Introduction - Faults are an important aspect of many reservoirs, particularly in the way that they control the flow of hydrocarbons during trap-filling or production. Any attempt at characterising a faulted reservoir must address not only the properties of the reservoir rocks and of the fault surfaces but also the distribution of faults through the rock volume. Ideally, we should be able to characterise the fault population, i.e. how many faults are there of different sizes, what are their geometries, azimuths and locations, and what is their effect on the hydraulic properties of the reservoir ?
However, faults in the sub-surface are typically sampled at two widely different scales:
(i) Seismic data provide information on faults whose throws are above the limit of seismic resolution (e.g. 20m). (ii) Well data provide spatially-isolated information on the fractures encountered in core material or imaged by logging tools (displacements typically millimetres-centimetres).
Faults at an intermediate scale (e.g. 1-20 metres displacement), which are unseen on seismic data and poorly-sampled in wells, can be of great importance in hydrocarbon production. Since these small faults cannot be directly seen, how can their effects be incorporated in models of reservoir heterogeneity, or in assessing risk in horizontal drilling? Can we make quantitative predictions of the numbers of small faults below seismic resolution? This paper presents a methodology for making such predictions, based on the demonstrated fractal nature of fault systems (e.g. King 1983, Scholz & Mandelbrot 1989).
Conclusions - (i) Seismic reflection data allow only the larger faults to be mapped; well data generally provide information on the very small-scale structures. Intermediate-size faults are ÔinaccessibleÕ.
(ii) Populations of fault displacements and lengths are characterised by power law distributions. Faults are therefore fractal, and possess the same geometric properties across a wide range of scales.
(iii)Extrapolation of fault populations to millimetre scale shows good agreement with fracture densities observed in well cores. Therefore the fault population follows the same power law over ca 6 orders of magnitude of fault size.
(iv) A prediction of the fault population below the limit of seismic
resolution is viable, since fault populations are systematic. Such predictions
can be used to help assess the degree of impairment or enhancement of fluid
flow through a faulted reservoir.
First Break 10, 449-460, 1992.