| Abstract |
‘Effective medium’ uniformity within a formation is the basis for most geological reservoir flow models. With reservoir structure fixed by geological formation boundaries from drilling and/or seismic imaging, model flow properties of constituent formations are assigned values from sparse formation sampling on the assumption that spatial variations in formation flow properties ‘effectively average out’ at important scale lengths. Corollary to the effective medium assumption is that formation properties are independent of other formation properties. The two assumptions imply that spatial variations in crustal rock are effectively uncorrelated. The central limit theorem then implies that well flow productivities within a reservoir are normally distributed. In reality, however, in situ well flow productivities are conspicuously lognormally distributed in groundwater, hydrocarbon, geothermal, and fossil reservoir flow systems worldwide. The statistical fact of lognormality of reservoir flow system well productivity implies that in situ spatial variations are spatially correlated rather than uncorrelated. While statistics do not reveal how the lognormality arises from in situ spatial correlations, a great deal of hydrocarbon reservoir well-log and well-core data gives a strong physical account of how in situ spatial correlations arise in crustal rock; incidental well-log and well-core data extend the hydrocarbon reservoir spatial correlation systematics to hydrogeological, geothermal, and fossil flow systems: • In situ porosity f(x,y,z) is spatially correlated with grain-scale fracture damage at all scales from mm to km through Fourier spectral scaling law, F(k) ~ 1/k, for five decades of spatial frequency k, 1/km less than k less than 1/km; • In situ permeability ?(x,y,z) is spatially correlated with in situ porosity f(x,y,z), df ~ dlog(?), with typical cross-correlation coefficient 85%. • In situ permeability lognormality arises as ?(x,y,z) ~ exp(af(x,y,z)) with values of fracture connectivity parameter a in the range 30-50; • For empirical value range 30 less than a less than 50, the occurrence probability P(?) of flow systems of characteristic size ? scales inversely with system size, P(?) ~ 1/?, plausibly leading to the observed Fourier spectral scaling property of crustal reservoirs, F(k) ~ 1/k. These well-attested spatial correlation phenomena, associated with the ‘geocritical state’ of in situ fracture systems keyed to power-law spatial scaling F(k) ~ 1/k, have strong implications for a range of geothermal reservoir operations as discussed in accompanying three presentations: I. Existing hydrothermal flow systems can significantly reduce drilling cost overhead by mapping on-going reservoir acoustic noise to precisely locate and assess large-scale permeability pathways within the reservoir; II. Direct energy use of geothermal resources, most particularly the hundreds of abandoned low-productivity wells in geothermal fields worldwide, can in principle improve heat return by using advection rather than conduction to extract heat from the surrounding rock; III. EGS development based on stimulated and controlled well-to-well flow can proceed by emulating natural permeability processes to artificially generate high values of fracture connectivity parameter a associated with high permeability. |