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This paper presents a fully-integrated methodology for managing reservoir uncertainties during history matching, production forecasting and production scheme optimization. Based on the traditional experimental design methodology, this innovative approach, called the Joint Modeling Method, allows to model the production recovery as a function of both the deterministic uncertain parameters, such as petrophysical and production parameters, as well as non-continuous parameters such as geostatistical realizations and equiprobable matched models. In this new approach, the dispersion due to the non-continuous uncertainties is modeled in a rigorous statistical framework through the variance of the production recovery. The method was successfully applied on data derived from a North Sea real field case. The objective was to quantify the impact of the principle reservoir uncertainties on the cumulative oil production and to optimize future field development in a risk analysis approach. The uncertainties were mainly on petrophysical data, geostatistical facies distribution and aquifer strength. The study was performed in the following steps:sensitivity study. The most influential parameters were identified and the impact of geostatistical uncertainties was highlighted.history matching. The influential parameters were constrained to the available production data. In particular, the geostatistical model was locally modified using both FFTMA technique and the gradual deformation method.production scheme optimization. Experimental design and joint modeling were used to obtain probabilistic distributions of the optimized location of new wells in a non-producing zone.risk analysis: Finally, probabilistic incremental oil production was obtained using Monte-Carlo technique. Results show that this integrated methodology successfully enables to quantify the risk associated with the main reservoir uncertainties during the whole process of a reservoir engineering study (sensitivity, history match, production optimization and forecast). Introduction Thanks to growing measurement and computational facilities, reservoir modeling is getting more and more complex. Hence more and more prior uncertain parameters can be introduced in reservoir studies. The difficulty is then to identify the ones that are influential on production recovery and on economic field profitability and to quantify their impact. The "simplest" case where the reservoir engineer needs to deal with reservoir uncertainties is the appraisal case, when there is no production data to match. In that case, the uncertainty domain cannot be highly constrained and the impact on production forecasts may hence be very significant. To deal with those uncertainties, reservoir and production engineers commonly perform many reservoir simulations for different values of the uncertain parameters. This approach gives a qualitative idea of the influence of each uncertain parameter on the production response. However this method can quickly become very expensive when the number of uncertain parameters increases. Moreover, this is not a rigorous method since the impact of each uncertain parameter as well as the possible interactions between those uncertain parameters cannot be easily detected. Finally no direct quantitative relation between the responses and the uncertainties can be established.

Résumé -Vers une quantification fiable des incertitudes sur les estimations de production : plans d'expériences adaptatifs -La quantification des incertitudes est une phase essentielle dans l'évaluation des réservoirs pétroliers. La précision des estimations de production est fortement liée à l'incertitude sur les variables qui contrôlent les performances du réservoir (perméabilité, contact huile-eau, etc.). Le problème est complexe parce que l'effet des variables sur les performances du réservoir est souvent nonrégulier, ce qui ne peut être détecté a priori. La méthode des plans d'expériences est généralement utilisée pour quantifier les incertitudes sur la production et obtenir une représentation probabiliste de cette dernière, avec par exemple la détermination de scenarii de production P90, P50 et P10. En sélectionnant de manière optimale les simulations à effectuer, les plans d'expériences permettent la construction d'un modèle approché qui reproduit l'impact des paramètres incertains sur les performances du réservoir. L'utilisation de plan d'expériences permet de réaliser des analyses de risque tout en effectuant un nombre limité de simulations potentiellement très coûteuses en temps de calcul. Toutefois, l'utilisation des plans d'expériences est généralement associée à la construction de surfaces de réponses polynomiales de faible degré, elle montre ses limites dès lors que les paramètres incertains ont un impact non-régulier sur la réponse en production. Nous présentons une nouvelle approche pour l'analyse de risque, fiable y compris lorsque l'impact des paramètres sur la réponse est non-régulier. Nous proposons de construire des plans d'expériences évolu-tifs, pour intégrer graduellement les non-régularités. Partant d'un plan d'expériences initial, la méthodo-logie détermine itérativement de nouvelles simulations susceptibles d'être informatives sur le comportement de la réponse. Inspirée de méthodes statistiques et de plans d'expériences, cette approche a montré son efficacité pour la modélisation de réponses complexes et non-régulières. Elle fournit une estimation fiable des incertitudes sur les estimations de production. (e.g. permeability, oil-water contact, etc.). The problem is complex, since the effect of the variables on the reservoir performance is often non-linear, which cannot be inferred a priori. Abstract

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