Fluid penetration into the rock during hydraulic fracturing has been an essential issue in studying the mechanism of fracture initiation, especially the seepage force caused by fluid penetration, which has an important effect on the fracture initiation mechanism around a wellbore. However, in previous studies, the effect of seepage force under unsteady seepage on the fracture initiation mechanism was not considered. In this study, a new seepage model that can predict the variations of pore pressure and seepage force with time around a vertical wellbore for hydraulic fracturing was established by using the method of separation of variables and the Bessel function theory. Then, based on the proposed seepage model, a new circumferential stress calculation model considering the time-dependent effect of seepage force was established. The accuracy and applicability of the seepage model and the mechanical model were verified by comparison with numerical, analytical and experimental results. The time-dependent effect of seepage force on fracture initiation under unsteady seepage was analyzed and discussed. The results show that when the wellbore pressure is constant, the circumferential stress induced by seepage force increases over time, and the possibility of fracture initiation also increases. The higher the hydraulic conductivity, the lower the fluid viscosity and the shorter the time required for tensile failure during hydraulic fracturing. In particular, when the tensile strength of rock is lower, the fracture initiation may occur within the rock mass rather than on the wellbore wall. This study is promising to provide a theoretical basis and practical guidance for further research on fracture initiation in the future.
With continuous global warming, growing urban population density and increasing compactness of urban buildings, VD (void deck) street design has become increasingly popular in city planning, especially in tropical countries. However, understanding on traffic pollutant dispersion in the VD street canyons is still at early stage. This paper quantitatively evaluates the effects of VD location and wind direction on the ventilation and traffic pollutant exposure inside the street canyon with VDs. The results show that the VD location and wind direction have significant effects on the flow field and pollutant dispersion inside the canyon. When VDs are located at the upwind building, downwind building, and both buildings, the wind directions with maximum ACH (air exchange rate) are 60°, 30° and 60°, respectively. Under seven wind directions (0°, 15°, 30°, 45°, 60°, 75°, and 90°), the VD provides higher ACH than that of the regular canyon, especially at high α (angle between the approaching wind and the canyon axis). When α = 90°, regular canyon has the lowest ventilation capacity, but ACH values of canyons with both VDs or the leeward VD are 189.1% and 177.6% of regular canyon, respectively. Also, mean K (dimensionless pollutant concentration) values of the canyon wall and pedestrian respiration plane on one side where VD is located are significantly reduced compared to the regular canyon. Therefore, when VDs are at both buildings, both pedestrian respiration planes and walls have the lowest K values, thus providing the best living environment for pedestrians and near-road residents. As α increases, the K values on both respiration planes significantly decrease except for the leeward respiration plane of the canyon with the windward VD. These findings can help to design urban street canyons for mitigating traffic pollution risk and improving ventilation in tropical cities with frequently changing wind directions.
With continuous global warming, growing urban population density and increasing compactness of urban buildings, VD (void deck) street design has become increasingly popular in city planning, especially in tropical countries. However, understanding on traffic pollutant dispersion in the VD street canyons is still at early stage. This paper quantitatively evaluates the effects of VD location and wind direction on the ventilation and traffic pollutant exposure inside the street canyon with VDs.The results show that the VD location and wind direction have significant effects on the flow field and pollutant dispersion inside the canyon. When VDs are located at the upwind building, downwind building, and both buildings, the wind directions with maximum ACH (air exchange rate) are 60°, 30° and 60°, respectively. Under seven wind directions (0°, 15°, 30°, 45°, 60°, 75°, and 90°), the VD provides higher ACH than that of the regular canyon, especially at high α (angle between the approaching wind and the canyon axis). When α = 90°, regular canyon has the lowest ventilation capacity, but ACH values of canyons with both VDs or the leeward VD are 189.1% and 177.6% of regular canyon, respectively. Also, mean K (dimensionless pollutant concentration) values of the canyon wall and pedestrian respiration plane on one side where VD is located are significantly reduced compared to the regular canyon. Therefore, when VDs are at both buildings, both pedestrian respiration planes and walls have the lowest K values, thus providing the best living environment for pedestrians and near-road residents. As α increases, the K values on both respiration planes significantly decrease except for the leeward respiration plane of the canyon with the windward VD.These findings can help to design urban street canyons for mitigating traffic pollution risk and improving ventilation in tropical cities with frequently changing wind directions.
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