Representation of high resolution rock properties on a coarser grid for hydraulic fracture modeling

This study presents a homogenization procedure for the high resolution rock properties that are used as an input data for hydraulic fracture simulations. In particular, the high resolution data for fracture toughness (both vertical and horizontal), elastic constants, leak-off coefficient, and stress are suitably upscaled for a given element size, so that the small scale variations within this element are captured implicitly. Homogenization of the elastic properties is performed assuming that each individual layer is transversely isotropic and is based on Backus averaging. Fracture energy is used to homogenize the fracture toughness and to account for the contrast of elastic properties on the fracture height containment. The average energy is used in the horizontal direction and the maximum energy is used in the vertical direction. To preserve the total force acting on the element, the weighted average is used for stress homogenization. In addition, a correction to the vertical fracture toughness that is caused by the difference between the high resolution stress and the homogenized stress is introduced. Finally, a weighted average is used to homogenize leak-off. A series of numerical examples that consider synthetic data with periodic variation of parameters is used to validate the homogenization procedure. One of the most important implications of using the homogenization is an increase of the apparent vertical fracture toughness (that represents small scale property variations), which can be of the same order or even larger than the intrinsic rock toughness. Thus, high resolution property variations have a potential to considerably alter fracture geometry and can lead to a more pronounced fracture height containment.