Optimization of simultaneously propagating multiple fractures in hydraulic fracturing to achieve uniform growth using data-based model reduction

In multi-stage hydraulic fracturing treatments, simultaneously propagating multiple fractures with close spacing often induce non-uniform fracture development due to stress-shadow effects, resulting in one or two dominant fractures due to the uneven distribution of fracturing fluids. Motivated by this, first, we present a dynamic model of hydraulic fractures to describe stress-shadow effects in simultaneously propagating multiple fractures. Second, we develop a new model order-reduction technique for simultaneously propagating multiple fractures by integrating the analytical models to calculate the pressure drop due to perforation friction and wellbore friction, and a data-based reduced-order model (ROM) developed using the data generated from the high-fidelity process model to describe the pressure drop along the fractures due to stress-shadow effects. Lastly, we propose a model-based design technique by utilizing the integrated ROM and the limited entry design technique to compute the flow rate of fracturing fluids and the perforation conditions which will promote equal distribution of fracturing fluids to achieve uniform growth of multiple fractures while mitigating the undesired stress-shadow effects. We present a base case with the uneven development of multiple fractures and demonstrate that the proposed design technique is able to outperform the base case with respect to achieving uniform fracture growth, by explicitly handling stress-shadow effects.