Power-law scaling of spatially correlated porosity and log(permeability) sequences from north-central North Sea Brae oilfield well core

Abstract

Summary The spatial cross-correlation and power spectra of porosity and log(permeability) sequences are analysed for a total of 750 m of reservoir rock drill-core from four vertical wells in the Brae Formation, an important coarse-grained clastic North Sea hydrocarbon reservoir rock. The well core sequences are 80 ± 4 per cent cross-correlated at zero lag and have power-law-scaling spatial power spectra S(k)∝1/kβ, β≈ 1 ± 0.4, for spatial frequencies 5 km−1 < k < 3000 km−1. The strong spatial cross-correlation of porosity and log(permeability) and the systematic power-law scaling of log(permeability) spatial fluctuation spectra fit into a broad physical context of (1) the 1/k spectral scaling observed in several hundred well logs of sedimentary and crystalline rock recorded world-wide; (2) the 1/f spectral scaling of temporal sequences in a wide range of physical systems; and (3) analogy with power-law-scaling spatial fluctuation spectra in a wide range of critical-state thermodynamic systems. In this physical context, the spatial fluctuations of log(permeability) of clastic reservoir rock are interpreted as due to long-range correlated random fracture-permeability networks in a fluid-saturated granular medium where the range ξ of spatial correlation is effectively infinite. Fracture-permeability spatial fluctuations with long-range correlations and 1/k-scaling spectra have practical implications for geofluid reservoir management. Inadequate models of reservoir flow structure are widely attributed to uncertainty in fault and fracture location and connectivity. As a general phenomenon, spatial configurations of large-amplitude, long-range spatially correlated random fluctuations are unpredictable from the statistics of small-scale samples. The observed 1/k spectral scaling of porosity and log(permeability) distributions thus implies that large-scale, large-amplitude fracture-related flow heterogeneity (1) can determine the drainage pattern of crustal reservoirs but (2) cannot be accurately predicted using statistical techniques based on small-scale reservoir samples. Incompatibility of the physics of reservoir heterogeneity and the statistical approaches to reservoir models can thus explain the persistent under-performance of stochastic reservoir models. Accurate reservoir flow models can, however, be determined by direct observation of fluid flow at the reservoir scale. Recent advances in seismic time-lapse reservoir-fluid monitoring may provide data for significantly more effective management of hydrocarbon reservoirs, waste burial sites, mining works and groundwater aquifers.