Fracture spacing during hydro‐fracturing of cap‐rocks

Layered low permeability rock units, like shales, represent seals or ‘cap‐rocks’ in a variety of geological settings. A continuous increase in the fluid pressure gradients across a virtually impermeable rock layer will ultimately lead to hydro‐fracturing. Depending on the boundary conditions, such fracturing may lead to the formation of a set of sub‐parallel cracks oriented more or less perpendicular to the cap‐rock layer. In this article, we propose a new numerical model that describes interactions between multiple cross‐cutting fractures in an elastic low permeability rock layer. The width of each fracture and the spacing between them are modeled as a force balance between the fluid pressure and the elastic forces in the cap‐rock and between each fracture. The model indicates that the system of fractures evolves toward a spatially periodic steady‐state distribution with a fixed fracture spacing and aperture. The results are similar for incompressible and compressible fluids. The steady‐state conditions depend on only two dimensionless parameters, and the fracture spacing is only weakly dependent on the cap‐rock thickness. This is in contrast to fracturing produced by simple extension of an elastic rock layer beyond the fracture strength, in which case fracture spacing is proportional to layer thickness.     

城市发展战略规划:透视激烈竞争环境中的地方政府管治

经济全球化和市场化给中国城市的发展营造了一个激烈竞争的环境,地方政府的企业化倾向更加明显,并对外界环境变化做出了种种反应。发展战略规划就是地方政府力图突破传统城市规划的制约,以增强城市竞争力为目标、强化地方发展利益的一种新城市管治方式。章通过城市发展战略规划的研究,分析了其作用以及地方政府在其中的主导角色,透视了在中国经济社会转型期地方政府管治的变化。