Reserves Uncertainty Calculation Accounting for Parameter Uncertainty
Authors: Babak O. , Deutsch C.V. 
Published: March 2010

Abstract
An important goal of geostatistical modelling is to assess output uncertainty after processing realizations through a transfer function; in particular, to assess the uncertainty in the reserves. The decisions regarding stationarity and a modelling method are critical for obtaining reasonable results. Uncertainty in reserves is affected by the amount of local data and uncertainty in the modelling parameters. Oftentimes, the uncertainty in the input parameters, such as mean, univariate distribution and variogram, to the geostatistical model is ignored. As result, global uncertainty is underestimated. The understatement of uncertainty is especially significant for large reservoirs with sparse well control/local fluctuations above and below average 'cancel out' and the realizations imply a very small uncertainty. Accounting for uncertainty in the parameters, especially the mean, is very important for a realistic assessment of uncertainty. The objective of this paper is to review methodologies developed for quantification of parameter uncertainty and describe guidelines for incorporation of parameter uncertainty in the reserves calculation. The importance of parameter uncertainty in the assessment of the reserves is also documented.

Introduction
An important task in reservoir management is the quantification of resource and reserve uncertainty. This uncertainty is valuable decision support information for many management decisions. Uncertainty in both local and global reservoir properties is of interest. Local uncertainty refers to rock properties at specific locations that we could potentially drill in the future. Local uncertainty can be checked by cross validation or new drilling; the proportions of true values falling within specified probability intervals are checked against the width of the intervals. Most often, fair local uncertainty predictions can be obtained by selecting appropriate geostatistical parameters. Global uncertainty refers to a calculated statistic that involves many locations simultaneously. Checking global uncertainty is more difficult. Geostatistical realizations are used increasingly for uncertainty quantification in this case. Common practice for uncertainty assessment consists of constructing alternative realizations of the spatially distributed variables of interest. These realizations are then passed through the transfer function to calculate uncertainty in reserves.
In most cases, geostatistical realizations are created with the same input parameters. The parameters are the input histogram and the variograms or the training images that contain the spatial features believed to apply to the reservoir under consideration. The experimental statistics calculated from the realizations will not be the same as the input parameters because of statistical fluctuations. These statistical fluctuations, called non-ergodic fluctuations, are solely due to the finite non-ergodic size of the domain under consideration. There would be no global uncertainty if we were considering a very large domain, since high and low areas would average out. Practitioners know that uncertainty is understated when uncertainty in the parameters is not considered. The understatement of uncertainty is especially true for large reservoirs with sparse well control/local fluctuations above and below average 'cancel out' and the realizations imply a very small uncertainty. Accounting for uncertainty in the parameters is very important for a realistic assessment of uncertainty.