Managing Reservoir Flow Uncertainty in Presence of Stochastic Parameters

@inproceedings{FetelRM2006,
 abstract = { This paper focuses on the modeling and analysis of non-linear reservoir production variables and, eventually, their evolution in time, in presence of stochastic input parameters considered in the construction of a numerical geological model. A stochastic input parameter is defined when the relationship between its variations and the reservoir flow response variations is purely random. Typical examples are the seed for geostatistical simulations, several structural maps, several possible fracture networks, etc. Alternatively, if the relationship, usually unknown and non-linear, is continuous the parameter is said deterministic. Classically, only deterministic parameters are taken into account. Then, the relationship is approximated with a unique response surface. Here, in presence of stochastic uncertainty, the key idea is to model not a single response surface but a normal probability density function following. Thus, two response surfaces are considered. The first one models the mean reservoir flow response and the other one represents the dispersion due to all the stochastic uncertain parameters. They are both built in the n-dimensional space defined by the deterministic parameters. This paper develops an approach to model such response surfaces using the discrete smooth interpolation algorithm. Then it proposes a novel approach for estimating the sensitivity of the output reservoir production to changes in the input uncertain parameters plus their possible interactions. Moreover, a bayesian inversion scheme is developed for integrating historical production data. And, finally the approach is validated on a fluviatile like reservoir model. Results show the strength of the approach. Particularly, it works for n-dimensional and non-linear problems, its is independent of any prior regression model and the sensitivity analysis as well as the bayesian inversion depend on simple Monte-Carlo techniques which increase their flexibility. },
 author = { Fetel, Emmanuel },
 booktitle = { 26th gOcad Meeting },
 month = { "june" },
 publisher = { ASGA },
 title = { Managing Reservoir Flow Uncertainty in Presence of Stochastic Parameters },
 year = { 2006 }
}