  Recent developments in hydraulic fracturing (fracking) have enabled the
recovery of large quantities of natural gas and oil from old, low permeability
shales. These developments include a change from low-volume, high-viscosity
fluid injection to high-volume, low-viscosity injection. The injected fluid
introduces distributed damage that provides fracture permeability for the
extraction of the gas and oil. In order to model this process, we utilize a
loopless non-trapping invasion percolation previously introduced to model
optimal polymers in a strongly disordered medium, and for determining minimum
energy spanning trees on a lattice. We performed numerical simulations on a 2D
square lattice and find significant differences from other percolation models.
Additionally, we find that the growing fracture network satisfies both
Horton-Strahler and Tokunaga network statistics. As with other invasion
percolation models, our model displays burst dynamics, in which the cluster
extends rapidly into a connected region. We introduce an alternative definition
of bursts to be a consecutive series of opened bonds whose strengths are all
below a specified value. Using this definition of bursts, we find good
agreement with a power-law frequency-area distribution. These results are
generally consistent with the observed distribution of microseismicity observed
during a high-volume frack.
