Fracture propagation mechanisms in coalbed methane (CBM) reservoirs are very complex due to the development of the internal cleat system. In this paper, the characteristics of initiation and propagation of hydraulic fractures in coal specimens at different angles between the face cleat and the maximum horizontal principal stress were investigated with hydraulic fracturing tests. The results indicate that the interactions between the hydraulic fractures and the cleat system have a major effect on fracture networks. “Step-like” fractures were formed in most experiments due to the existence of discontinuous butt cleats. The hydraulic fractures were more likely to divert or propagate along the butt cleat with an increase in the angles and a decrease in the horizontal principal stress difference. An increase in the injection rate and a decrease in the fracturing fluid viscosity were more conducive to fracture networks. In addition, the influence on fracture propagation of the residual coal fines in the wellbore was also studied. The existence of coal fines was an obstacle in fracturing, and no effective connection can be formed between fractures. The experimental investigation revealed the fracture propagation mechanisms and can provide guidance for hydraulic fracturing design of CBM reservoirs.

The consensus control of multiple AUVs recovery system is the key to complete the multi-AUV recovery mission. This paper proposes consensus control of multiple AUVs recovery system under switching communication topologies and time delays including input delay and communication delay. Consensus control algorithm for a multi-AUV recovery system is assumed to guarantee all the members to reach a common motion state and desired point. The mothership is regarded as the point which all AUVs have to catch up with, the recovery problem of multiple AUVs can be seen as the consensus problem of multi-agents system. A randomly changing consensus stability criteria and stabilization conditions are derived by a suitable Lyapunov-Krasovskii functional for the Markovian switching recovery system with time delays, and then a consensus controller design method is derived. Finally, the correctness of the proposed method is proved by simulation experiments.

A numerical model was established by using the 3D lattice method to investigate the synchronous propagation mechanism of multiple clusters of hydraulic fractures in interlayered tight sandstone reservoirs in the Songliao Basin in China. The multi-fracture synchronous propagation model under different geological factors and fracturing engineering factors was simulated. The results show that the vertical stress difference, interlayer Young’s modulus, and lithologic interface strength are positively correlated with the longitudinal propagation ability of multiple hydraulic fractures. The three clusters of hydraulic fractures can have adequate longitudinal extension capacity and transverse propagation range with 15 m cluster spacing and a 12 m³/min pumping rate. The viscosity of the fracturing fluid is positively correlated with the ability of hydraulic fracture to penetrate the interlayer longitudinally but negatively correlated with the transverse propagation length. It is recommended that high viscosity fracturing fluid is used in the early stage of multi-clustered fracturing in interlayered tight sandstone reservoirs to promote hydraulic fractures to penetrate more interlayers and communicate more pay layers in the longitudinal direction, and low viscosity fracturing fluid in the later stage to make multiple clusters of fractures propagate to the far end where possible and obtain a more ideal SRV.

Accurate prediction of the fracture geometry before the operation of a hydraulic fracture (HF) job is important for the treatment design. Simplified planar fracture models, which may be applicable to predict the fracture geometry in homogeneous and continuous formations, fail in case of fractured reservoirs and laminated formations such as shales. To gain a better understanding of the fracture propagation mechanism in laminated formations and their vertical geometry to be specific, a series of numerical models were run using XSite, a lattice-based simulator. The results were studied to understand the impact of the mechanical properties of caprock and injection parameters on HF propagation. The tensile and shear stimulated areas were used to determine the ability of HF to propagate vertically and horizontally. The results indicated that larger caprock Young’s modulus increases the stimulated area (SA) in both vertical and horizontal directions, whereas it reduces the fracture aperture. Also, larger vertical stress anisotropy and tensile strength of caprock and natural interfaces inhibit the horizontal fracture propagation with an inconsiderable effect in vertical propagation, which collectively reduces the total SA. It was also observed that an increased fluid injection rate suppresses vertical fracture propagation with an insignificant effect on horizontal propagation. The dimensionless parameters defined in this study were used to characterize the transition of HF propagation behavior between horizontal and vertical HFs.