Reservoir Flow Uncertainty Management in Presence of Stochastic Parameters

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.