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Experimental and Numerical Modelling of Deformation and Fluid Flow |
Department of Geology & Geophysics, University of Edinburgh, Grant Institute, West Mains Road, Edinburgh EH99 3JW, UK
Borehole logs of rock-property spatial fluctuations in the metre to kilometre scale range have power-law Fourier power-spectra that scale inversely with spatial frequency to a power near unity, S(k)
1/k
. The spectral scaling is ‘universal’ in the sense that a narrow range of scaling exponents, v 
1.1 ± 0.1 for vertical wells and h 1.34 ± 0.1 for horizontal wells, describes rock density, elastic modulus, porosity and lithology fluctuation spectra of a sample of 50 well logs; for 35 vertical logs the bounds on v hold for both sedimentary and crystalline rock types. The power-law nature of rock-property fluctuation spectra are modelled as long range spatial correlations arising from short range (grain scale) uncorrelated random fluctuations. Such long range random spatial correlations occur in thermodynamic order-disorder phase transitions. Applying to rock the statistical physics of thermodynamic order-disorder transitions, rock heterogeneity observed in borehole logs formally emerges from grain-scale elastic interactions and long range spatial organization of finite strain induced grain-scale defects associated with fluid percolation. If fluid flow paths in rock are significantly influenced by long range correlated random structures, reservoir management cannot be accurately conducted from flow models constrained by small-scale sampling of the reservoir rock; macro scale measurements of site-specific long range random correlation structures are needed.
