Coupling EGS Crustal Seismicity to Ambient Crustal Permeability – the Power-law Spatial Correlation Function Γmeq(r) ~ 1/r^1/2 for Stimulation Microseismicity

Abstract

Direct association of induced-seismicity with crustal fluid flow properties has long been assumed, but for a variety of reasons it has been difficult to define the association using subsurface measurements. We show here that a pervasive rock-fluid interaction is naturally expressed in terms of a critically stressed brittle crust exhibiting power-law scaling distributions of poroperm properties, and that this rock-fluid interaction gives rise to a power-law scaling spatial correlation relation for fluid-injection-induced microearthquake event locations. In mathematical terms, Enhanced/Engineered Geothermal System (EGS) stimulated induced-seismicity multi-scale clustering at 6km depth in basement rock is described by a two-point spatial correlation function, Γmeq(r) ~ 1/r^1/2, that can be derived from two widely attested empirical poroperm relations. These empirical relations are (i) power-law spectral scaling of crustal porosity well-log sequences φ(:), Sφ(k) ~ 1/k over five decades of scale length 1/km less than k less than 1/cm; and (ii) well-core evidence for permeability distributions given by κ(:) ~ exp(αφ(:)), where empirical parameter α has values such that the mean exponent value is tightly bounded, 3 less than mean(αφ) less than 4, across the two decades of mean porosity range 0.003 less than φ less than 0.3 ranging from deep basement crystalline rock to standard crustal reservoir rock. The observed spatial correlation function for EGS induced seismicity Γmeq(r) ~ 1/r^1/2 is a numerical result related to the Wiener-Khinchin theorem applied to wide-sense stationary randomly fluctuating media, P(k) ~ ∫exp(ikr)Γ(r)dr. More particularly, numerical simulation of 3D permeability volumes can be generated for the complete range porosity spatial correlation Pφ(k) ~ 1/k^m from m ~ 0 for low spatial correlation (white or Gaussian) spatial noise to m ~ 2 for high spatial correlation (red or Brownian) spatial noise. The two-point spatial correlation functions Γ(r) ~ 1/r^p computed across the 0 less than m less than 2 sequence of simulation permeability volumes indicate that exponent p ~ ½ occurs for porosity spatial correlation scaling exponent m ~ 1, the value seen universally in crustal well-logs for deep basement rock to standard crustal reservoir rock, 0.003 less than φ less than 0.3. The observed correlation property Γmeq(r) ~ 1/r^1/2 for EGS basement rock induced seismicity is a statistical indication that stimulation slip events occur in close spatial association with the ability of fluid to flow within a crustal volume. A close spatial association of naturally occurring fluid flow pathways with low-level energy seismic release has been extensively observed in shale formations undergoing frack-stimulation. There is a logical inference that EGS-induced seismicity observed at close range by 3C seismic sensors in stimulation wellbores can map the flow structure of an EGS doublet, thus constituting a precision tool by which to monitor and control the mechanics of EGS stimulation.