期刊
ENGINEERING FRACTURE MECHANICS
卷 254, 期 -, 页码 -出版社
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.engfracmech.2021.107905
关键词
Hydraulic fracture; Fluid lag; Two dimensional
类别
The paper discusses the trajectory and topology of hydraulic fractures in a non-dimensional evolutionary parameter space, as well as the description and parameterization of fracture configurations in specific cases, providing a method for setting approximate initial conditions for more detailed hydraulic fracture simulations.
During its lifetime, a hydraulic fracture is known to traverse a trajectory in a region of a parametric space of non-dimensional evolutionary parameters. The topology of this diagram depends upon the phenomena considered. For the specific case of a 2D-plane strain fracture propagating in an elastic solid on a straight path normal to the minimum compressive stress, with a constant rate of injection of an incompressible newtonian fluid, and without leak-off, the diagram is a triangle whose vertices are typically called O, M, and K. The non-dimensional parameters are the toughness K and remote stress T (monotonically increasing with time). At each point in the trajectory Rho(t) = (K,T)(t), the configuration of the fracture is essentially described by several non-dimensional variables, in this case the opening Omega(0) and pressure. Pi(0) at the inlet, and the length gamma. When fluid lag is considered, as in this case, a fourth variable (e.g., the fluid fraction xi(f)) can be appended to build the descriptive set Tau(0) = {Omega(0), Pi(0), gamma, xi(f)}. Various propagation regimes are observed across the MKO triangle. As the main results, we: (1) provide specific, K-dependent transition times among the propagation regimes; and (2) found that the transient evolutions of all propagating cracks with moderate values of the non-dimensional toughness (K greater than or similar to 0.3), from the OK edge to the MK edge, are contained in a thin bundle about a universal curve in the F-0-space. This result can be applied, e.g., to readily setup approximate initial conditions for more detailed hydraulic fracture propagation simulations. In addition, we developed a four-parameter family of parametrizations of the MKO triangle suitable for plotting trajectories and other loci on the triangle.
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