This paper discusses the abnormal driving forces induced by highly curved micro/nano matter spaces. It is pointed out that such abnormal driving forces are constructed by two fundamental factors: the bending extent of the space, i.e. the curvatures, and the non-uniform extent of the bending of the space, i.e. the the gradients of the curvatures.
The flow mechanism in the shale reservoir involves the seepage, the diffusion and the desorption. A productivity formula for the shale gas is obtained under the stable condition with considerations of both the Knudsen diffusion and the desorption. With this formula, a productivity equation for the fractured vertical wells is established by the method of percolating resistance, with consideration both of the desorption and the diffusion. According to the formula derived and the production examples, the influence of the diffusion coefficient, the half-length of fractures and the fracture conductivity on the well gas productivity is studied. It is shown that the gas production increases with the increase of the diffusion efficiency. The greater the fracture conductivity, the larger the gas production will be. When the fracture conductivity adds up to 0.12 μm2·cm, the amplification of the gas production decreases significantly. The contribution of the free gas accounts for 85%～90%. So the free gas has a great contribution on the productivity. The model provides a theoretical basis for the production prediction and the optimization of the development index.
In the first part of paper, we discuss the application of the Saint-Venant's principle of the elasticity to fracture mechanics, pointing out that misusing of the principle may cause extremely large error by using sone examples. In the second part, we discuss methods for determining the shape and size of Tresca and Mises yielding surfaces and make an extension to the description of Mohr-Coulomb and Drucker-Prager yielding surfaces. We present a three-dimensional image showing the shape and size of Tresca and Mises yielding surfaces in the principal stress space to correct the errors in existing textbooks and monographs on elasto-plasticity.