Simulation of Subseismic Faults Using Fractal and Multifractal Geometry

Abstract

SPE Member Abstract An important problem of reservoir description is the prediction of faults that are not detected by seismic techniques. Such faults can disrupt flow unit continuity or may be potential targets for horizontal drilling. One approach to describing their distribution is stochastic modeling. This paper describes a technique to simulate the number, length, orientation, and spatial distribution of subseismic faults using fractal and multifractal concepts. The approach exploits the fractal nature of faults to determine their true length distribution. Faults are characterized by a multifractal spectrum rather than just a single fractal dimension. The multifractal distribution of mapped seismic faults forms the basis for the areal allocation of stochastic faults. One use of the stochastic fault simulations is to predict the probability of intersecting a fault as a function of well length. Introduction Natural faults can represent an important component of reservoir heterogeneity. They can disrupt flow unit continuity or may be potential targets for horizontal drilling. Horizontal drilling applications arise in faulted reservoirs because horizontal wells have a higher probability of intersecting a greater number of vertical faults/fractures compared to vertical boreholes. The fundamental problem in exploiting this approach is determining, in a predictable fashion, the location and orientation of permeable faults or fractures. The amount of vertical fault displacement is often a limiting factor in seismic detection of faults. The inability to resolve minor displacement faults leads to an underestimate of the actual number of shorter length faults. A stochastic modeling approach can be used to simulate the subseismic fault distribution. Beginning with a 3-D seismic dataset from an oilfield, fractal and multifractal approaches are used to simulate the number, length, and spatial distribution of subseismic faults. The resulting stochastic fault distribution is used to determine the probability of a horizontal well intersecting a fault as a function of well length in the field. The Seismic Dataset A seismic fault map is the main input for simulating subseismic faults. In this study, faults interpreted from a reservoir 3-D seismic survey (Fig. 1) are used. This 8 square mile area contains 320 interpreted faults. P. 903^