1) compared with slickwater, the proppant transport channel in supercritical carbon dioxide is 30% smaller at 305 K and 10 MPa. (2) The transport capacity of supercritical carbon dioxide increases with the increase of pressure and decreases with the increase of temperature. But when the pressure or temperature is too high, they have little effect on it. (3) In wedge-shaped fractures, the proppant stack height and length increase initially as the shrinkage rate of fracture width (the ratio of the fracture reduced width to the fracture length) increases. However, as the fracture width ratio increases, the maximum proppant stack height decreases in the later stage. (4) In bifurcated fractures, with the increase of bypass angle, the area of proppant in the bypass zone tends to decrease. The width of the bypass inlet has little effect on the proppant settlement in the bypass. This study further understands the migration law of proppant in supercritical carbon dioxide in fractures.