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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