Quantification of Conceptual and Parametric Uncertainties in Fractured Reservoir Models
Paul R. La Pointe, Aaron Fox, 2011. "Quantification of Conceptual and Parametric Uncertainties in Fractured Reservoir Models", Uncertainty Analysis and Reservoir Modeling: Developing and Managing Assets in an Uncertain World, Y. Zee Ma, Paul R. La Pointe
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The characterization of fractured reservoirs includes complexities not found in the matrix. These differences challenge accurate and meaningful quantification of uncertainty, and require different approaches than are commonly used for the matrix component.
The degree of fracture network connectivity at the scale of tens or hundreds of meters significantly impacts the reservoir-scale flow and transport properties. Uncertainties that impact fracture network connectivity significantly affect hydraulic and geomechanical performance, and are thus of primary importance in uncertainty characterization. Fracture network connectivity includes the combined effects of fracture intensity, fracture size, and fracture orientation, and so uncertainties in these parameters lead to uncertainty in connectivity. The aperture, intrinsic permeability, and geomechanical properties of the fractures also impact hydromechanical response.
The approach to characterizing uncertainty in fractured reservoir models depends upon the intended use of the characterization. Four approaches are described in detail: (1) ranking realization in terms of percolation properties to select median and bounding cases; (2) quantifying fracture intensity uncertainty arising from parametric uncertainty through Jackknife procedures, and using the results for fracture model validation; (3) selecting the best geological conceptual scenarios from among multiple alternative conceptual models through nonparametric ANOVA methods; and (4) quantifying the impact of these conceptual uncertainties and propagating them into downstream models through tensor-projection methods to quantify larger scale mechanical and hydraulic response. All of these approaches are illustrated using fractured rock case studies.
Fractured reservoir models quantify the geometry and fluid-flow properties of the natural joints and faults in a static reservoir model or their upscaled property values in a dynamic model. Many aspects of a natural fracture system exist that make them more complex to describe than the matrix. Matrix porosity, permeability, saturation, and other properties are scalar parameters. The mathematical methods used to interpolate them are mostly continuum mathematical formulations that presume that the parameters have point supports or a support much smaller than the geocellular discretization. Geostatistical algorithms commonly used for matrix interpolation make these assumptions. Fractures, however, are finite objects that cannot be reduced to a point support and occur over a large variety of scales (Barton, 1995). Fractures also have vector properties, such as orientation, in addition to scalar values, and many highly coupled parameters such as fracture size, aperture, and intrinsic permeability. Because of these mathematical aspects of natural fractures and the networks they form, the types of uncertainties and their importance in a fractured reservoir differ from those in a matrix model, and consequently, require a different approach for quantifying uncertainty.