| Abstract |
Population statistics of in situ permeability, trace element abundance, and ore grade data typically range from normal to long-tailed/lognormal distributions. A range of permeability statistics is simply expressed by ê = ê0 exp(á(ö-ö0)), ê = permeability, ö = porosity (empirically normally distributed), with parameter á ratioing the standard deviation of logê to the standard deviation of ö. For á small, permeability is normally distributed in accordance with ö; for á large, permeability is manifestly long-tailed/lognormal, logê ~ áö. Relation by ê = ê0 exp(á(ö-ö0)) derives from extensive well-log and well-core data. Well-log power-spectra scale inversely with spatial frequency, S(k) ~ 1/k over five decades ~1/km < k < ~1/cm, characterizing long-range spatially-correlated in situ grain-scale-density fluctuations. While grain-scale fracture densities are normally distributed, fracture-connectivity ranges from normal (low levels of connectivity) to lognormal (high levels of connectivity). Fracture connectivity ranges are attested by well-core poroperm data relating fluctuations in porosity ö to fluctuations in permeability ê, ä öj ~ älogêj, j = 1….N, for äöj and älogêj = zero-mean/unit-variance fluctuation sequences of well-core porosity and log(permeability). Naturally occurring fracture connectivity ranges in the crust thus explain the normal-to-lognormal range of statistical descriptions of well-core permeability, trace element abundance, and ore grade data. Expression ê = ê0 exp(á(ö-ö0)) implies that for fixed porosity distribution ö increased permeability is associated with increased fracture connectivity of grain-scale fractures. Finite shear strain in a crustal volume inducing new grain-scale defects in association with existing grain-scale fracture porosity hence can create greater permeability through greater fracture connectivity. Naturally occurring finite-strain injection can explain the range of fracture-connectivity observed in normal-to-lognormal distributions for well-core permeability, trace element abundance, and ore body grades, from which we may infer that permeability enhancement for EGS heat-exchange volumes can be achieved through properly designed strain-damage-inducing wellbore pressurization. |