This paper presents asymtotic analytical and numerical solutions for two-dimensional (2-D) and three-dimensional (3-D) type hydraulic fracture geometries. The fracture propagation models investigated include: a Geertsma-Deklerk (GDK), a Perkins-Kern/Nordgren (PKN) and a 3-D type model.

Comprehensive 2-D and 3-D design formulae for power-law fracturing fluids are given for various cases of fluid loss and containment. These formulae can be used to benchmark 2-D and 3-D hydraulic fracturing simulators. Characteristics of equilibrium 3-D height growth are also discussed. Parametric studies based on the design formulae are performed to show the effect of any one variable.

Typical fracture designs are simulated for various containment and leak-off examples using each of the fracture propagation models, along with a comparison of proppant scheduling and design. The simulation studies identify and illustrate the basic characteristics and design differences of each model.

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