title: Loopless nontrapping invasion-percolation model for fracking.
abstract: 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 nontrapping 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 two-dimensional 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.
authors.affiliation: Department of Physics, One Shields Ave., University of California, Davis, California 95616, USA.
authors.forename: J Quinn
authors.initials: JQ
authors.lastname: Norris
authors.affiliation: Department of Geology, One Shields Ave., University of California, Davis, California 95616, USA.
authors.forename: Donald L
authors.initials: DL
authors.lastname: Turcotte
authors.affiliation: Department of Physics, One Shields Ave., University of California, Davis, California 95616, USA and Department of Geology, One Shields Ave., University of California, Davis, California 95616, USA and Santa Fe Institute, Santa Fe, New Mexico 87501, USA.
authors.forename: John B
authors.initials: JB
authors.lastname: Rundle