Elasticity and Characteristic Stress Thresholds of Shale under Deep In Situ Geological Conditions.

The mechanical properties of shale are generally influenced by in situ geological conditions. However, the understanding of the effects of in situ geological conditions on the mechanical properties of shale is still immature. To address this problem, this paper provides insight into the elasticity and characteristic stress thresholds (i.e., the crack closure stress σcc, crack initiation stress σci, and crack damage stress σcd) of shales with differently oriented bedding planes under deep in situ geological conditions. To accurately determine the elastic parameters and crack closure and initiation thresholds, a new method-i.e., the bidirectional iterative approximation (BIA) method-which iteratively approaches the upper and lower limit stresses of the linear elastic stress-strain regime, was proposed. Several triaxial compression experiments were performed on Longmaxi shale samples under coupled in situ stress and temperature conditions reflecting depths of 2000 and 4000 m in the study area. The results showed that the peak deviatoric stress (σp) of shale samples with the same bedding plane orientation increases as depth increases from 2000 m to 4000 m. In addition, the elastic modulus of the shale studied is more influenced by bedding plane orientation than by burial depth. However, the Poisson's ratios of the studied shale samples are very similar, indicating that for the studied depth conditions, the Poisson's ratio is not influenced by the geological conditions and bedding plane orientation. For the shale samples with the two typical bedding plane orientations tested (i.e., perpendicular and parallel to the axial loading direction) under 2000 and 4000 m geological conditions, the ratio of crack closure stress to peak deviatoric stress (σcc/σp) ranges from 24.83% to 25.16%, and the ratio of crack initiation stress to peak deviatoric stress (σci/σp) ranges from 34.78% to 38.23%, indicating that the σcc/σp and σci/σp ratios do not change much, and are less affected by the bedding plane orientation and depth conditions studied. Furthermore, as the in situ depth increases from 2000 m to 4000 m, the increase in σcd is significantly greater than that of σcc and σci, indicating that σcd is more sensitive to changes in depth, and that the increase in depth has an obvious inhibitory effect on crack extension. The expected experimental results will provide the background for further constitutive modeling and numerical analysis of the shale gas reservoirs.

Fracture Toughness Testing of Brittle Laminated Geomaterials Using Hollow Double-Wing Slotted Specimens.

The fracture toughness of shale is a key parameter guiding hydraulic fracturing design and optimization. The hollow double-wing slotted (HDWS) specimen is a typical specimen configuration for measuring the mode I fracture toughness of rock. The calibration of the shape factor (f) is the basis for accurately obtaining the fracture toughness of rocks. In this study, the influences of crack length, hole size, and the anisotropy of elastic parameters on f for specimens with three typical bedding orientations-arrester (A), divider (D), and short-transverse (ST) orientations-are systematically investigated using finite element software. The numerical simulation results support the following findings. The mode I f increases monotonically with an increase in hole size. The influence of crack length on f varies depending on hole sizes. Under different bedding orientations, significant anisotropy in f was observed. In addition, the degree of anisotropy in Young's modulus has a major impact on f, which is related to the bedding orientation of the specimen. The apparent shear modulus ratio has relatively little influence on f. As the hole size and crack length increase, the influence of the anisotropy of elastic parameters on f increases. Based on numerical calculations, hydraulic fracturing experiments were conducted on HDWS specimens of Longmaxi shale with three bedding orientations, and the results showed that the peak pressure and fracture toughness of the samples in the ST direction were the lowest, while those in the A direction were the highest.

[Numerical study on the effect of the geometry size of multi-chamber infusion bag on its bursting force].

This study explored the variation of bursting force of multi-chamber infusion bag with different geometry size, providing guidance for its optimal design. Models of single-chamber infusion bag with different size were established. The finite element based on fluid cavity method was adopted to calculate the fluid-solid coupling deformation process of infusion bag to obtain corresponding critical bursting force. As a result, we proposed an empirical formula predicting the critical bursting force of one chamber infusion bag with specified geometry size. Besides, a theoretical analysis, which determines the force condition of three chamber infusion bag when falling from high altitude, was conducted. The proportion of force loaded on different chamber was gained. The results indicated that critical bursting force is positively related to the length and width of the chamber, and negatively related to the height of the chamber. While the infusion bag falling, the impact force loaded on each chamber is proportional to the total liquid within it. To raise the critical bursting force of in fusion bag, a greater length and width corresponding to reduced height are recommended considering the volume of liquid needed to be filled in.