  Hydraulic fracturing (fracking) using high pressures and a low viscosity
fluid allow the extraction of large quantiles of oil and gas from very low
permeability shale formations. The initial production of oil and gas at depth
leads to high pressures and an extensive distribution of natural fractures
which reduce the pressures. With time these fractures heal, sealing the
remaining oil and gas in place. High volume fracking opens the healed fractures
allowing the oil and gas to flow the horizontal productions wells. We model the
injection process using invasion percolation. We utilize a 2D square lattice of
bonds to model the sealed natural fractures. The bonds are assigned random
strengths and the fluid, injected at a point, opens the weakest bond adjacent
to the growing cluster of opened bonds. Our model exhibits burst dynamics in
which the clusters extends rapidly into regions with weak bonds. We associate
these bursts with the microseismic activity generated by fracking injections. A
principal object of this paper is to study the role of anisotropic stress
distributions. Bonds in the $y$-direction are assigned higher random strengths
than bonds in the $x$-direction. We illustrate the spatial distribution of
clusters and the spatial distribution of bursts (small earthquakes) for several
degrees of anisotropy. The results are compared with observed distributions of
microseismicity in a fracking injection. Both our bursts and the observed
microseismicity satisfy Gutenberg-Richter frequency-size statistics.
