This paper focuses on the management of uncertainty associated with production variables in presence of stochastic uncertain input parameters. In particular, it aims at dealing with n-dimensional non-linear response surfaces. A stochastic parameter is defined when the relationship between its variations and flow response variations is purely random. A typical example is the seed for geostatistical simulations. Alternatively, if the relationship is not random the parameter is said continuous. Here, the key idea is to model not a single response surface but a probability density function varying in the n-dimensional space of the continuous parameters. In this framework, this paper develops (1) a response surface building approach, (2) a variance based sensitivity analysis scheme for identifying influential parameters and (3) a bayesian inversion technique for integrating a given production history. The proposed techniques do not require any prior regression model and are based on Monte Carlo sampling. Thus, the developed approach is suitable for n-dimensional and non-linear problems. Finally, the approach is validated on a fluviatile-like reservoir model.


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