Analysis of the power input needed to propagate multiple hydraulic fractures

Emerging applications in unconventional gas production, geothermal power generation, and mining are driving an intensifying focus on the effective creation of arrays of hydraulic fractures from a single wellbore. Relative to creating each of the hydraulic fractures in the array individually, it is often cost effective to simultaneously create more than one hydraulic fracture. However, it remains unclear how the energy requirements for hydraulic fracture growth depend on the fracture geometry and on the number of hydraulic fractures in the array, and this question is foundational for the development of models aimed at predicting conditions under which multiple hydraulic fractures will grow simultaneously and conditions which will favor localization to fewer, or in some cases, a single dominant hydraulic fracture. As a first step to addressing this question, this paper presents an energy balance for an array of multiple, parallel hydraulic fractures for three geometries, namely plane strain, radially-symmetric, and blade-like (PKN) geometries. Both geometry and coupled fluid flow are found to have a profound impact, and two cases were found for which an array of multiple hydraulic fractures requires less input power for propagation than is required for a single hydraulic fracture. The first is radially symmetric hydraulic fractures under viscosity dominated conditions prior to the onset of stress interactions between neighboring hydraulic fractures. The second is the viscosity dominated PKN case, wherein the minimum input power when the hydraulic fracture length is much greater than both the fracture height and spacing occurs when the spacing is around 2.5 times the fracture height. Hence, in the PKN case, this analysis provides the first indication that a natural, or energetically optimal, spacing exists when multiple height constrained hydraulic fractures are simultaneously propagated.