论文标题
液压骨折
Hydraulic Fracture
论文作者
论文摘要
我们考虑了格里菲斯（Griffith）对破裂的分析的一种变化，该分析模拟了氢反骨的过程，其中被迫进入裂缝的流体会升高流体压力，直到裂纹开始生长。与格里菲斯（Griffith）不同，在这种分析中，随着氢铁的生长，流体压力下降。我们发现骨折的生长取决于流体和断裂的符合性的比率，这是一个非二维参数，称为$α_0$。发现启动氢铁所需的压力与格里菲斯（Griffith）得出的压力相同。一旦骨折启动，对于模型参数的相对较低的值$α_0$（$α_0\ leq 0.2 $），裂缝自发地向新的半径延伸，取决于$α_0$的值。对于$α_0\ leq 0.2 $，需要进一步的流体注入才能增加自发生长停止后的断裂半径。对于$α_0> 0.2 $每次骨折生长增量的情况，需要注入更多的流体。对于$α_0= 0 $的极端情况，我们的结果与Griffith的结果相同，即，一旦启动的裂缝就会生长而无限。
We consider a variation of Griffith's analysis of rupture, one which simulates the process of hydrofracturing, where fluid forced into a crack raises the fluid pressure until the crack begins to grow. Unlike that of Griffith, in this analysis fluid pressure drops as a hydrofracture grows. We find that growth of the fracture depends on the ratio of the compliances of the fluid and the fracture, a non-dimensional parameter called $α_0$ here. The pressure needed to initiate a hydrofracture is found to be the same as that derived by Griffith. Once a fracture initiates, for relatively low values of the model parameter $α_0$ ($α_0 \leq 0.2$) the fracture advances spontaneously to a new radius which depends on the value of $α_0$. For $α_0 \leq 0.2$ further fluid injection is required to increase the fracture radius after spontaneous growth stops. For the case where $α_0 > 0.2$ each increment of fracture growth requires injection of more fluid. For the extreme case where $α_0 = 0$ our results are the same as Griffith's, i.e., a fracture once initiated grows without limit.
