(186a) A Minimalist Model for Rapid Simulation Enabling Optimization of the Uniformity of Multiple Simultaneous Hydraulic Fracture Growth

Hydraulic fracturing is vital for stimulating production of oil and gas, especially from low permeability reservoirs. There has been an increasing drive to optimize hydraulic fracturing treatments. One of the senses in which there is a growing desire for optimization is to maximize the uniformity of the stimulation obtained when attempting to simultaneously generate multiple hydraulic fractures growing from several entry points distributed along a horizontal. Simulations show that maximizing uniformity can be equivalent to maximizing the surface area generated by stimulation which, in turn, is expected to maximize recovery. Hence, a typical desire is to choose the controllable parameters (spacing between fractures, fluid viscosity and pumping rate, etc.) to generate a maximally-uniform hydraulic fracture growth pattern. However, a pre-requisite to optimization is a forward model that both captures the relevant physical behaviors and that executes rapidly enough to be called upon hundreds or thousands of times by an optimization scheme. Fully coupled models can take days or even weeks for a single simulation, hence optimization is often impractical or impossible with current numerical models.

Motivated, then, by the need for rapidly computing models, we present a minimalist approach for modeling simultaneous growth of multiple, radially-symmetric hydraulic fractures. Our approach leads to a drastic reduction in simulation time wherein simulations that take 1 week to solve with a fully coupled simulator can be simulated in seconds to minutes. This reduced model nonetheless maintains sufficient fidelity to track even complex dynamics of interacting hydraulic fracture growth that are predicted by a fully coupled simulator that is used for benchmarking purposes. The first key to the minimalist model is to avoid the need to mesh the hydraulic fractures or the domain around them through a judicious choice of functional approximation of the internal fluid pressure. The second key is to make use of a global energy balance relationship to enforce partitioning of the fluid among the multiple fractures in a manner compatible with energy minimization principles. The simulator is then used to demonstrate how optimization can substantially increase the predicted uniformity and generated surface area associated with stimulation of a given interval of a horizontal well at different stage lengths, entry point locations, injection rates, and fracturing times.