A NEW APPROACH FOR QUANTIFYING THE IMPACT OF GEOSTATISTICAL UNCERTAINTY ON PRODUCTION FORECASTS : THE JOINT MODELING METHOD IAMG , Cancun , September 6-12 , 2001

__________________________________________________________________________ This paper presents a new approach to quantify the uncertainties which exist in reservoir description. We focus particularly on the uncertainties due to geostatistical modeling. Our approach, which relies on both experimental design theory and statistics, allows efficient and reliable production forecasts in a strongly uncertain environment. Several approaches have been dedicated to the estimation of uncertainty, but few of them address the problem of combining the impact of both stochastic (geostatistical context) and deterministic uncertainty on production forecasts. Typically, geostatistics allows to obtain a realistic reservoir description, which honors geological properties and takes into account rock heterogeneities. But, in terms of production forecasts, this modeling induces a large uncertainty since several equiprobable realizations may fit the available data, but each of them leads to a different production behavior. Furthermore, this uncertainty increases with the scarcity of data, since the geostatistical realizations are then poorly or not constrained. In this framework, we suggest an approach which integrates both "classical reservoir uncertainties" (petrophysical parameters, aquifer strength ...) and the uncertainty due to geostatiscal modeling. This approach combines the experimental design technique, which has already proven its efficiency in terms of uncertainty quantification, with a new concept: the Joint Modeling method, which is dedicated to the quantification of the geostatistical uncertainty. In particular, since the production response behavior can be modified by the uncertainties on "classical parameters" (like permeability, porosity, aquifer strength ...), and by the uncertainty due to the multiple equiprobable geostatistical realizations, we suggest to quantify the uncertainty on production forecasts using two statistical models : A mean model, which allows to quantify the uncertainty due to classical parameters, A variance model, which characterizes the dispersion of the production response, due to the uncertainty on the set of equiprobable realizations. In such a way, the production response behavior can be estimated using a prediction interval which encompasses both the classical and the geostatistical uncertainty. This methodology was successfully applied to a synthetic case derived from a real field case. The objective was to quantify the impact of both the main reservoir uncertainties (horizontal and vertical permeabilities, aquifer strength) and the geostatistical modeling on the cumulative oil production. Using the Joint Modeling method we were able to predict variation intervals for the cumulative oil production, within a risk prone environment. Finally, we validate the accuracy of the predictions by performing a posteriori reservoir simulations to check if the corresponding cumulative oil production falls into the prediction intervals. ___________________________________________________________________________