The New York Academy of Sciences, New York, 10007-217, USA
Philos Trans A Math Phys Eng Sci. 2015 Mar 28;373(2038). doi: 10.1098/rsta.2014.0119.
By way of introduction, the general invariant integral (GI) based on the energy conservation law is presented, with mention of cosmic, gravitational, mass, elastic, thermal and electromagnetic energy of matter application to demonstrate the approach, including Coulomb's Law generalized for moving electric charges, Newton's Law generalized for coupled gravitational/cosmic field, the new Archimedes' Law accounting for gravitational and surface energy, and others. Then using this approach the temperature track behind a moving crack is found, and the coupling of elastic and thermal energies is set up in fracturing. For porous materials saturated with a fluid or gas, the notion of binary continuum is used to introduce the corresponding GIs. As applied to the horizontal drilling and fracturing of boreholes, the field of pressure and flow rate as well as the fluid output from both a horizontal borehole and a fracture are derived in the fluid extraction regime. The theory of fracking in shale gas reservoirs is suggested for three basic regimes of the drill mud permeation, with calculating the shape and volume of the local region of the multiply fractured rock in terms of the pressures of rock, drill mud and shale gas.
作为介绍，本文提出了基于能量守恒定律的广义不变积分（GI），并提及宇宙、引力、质量、弹性、热和电磁物质能的应用，以展示该方法，包括广义化的库仑定律用于运动电荷、广义化的牛顿定律用于引力/宇宙场的耦合、考虑引力和表面能的新阿基米德定律等。然后，利用该方法找到了运动裂缝后的温度轨迹，并建立了断裂过程中弹性和热能的耦合。对于充满流体或气体的多孔材料，使用二元连续体的概念来引入相应的 GI。应用于水平钻井和井眼压裂，在采油阶段导出了压力和流速以及水平井和裂缝的流体产量领域。提出了页岩气储层压裂的理论，针对钻井泥浆渗透的三个基本阶段，计算了多裂缝岩石局部区域的形状和体积，涉及岩石、钻井泥浆和页岩气的压力。
