THE DYNAMICS OF VISCOUS COMPRESSIBLE FLUID IN A FRACTURE
THE DYNAMICS OF VISCOUS COMPRESSIBLE FLUID IN A FRACTURE
复制标题
裂缝中粘性可压缩流体的动力学
作者：
J. Dvorkin;G. Mavko;A. Nur
我们解决了含有支撑剂的任意形状裂缝中的流体动力学问题。骨折嵌在绝对坚硬的固体中。流体流动是由可渗透的裂缝壁的正常简谐振荡引起的，允许流体渗入周围的地层。振荡的幅度可以描述为沿裂缝的空间坐标的函数。裂缝内的流体流动用毕奥对达西定律的修正来描述，其中既包括惯性项，也包括滤失项。裂缝内部的过滤可能会极大地改变其声学特性。只有当支撑剂的渗透率极高时，才能观察到沿充满支撑剂的裂缝长度方向的声波共振；否则，裂缝中流体的过滤会抑制共振。如果观察到共振，其周期不同于无内滤的骨折。裂缝中的表观声速低于声速。
We solve a problem of fluid dynamics in an arbitrarily shaped fracture containing proppant. The fracture is embedded in an absolutely rigid solid. The fluid flow is induced by normal harmonic oscillations of fracture walls that are permeable, allowing the fluid to filtrate into the surrounding formation. The amplitude of oscillations can be described as a function of a spatial coordinate along the fracture. Fluid flow inside the fracture is described by Biot’s modification of Darcy’s law that includes both inertia and filtration terms. Filtration inside the fracture may drastically change its acoustic characteristics. The acoustic resonance along the length of the fracture filled with proppant can be observed only if the permeability of the proppant is extremely high; otherwise filtration of the fluid in the fracture dampens the resonance. If the resonance is observed, its period differs from that in a fracture without internal filtration. The apparent acoustic velocity in the fracture is lower than sound...