Scaling Relationships in Natural Fractures: Data, Theory, and Application

Abstract

Length frequency distributions of fractures are shown to have a power-law trend across many orders of magnitude. This allows an estimate to be made of the full number of fractures and faults existing in a reservoir over that which can be measured from core and seismic data. This relationship has been applied to reservoir studies involving the continuity of juxtaposed sands, permeability impairment, and estimating the number of fractures that a horizontal well may intersect. Many more fractures and faults exist in reservoirs than those that can he observed from seismic and core data, which have significant implications for reservoir characterisation, geomechanical properties and waterflood behaviour. Introduction There is a tendency for natural fractures in reservoirs to gain the attention of development teams only when the fractures provide permeability significantly greater than that of the matrix: usually in reservoirs which would not be commercially productive without the presence of those fractures. These reservoirs are deemed as 'naturally fractured' and are, of course, an important resource in the hydrocarbon industry. However, the somewhat loose application of this term tends to lead to the neglect of natural fractures as a component in the description of a much larger set of reservoirs. By the term 'fractures' we encompass both joints (extension fractures) and faults (all fractures whose walls have undergone shear displacements). The wider importance of natural fractures includes the following:Juxtaposition of different lithologies across faults can cause either an interruption in reservoir continuity, or enhancement due to the juxtaposition (across non-sealing faults) of depositionally isolated units.Fractures provide surfaces with an intrinsic conductivity that is almost certainly different from that of the surrounding matrix, occurring either through genesis (e.g. the cataclastic grain comminution in a granulation seam), diagenesis (i.e. mineralisation) or aperture governed by present-day effective stress. These altered surfaces can form a first-order perturbation to the permeability variations arising from depositional processes. In addition, the intrinsic conductivity of a fracture can change as stresses change in the reservoir rock during the development life of a field. There is growing evidence of the dominant influence of fractures in the lateral anisotropy of waterfloods, a process in which the reduction in stresses due to injection probably plays a significant role. The geomechanical behaviour of natural fractures during depletion may manifest itself as an influence upon compaction drive, subsidence and even casing failures. The presence of natural fractures carries particular implications when development of a reservoir with horizontal or high-angle wells is considered. The most obvious change is that high-angle wells have a greater probability than conventional wells of intersecting sub-vertical or vertical fractures. This fact has led to spectacular successes in the exploitation of reservoirs containing conductive natural fractures, for example in the Austin chalk of Texas. Additionally, the influence of natural fractures on the viability of horizontal or high-angle wells may be effective in at least two other ways:The productivity benefit of a high-angle well is very dependent upon the effective ratio of vertical to horizontal permeability. Fractures can increase or decrease this ratio.Conductive natural fractures and faults may provide pathways forextraneous water production from an underlying aquifer or gas production from a gas cap. In all these applications a knowledge of the true frequency distribution of fractures is a necessary component in a complete synthesis of the process. However, direct measurement of the distribution is hindered because reservoir fractures are observable only in the relatively limited ranges in scale of seismic and core data. We examine in this paper the concept that scaling relationships in fracture distributions enable the quantitative interpolation between the ranges of observable fracture sizes. We are concerned here primarily with spatial frequency distributions of fractures. A knowledge of the true form of these is a first step towards being able to predict the effect of fractures on fluid flow, but the subsequent steps of connectivity and conductivity are beyond the scope of this paper. REVIEW OF FRACTURE DISTRIBUTIONS The literature dealing with fractures in rock covers many disciplines and industries. Many assessments of frequency distributions of fracture lengths and spacings have been reported. The distributions have usually been given as one of log normal, negative exponential, gamma, Weibull, or occasionally power law or Pareto. P. 367

Scaling of fault attributes: A review

“…Discrete frequency distribution (Kakimi, 1980;Heffer and Bevan, 1990;and Barton and Zoback, 1992) is another approach for presenting data;…”

“…Heffer and Bevan, 1990;Scholz et al, 1993;Knott et al, 1996;Yielding et al, 1996;Odling, 1997). When compiling data from different sources, we should remember that all methods are constrained by resolution and biases and the choice of sampling method affects the distribution of data.…”

“…The two larger sample populations (grey squares and diamonds) exhibit smoother curves, but still far from the straight line of an ideal power-law distribution. This can be explained by the limited resolution of seismic data (Heffer and Bevan, 1990), in which the lengths of small faults are underestimated.…”

“…Apart from resolution, there are other factors influencing power-law distribution at small scales. The truncation effect could be due to a 2D cut through a 3D population of small faults (Heffer and Bevan, 1990) or a physical lower cut-off to the power-law size distributions (Odling, 1997;Bonnet et al, 2001).…”

The fracture criticality of crustal rocks

“…The distributions of cracks are also known to be fractal, both in sedimentary (Heffer & Bevan 1990;Yielding, Walsh & Watterson 1992) and igneous and metamorphic rocks (King 1983;Leary 1991;Leary & Abercrombie 1993). Fractal distributions of cracks have two important properties: first, cracks are scale invariant over a wide range of dimensions; and secondly, cracks tend to cluster in space.…”