Accounting for Parameter Uncertainty in Reservoir Uncertainty Assessment: The Conditional Finite-Domain Approach

摘要

An important aim of modern geostatistical modeling is to quantify uncertainty in geological systems. Geostatistical modeling requires many input parameters. The input univariate distribution or histogram is perhaps the most important. A new method for assessing uncertainty in the histogram, particularly uncertainty in the mean, is presented. This method, referred to as the conditional finite-domain (CFD) approach, accounts for the size of the domain and the local conditioning data. It is a stochastic approach based on a multivariate Gaussian distribution. The CFD approach is shown to be convergent, design independent, and parameterization invariant. The performance of the CFD approach is illustrated in a case study focusing on the impact of the number of data and the range of correlation on the limiting uncertainty in the parameters. The spatial bootstrap method and CFD approach are compared. As the number of data increases, uncertainty in the sample mean decreases in both the spatial bootstrap and the CFD. Contrary to spatial bootstrap, uncertainty in the sample mean in the CFD approach decreases as the range of correlation increases. This is a direct result of the conditioning data being more correlated to unsampled locations in the finite domain. The sensitivity of the limiting uncertainty relative to the variogram and the variable limits are also discussed.