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The parameters of fractures, such as fracture geometries, placement, and conductivity, are critical for the production of horizontal wells in tight gas reservoirs. Current studies on fracture parameter optimization, especially those using the optimization algorithms, are often based on the assumptions that the fractures are uniformly placed with equal length and conductivity. However, non-uniform designs of fracture spacing have been proved to be effective in reducing fracture interference as well as increasing the well production, especially with strong rock heterogeneity. In addition, most of the current literature focuses on identifying optimal hydraulic fracture geometries without considering the fracture propagation process, which may oversimplify the evaluation of completion cost and result in fracture geometries that cannot be realized in practice. In this paper, an automatic optimization process, which could efficiently couple the fracture propagation, is proposed to optimize the fracture parameters. The genetic algorithm (GA) with penalty function method is used to optimize the constraint and non-linear problem. A modified PKN fracture propagation model is established to quickly predict the hydraulic fracture geometries. Fracture locations and fluid injection volume are sequentially optimized with consideration of heterogeneous rock properties. Model parameters are taken from typical tight gas horizontal wells in Jinqiu gas field in Sichuan Province, China. The results show the importance of permeability on both fracture length and production in tight gas well. The lower the permeability, the more significant the production increase after fracture location optimization. More fractures tend to be placed in area with small permeability and fewer fractures are required in highly permeable regions. With an increase in rock heterogeneity, the distribution of fractures becomes more uneven. Conversely, increasing the number of fractures can lead to a more even distribution of fractures. More fluid should be injected in low-permeability regions according to the optimization results. The optimization method is applied to a practical tight gas well in Sichuan Basin and the cumulative gas production can be increased by 6.5% to 8% when compared with the initial uniform designs. • A modified PKN model is proposed for quick prediction of fracture propagation, validated against numerical simulations. • GA is used to optimize fracture locations by considering rock heterogeneity's impact on fracture propagation and production. • Sequential optimization of fracture placement and injection volume is conducted with its reliability verified. [ABSTRACT FROM AUTHOR]

Deep shale gas reservoirs, compared to shallow and intermediate shale gas reservoirs, usually exhibit lower fracture complexity, smaller stimulated volume, poorer conductivity, and faster production decline when the same injection scheme and construction parameters are used. As a result, specific injection scenarios for deep shale reservoirs must be investigated. In this paper, a series of laboratory fracturing tests were conducted to investigate the influence of injection scenarios on deep shale hydraulic fracture initiation and propagation. The black shale of the Lower Silurian Longmaxi formation in the Sichuan Basin was adopted, and four different injection schemes (constant fluid rate injection, cyclic injection, shut-in intermittent injection, and low-frequency pulse pressurization injection) were utilized in these experiments. The energy evolution during hydraulic fracturing with different injection schemes was analyzed by an array of acoustic emission (AE) sensors. Furthermore, the internal fracture geometry of the shale specimens after failure was determined using high-resolution CT scanning. Two parameters, fracture bulk density and fractal dimension were defined to quantitatively characterize the post-pressure fracture complexity. The results indicate that the rock breakdown pressure rises rapidly as the injection rate increases, for conventional monotonic rate injection. Although increasing the injection rate can serve the purpose of increasing the net pressure in the seam and enhancing the fracture complexity, it makes it easier to approach the equipment pressure limit. Unlike conventional hydraulic fracturing, which mainly induces tensile fractures near the wellbore, cyclic fracturing is more likely to cause fatigue damage to the rock, resulting in the formation of subcritical microcracks, which gradually grow into macroscale fractures. In addition, the cyclic injection method can reduce the rock breakdown pressure by approximately 24% compared with the conventional continuous injection method. The shut-in intermittent injection method can also reduce the breakdown pressure of shale by 22%, but this method is not conducive to enhancing the fracture complexity. Pulse fracturing creates the most complex fracture morphology among the four injection schemes tested. The rapid changes in wellbore pressure over a short time can easily result in the formation of multiple fractures around the borehole. Our experimental results and theoretical analysis can provide theoretical support for the optimization of injection schemes for deep shale hydraulic fracturing. • Laboratory tests were conducted to investigate the influence of injection scenarios on deep shale hydraulic fracturing. • All the experiments were monitored by an array of AE sensors. • The internal fractures geometry of the shale specimens after failure was determined by high-resolution CT scanning. • The cyclic fracturing can reduce the breakdown pressure by about 24% compared with the conventional continuous injection method. [ABSTRACT FROM AUTHOR]

• Seismic vulnerability analysis of a masonry pagoda through FE simulations in Abaqus. • Good agreement between FE modal analysis and cantilever beam first mode formula. • Sensitivity analysis on the CDP material parameters for Pushover Analyses POs. • NLDAs that confirmed the collapse acceleration results given by POs. • Slenderness influence studied using taller/shorter pagodas with 3D models artificially created. As an important historical building type for human beings, ancient masonry pagodas have key research significance. They are widely diffused in China, and they are tower-like masonry structures, usually massive and tall. This paper takes the Longhu pagoda as a case-study: it was built in 1342 CE, and it is the only masonry pagoda from the Yuan Dynasty. It is located in the Sichuan Province (China), it has a square plane, and the height is about 33 m. This construction severely suffered the so-called "2008 Sichuan Earthquake". A full 3D model of the Longhu Pagoda has been obtained and subsequently meshed. The FE software Abaqus/CAE has been used for carrying out static analyses, pushover analyses and non-linear dynamic analyses. The material non-linearities have been taken into consideration employing the so-called Concrete Damage Plasticity (CDP) model available in Abaqus. Modal analyses have shown that FEM results and simplified cantilever model results may agree. Pushover analyses (POs) have been performed under different load conditions and along the four principal bending directions to estimate the global capacities and the corresponding collapse mechanisms. Non-linear dynamic analyses (NLDAs) allowed putting in evidence the accuracy of the results provided by the pushover analyses; besides, they gave helpful information about the crack propagation, confirming the damage reported on-site after the 2008 earthquake. The state of damage found and the related failure mechanisms have been deeply commented. Moreover, some sensitivity analyses have been performed to study the influence of some material parameters on the pushover results. Furthermore, two fictitious 3D models of the pagoda have been created by doubling and removing two floors to investigate the influence of the tower slenderness. The before mentioned analyses have also been performed on such models, and the impact of the slenderness on this structural typology has been studied. Finally, the kinematic theorem of limit analysis has been applied, and some values of collapse acceleration have been consequently computed using different a-priori established collapse mechanisms. The results have been compared with FE simulations results, and the ability of limit analysis to quickly predict the seismic vulnerability has been discussed. [ABSTRACT FROM AUTHOR]