Abstract - Flow is influenced by the incidence, spatial arrangement and petrophysical properties of faults. Seismically resolved faults can be incorporated discretely in flow models, but there are over four orders of magnitude of sub-seismic faults, with unknown characteristics, to be taken into account. Fault population analysis permits estimation of sub-seismic fault densities from the scaling properties of the seismically imaged faults. As the positions of sub-seismic faults cannot be predicted, it is tempting to include their influence within continuum flow properties. This paper outlines a method for calculating the continuum permeability structure of realistically faulted but lithologically homogeneous reservoirs in 2D, based on a quantitative geological description of the fault system. The assumptions and simplifications in the method are discussed with reference to (a) the uncertainties in quantifying sub-seismic populations and properties, and (b) the non-stationarity of fault system parameters.
Fault systems are described in terms of three power-law scaling relationships (maximum displacement frequency, displacement / length and displacement / thickness), a fault orientation descriptor (related to fault orientation and system connectivity), fault and matrix permeabilities and the spatial variabilities of these properties. This continuous fault system description is simplified to a discrete hierarchy at particular scale transitions on a grid. Effective permeabilities at each position are calculated analytically using an up-scaling scheme derived from numerical and theoretical modelling.
Flow through a fault system is a complex function of tortuosity and transmissibility effects at a variety of length-scales and there are no hard-and-fast rules as to which fault system variables are most influential. Many sub-seismic fault system variables can be predicted only with considerable uncertainty and small differences in these variables can have a significant effect on the calculated permeability. The proposed method is amenable to Monte Carlo simulations as it allows rapid determination of effective permeability for a range of fault system models. This feature allows quantification of the confidence with which the permeability of a system has been estimated.
In a system described by power-laws, there is no representative elementary volume and hence no rigorous effective permeability. The transformation from a continuous to a discrete scaling hierarchy, coupled with a known upper size threshold (seismic resolution), allows a representative fault system at each scale separation to be defined. This simplification is only acceptable if the distances over which the density and scaling characteristics of the fault system vary significantly are large relative to the areas needed to define both geologically and geometrically representative samples of sub-seismic faults. Although these conditions are seldom satisfied in natural systems, a continuum approximation of the effects of sub-seismic faults on permeability is of value in light of the imprecision with which the relevant sub-seismic fault system properties can be determined.
Abstract of poster presented at:
Modelling Permeable Rocks. Institute of Mathematics and its Applications Conference, Cambridge, March 1998