This is Part II of a two-part paper which reviews in depth the modeling of the propagation of large hydraulic fractures in underground rock formations. Based on experimental observations reviewed in Part I the need for models of the growth of general-shaped planar hydraulic fractures has been demonstrated. Part II contains reviews of both coupled fluid/solid three-dimensional fracture models and some more basic two and three-dimensional problems in linear elastic fracture mechanics applicable to the growth of fractures in the vicinity of in-situ discontinuities (interfaces) in rock-type and/or tectonic stress. The latter is referred to as the vertical growth problem since hydraulic fractures are quite often oriented vertically with respect to horizontal layering or stratification. The state of current research in both overall modeling and basic vertical growth studies is assessed and recommendations for future research are made.
This is Part I of a two-part paper which reviews in depth the literature on the modeling of the propagation of large hydraulic fractures in underground rock formations. Part I presents a general formulation of the problem, its geometry and only the most fundamental and unrestrictive physical assumptions. The two basic two-dimensional models of constant height (rectangular) fractures which formed the core of modeling efforts from 1960 through the late 1970’s are discussed in detail followed by a brief review of the effects of fluid diffusion in the fractured medium on crack propagation. The recent field and laboratory observations which have shown that nonrectangular fractures can occur quite often are discussed, as are their impact on the modeling effort, specifically the need for three-dimensional models of crack propagation in layered environments. Part II of the paper deals with the three-dimensional modeling efforts and some fundamental crack and fracture mechanics problems related to the vertical growth of a hydraulic fracture.
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