In this paper, we describe efforts to create a computationally efficient model that is accurate for multiple, three dimensional fracture problems. The accuracy of a fast pseudo-3D method (Olson, 2004) for describing fracture interaction is investigated through comparing with a fully 3D displacement discontinuity method (DDM). Results demonstrate that the pseudo- 3D solution underestimates the mechanical interaction between nearby fractures. The apertures of both interior and exterior fractures given by the pseudo-3D method are larger than the fully 3D solutions. However, 3D DDM is computationally far more expensive than the pseudo-3D method because a) more elements are required to describe a fracture in three dimensions and b) the computational cost per element is higher in 3D. We show that using 1 element in the fracture height direction with the standard 3D equations is unacceptably inaccurate, but by employing an analytically based correction factor, that accuracy can be significantly improved, eliminating the need for extra elements for height-contained hydraulic fracture problems. The higher per element computation cost in 3D is largely the result of the fact that the 3D displacement discontinuity method has three unknowns (opening, strike-slip shear and dip-slip shear). Further speed advantage is gained by dictating all fractures must be vertical, which allows elimination of equation components related to the dip-slip shear. We demonstrate how this model can be applied to problems of multiple hydraulic fracture propagation in horizontal wells.


In recent years, production of tight oil and shale gas has increased exponentially in the United States. Multiple fracture treatments in horizontal wellbores are becoming a prevalent approach to economically develop unconventional reservoirs. A better understanding of multiple fracture growth is essential for accurately predicting fracture geometry. Mechanical interaction between multiple fractures, also referred to as stress shadow effects, is a critical factor controlling fracture geometry and inducing complex fracture geometry. To better model fracture interaction, an efficient and accuracy method is required.

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