Conditional Simulation of Reservoir Heterogeneity With Fractals

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Abstract
Summary: The displacement efficiency of fluids injected into heterogeneous formations depends on the nature of reservoir-property variations and their spatial correlations. Conditional simulation is a geostatistical technique for creating property distributions, with any desired resolution, that have a prescribed spatial correlation structure and that match measured data at their sampling locations. Conditional simulations of reservoir heterogeneity can be used to address the two major issues in characterizing reservoirs for performance modeling: scaling of flow processes and properties and dealing with the uncertainty resulting from missing information in reservoir descriptions. The correlation structure emphasized in this study is a fractal model. Examples of conditional simulations of areal distributions and vertical cross sections of properties are presented. Simulations of fluid flow through different realizations of the simulated geology are compared with each other and with simulations of fluid flow through more homogeneous distributions derived by lumping parameters into discrete flow units or by smoothly interpolating well-log data. Results show that flow predictions in conditional simulations of the geology have greater fluid channeling, with earlier breakthrough of the injected fluids and less complete sweep of the formation. Flow simulations in multiple realizations of the heterogeneous geology provide a probability distribution of reservoir performance that may be used to evaluate the risk associated with a project caused by incomplete sampling of the reservoir-property distribution.