An exact closed-form solution of free vibration of a simply supported and multilayered one-dimensional (1D) quasi-crystal (QC) plate is derived using the pseudo-Stroh formulation and propagator matrix method. Natural frequencies and mode shapes are presented for a homogenous QC plate, a homogenous crystal plate, and two sandwich plates made of crystals and QCs. The natural frequencies and the corresponding mode shapes of the plates show the influence of stacking sequence on multilayered plates and the different roles phonon and phason modes play in dynamic analysis of QCs. This work could be employed to further expand the applications of QCs especially if used as composite materials.

Although nano- and micro-scale phenomena for fluid flows are ubiquitous in tight oil reservoirs or in nano- or micro-sized channels, the mechanisms behind them remain unclear. In this study, we consider the wall–liquid interaction to investigate the flow mechanisms behind a compressible liquid flow in nano- or micro-sized circular tubes. We assume that the liquid is attracted by the wall surface primarily by the Lifshitz–van der Waals (LW) force, whereas electrostatic forces are negligible. The long-range LW force is thus introduced into the Navier–Stokes equations. The nonlinear equations of motion are decoupled by using the hydrodynamic vorticity-stream functions, from which an approximate analytical perturbation solution is obtained. The proposed model considers the LW force and liquid compressibility to obtain the velocity and pressure fields, which are consistent with experimentally observed micro-size effects. A smaller tube radius implies smaller dimensionless velocity, and when the tube radius decreases to a certain radius R_m, a fluid no longer flows, where R_m is the lower limit of the movable-fluid radius. The radius R_m is calculated, and the results are consistent with previous experimental results. These results reveal that micro-size effects are caused by liquid compressibility and wall–liquid interactions, such as the LW force, for a liquid flowing in nano- or micro-sized channels or pores. The attractive LW force enhances the flow’s radial resistance, and the liquid compressibility transmits the radial resistance to the streaming direction via volume deformation, thereby decreasing the streaming velocity.

Hydraulic fracturing of gas and oil reservoirs is the primary stimulation method for enhancing production in the field of petroleum engineering. The hydraulic fracturing technology plays a crucial role in increasing shale gas production from shale reservoirs. Understanding the effects of reservoir and fracturing conditions on fracture propagation is of great significance for optimizing the hydraulic fracturing process and has not been adequately explored in the current literature. In the context of shale reservoirs in Yibin, Sichuan Province, China, the study selects outcrops to prepare samples for uniaxial compression and Brazilian splitting tests. These tests measure the compressive and tensile strengths of shale in parallel bedding and vertical bedding directions, obtaining the shale’s anisotropic elastic modulus and Poisson’s ratio. These parameters are crucial for simulating reservoir hydraulic fracturing. This paper presents a numerical model utilizing a finite element (FE) analysis to simulate the process of multi-cluster hydraulic fracturing in a shale reservoir with natural fractures in three dimensions. A numerical simulation of the intersection of multiple clusters of 3D hydraulic fractures and natural fractures was performed, and the complex 3D fracture morphologies after the interaction between any two fractures were revealed. The influences of natural fractures, reservoir ground stress, fracturing conditions, and fracture interference concerning the spreading of hydraulic fractures were analyzed. The results highlight several key points: (1) Shale samples exhibit distinct layering with significant anisotropy. The elastic compressive modulus and Poisson’s ratio of parallel bedding shale samples are similar to those of vertical bedding shale samples, while the compressive strength of parallel bedding shale samples is significantly greater than that of vertical bedding shale samples. The elastic compressive modulus of shale is 6 to 10 times its tensile modulus. (2) The anisotropy of shale’s tensile properties is pronounced. The ultimate load capacity of vertical bedding shale samples is 2 to 4 times that of parallel bedding shale samples. The tensile strength of vertical bedding shale samples is 2 to 5 times that of parallel bedding shale samples. (3) The hydraulic fractures induced by the injection well closest to the natural fractures expanded the fastest, and the natural fractures opened when they intersected the hydraulic fractures. When the difference in the horizontal ground stress was significant, natural fractures were more inclined to open after the intersection between the hydraulic and natural fractures. (4) The higher the injection rate and viscosity of the fracturing fluid, the faster the fracture propagation. The research findings could improve the fracturing process through a better understanding of the fracture propagation process and provide practical guidance for hydraulic fracturing design in shale gas reservoirs.

Volume fracturing is a key technology in developing unconventional gas reservoirs that contain nano/micron pores. Different fracture structures exert significantly different effects on shale gas production, and a fracture structure can be learned only in a later part of detection. On the basis of a multiscale gas seepage model considering diffusion, slippage, and desorption effects, a three-dimensional finite element algorithm is developed. Two finite element models for different fracture structures for a shale gas reservoir in the Sichuan Basin are established and studied under the condition of equal fracture volumes. One is a tree-like fracture, and the other is a lattice-like fracture. Their effects on the production of a fracture network structure are studied. Numerical results show that under the same condition of equal volumes, the production of the tree-like fracture is higher than that of the lattice-like fracture in the early development period because the angle between fracture branches and the flow direction plays an important role in the seepage of shale gas. In the middle and later periods, owing to a low flow rate, the production of the two structures is nearly similar. Finally, the lattice-like fracture model is regarded as an example to analyze the factors of shale properties that influence shale gas production. The analysis shows that gas production increases along with the diffusion coefficient and matrix permeability. The increase in permeability leads to a larger increase in production, but the decrease in permeability leads to a smaller decrease in production, indicating that the contribution of shale gas production is mainly fracture. The findings of this study can help better understand the influence of different shapes of fractures on the production in a shale gas reservoir.

In this paper, based on the gneiss outcrop of Bozhong 196 gas field in China, uniaxial compression and Brazil splitting tests were conducted by using cores of different orientations. The following compression properties were studied: the elastic compression modulus, Poisson’s ratio and compressive strength of the gneiss outcrop. The following tensile properties were studied: the tensile modulus, the tensile strength and peak energy rate of gneiss outcrop. The results demonstrate the following: (1) The elastic compression modulus, compressive strength, tensile strength and peak energy rate of gneiss specimens with horizontal core-taking are greater than those with vertical core-taking. (2) The elastic compression modulus, Poisson’s ratio and compressive strength of horizontally cored gneiss specimens are 29.688–45.760 GPa, 0.186–0.386, and 174.94–147.80 MPa, respectively; the elastic compression modulus, Poisson’s ratio and compressive strength of the vertical gneiss specimens are 26.541–32.602 GPa, 0.429–0.476 and 169.37–134.46 MPa. (3) The tensile modulus of the horizontal gneiss specimens is 4.93–5.98 GPa. The tensile modulus of the vertical gneiss specimens is 0.96–2.11 GPa. The tensile modulus of the horizontal gneiss specimens is five times that of the vertical gneiss specimens. The elastic compression modulus of gneiss is 5–20 times that of the tensile modulus. (4) The tensile strength and peak energy rate of horizontally cored gneiss specimens are 14.33–17.55 MPa and 2598.67–4049.53 J/m², respectively. The tensile strength of the vertical gneiss specimens is 6.12–9.65 MPa, and the peak energy rate is 715.74–1515.30 J/m². (5) There is a good linear relationship between the peak energy rate and tensile strength of gneiss. The research results can provide a scientific and reasonable reference for in situ fracturing of Bozhong 196 gas field.