Theories of fluid flow in heterogeneous porous media show that their transport properties are determined by the structure of spatial correlations in the permeability distribution. When the range of these correlations is comparable to or larger than the fluid flow path, solutions of the convective-dispersion equation with an effective dispersivity augmented to account for the dispersive effects of reservoir heterogeneity do not provide accurate predictions of the transport characteristics of the medium. Measurements of property distributions in sedimentary environments show a fractal character with long range correlations. Evaluation of the influence of fractal distributions of permeability on oil recovery process performance requires simulation on a distributed field of properties with a correlation structure matching that in field measurements. The geometric properties and spatial correlation structure of fractal distributions are discussed and methods for measuring the fractal character of field data and synthesizing fields with a similar correlation structure are reviewed.

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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 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 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 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. Introduction The two major issues that need to be addressed in characterizing reservoirs for performance modeling are process and flow-property scale averaging and dealing with incomplete information and uncertainty in the reservoir description. The first arises from the vast range of scales over which reservoir processes operate and flow properties must be defined. The second stems from the relatively properties must be defined. The second stems from the relatively small volume of any subterranean reservoir that actually is sampled by cored or logged wells and the intrinsic variability of geologic properties. properties. Reservoir-simulation studies address a variety of objectives, some of which may be incompatible. On the one hand, we are interested in modeling the global energy balances of reservoirs to understand the importance of aquifer influx, gas-cap expansion, pressure decline, and the expulsion of solution gas below the bubblepoint. Models that address these objectives must treat the reservoir as a whole. Given the size of most fields and the size limits of currently available computer resources, these models typically have gridblocks that are measured in tens or hundreds of feet, and often have only a few cells between adjacent wells. On the other hand, we are interested in accurately modeling flow between wells to understand how the variable distribution of reservoir flow properties affects the displacement efficiency and volumetric sweep of fluids we inject. Models that address these questions require the resolution of interwell property variations on a scale where the rock-property variations are sufficiently resolved to reproduce the effect of permeability variations on fluid-displacement fronts. Although production data used for comparison generally are integrated along a wellbore, high resolution is often required to produce simulation results that match individual fluid cuts. Given the limits of current computers, studies at this level of detail are necessarily limited to the study of flow between individual well pairs, or at most, a few well patterns. In any simulation study, it pairs, or at most, a few well patterns. In any simulation study, it is important to understand the study objectives, the modeling scale appropriate to addressing those objectives, and how the flow parameters used in the simulation are related to the resolution of the parameters used in the simulation are related to the resolution of the model and the variability of properties at finer scales. In this paper we review the problem of scale averaging of flow properties and process performance and give examples showing the properties and process performance and give examples showing the limits of using measured rock properties and address and illustrate the problem of uncertainty resulting from incomplete information in reservoir descriptions. We argue that the geostatistical approach to reservoir characterization and the use of conditional simulations of reservoir heterogeneity provide a systematic way of dealing with these difficult problems. We begin with a review of the literature and the important issues involved in modeling fluid flows and oil-recovery-process performance in heterogeneous reservoirs.