The Ghost in the Machine: Fracking in the Earth's Complex Brittle Crust

Abstract:

This paper discusses in the impact of complex rock properties on practical applications like fracking and its associated seismic emissions. A variety of borehole measurements show that the complex physical properties of the upper crust cannot be characterized by averages on any scale. Instead they appear to follow 3 empirical rule: a power law distribution in physical scales, a lognormal distribution in populations, and a direct relation between changes in porosity and log(permeability). These rules can be directly related to the presence of fluid rich and seismically active fractures – from mineral grains to fault segments. (These are the “ghosts” referred to in the title.)

In other physical systems, such behaviors arise on the boundaries of phase changes, and are studied as “critical state physics”. In analogy to the 4 phases of water, crustal rocks progress upward from a un-fractured, ductile lower crust to nearly cohesionless surface alluvium. The crust in between is in an unstable transition. It is in this layer methods such as hydrofracking operate – be they in Oil and Gas, geothermal, or mining. As a result, nothing is predictable in these systems.

Crustal models have conventionally been constructed assuming that in situ permeability and related properties are normally distributed. This approach is consistent with the use of short scale-length cores and logs to estimate properties. However, reservoir-scale flow data show that they are better fit to lognormal distributions. Such “long tail” distributions are observed for well productivity, ore vein grades, and induced seismic signals.

Outcrop and well-log data show that many rock properties also show a power-law-type variation in scale lengths. In terms of Fourier power spectra, if peaks per km is k, then their power is proportional to 1/k. The source of this variation is related to pore-space connectivity, beginning with grain-fractures. We then show that a passive seismic method, Tomographic Fracture Imaging^TM (TFI), can observe the distribution of this connectivity. Combined with TFI data, our fracture-connectivity model reveals the most significant crustal features and account for their range of passive and stimulated behaviors.