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.

Fluid Flow and Heat Transport Computation for Power-Law Scaling Poroperm Media

“…The impact on fluid flow of spatially correlated porosity distributions in crustal volumes emerges from considering well-core poroperm systematics. Well-core poroperm sequences worldwide [11,15] show that changes in the logarithm of core permeability closely track spatial changes in core porosity ,…”

“…It was not understood at the time and remained overlooked a century later (e.g., [4][5][6][7][8]) that unconsolidated sands with little or no internal structure are a faulty model for poroperm properties of subsurface clastic rock. An array of present-day well-log, well-core, and well-production evidence indicates that the process of sediment consolidation imprints on sedimentary crustal formations a set of scale-independent random spatial correlations that control 2 Geofluids formation permeability at all scales [9][10][11][12][13][14][15][16]. Of particular significance is the existence of through-going fluid flow paths at the largest spatial correlation scales.…”

Prospects for Assessing Enhanced Geothermal System (EGS) Basement Rock Flow Stimulation by Wellbore Temperature Data

“…Key features of rock granularity emerge from considering the empirical spatial fluctuation relation between well-core porosity and well-core permeability, δφ ∝ δlog(κ) [5,6,[14][15][16][17]. …”

“…(i) Well-log spatial fluctuation power S(k) that scales inversely with spatial frequency k, S(k)~k β , β~1.2 ± 0.1, over five decades of scale length,~1/km < k <~1/cm, recorded at 1-9 km depths in a wide range of geological settings [9][10][11][12][13]; (ii) Well-core spatial fluctuation sequence correlation between porosity φ and the logarithm of permeability κ, δφ ∝ δlog(κ), recorded at numerous oil/gas field reservoirs and for selected metamorphic well core [5,6,[14][15][16][17]; (iii) Well-productivity lognormality due to spatially correlated porosity, κ ∝ exp(αφ), with 20 < α < 40 in conventional reservoir rock with normally distributed porosity 0.1 < φ < 0.3, and 300 < α < 700 in metamorphic rock with normally distributed porosity φ~0.01 [5,6,[18][19][20][21].…”

Seismic‐Wave Propagation in Shallow Layers at the GONAF‐Tuzla Site, Istanbul, Turkey

“…Spectra of well-log sequences usually follow a power-law scaling of k −α , with spatial frequency k and α ≈ 1. This rule is irrespective of rock type or observation scale (e.g., Shiomi et al, 1997;Leary and Al-Kindy, 2002). The α value of the Tuzla P-wave log is 1.01, a typical value for fractured rock, whereas the value for the S-wave log is 0.28.…”