Reducing Uncertainty in Geostatistical Description with Well-Testing Pressure Data
Albert C. Reynolds, Nanqun He, Dean S. Oliver, 1999. "Reducing Uncertainty in Geostatistical Description with Well-Testing Pressure Data", Reservoir Characterization—Recent Advances, Richard A. Schatzinger, John F. Jordan
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Geostatistics has proven to be an effective tool for generating realizations of reservoir properties conditioned to static data (for example, core and log data, and geologic knowledge); however, in situations when data are not closely spaced in the lateral directions, there will be significant variability in reservoir descriptions generated by geostatistical simulation (that is, significant uncertainty in the reservoir descriptions). Procedures based on inverse problem theory were previously presented for generating reservoir descriptions (rock property fields) conditioned to pressure data and to geostatistical information represented by prior means and variograms for log-permeability and porosity. Although it has been shown that incorporation of pressure data reduces the uncertainty below the level contained in the geostatistical model based only on static information (the prior model), these previous results did not explicitly account for uncertainties in the prior means and the parameters defining the variogram.
This paper specifically investigates how pressure data can help detect errors in the prior means. If errors in the prior means are large and are not taken into account, realizations conditioned to pressure data represent an incorrect sampling of the a posteriori probability density function for the rock properties; however, if the uncertainty in the prior mean is properly incorporated, realistic realizations of the rock property fields are obtained.