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.

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